The scramble number of a graph, a natural generalization of bramble number, is an invariant recently developed to study chip-firing games and graph gonality. We introduce the carton number of a graph, defined to be the minimum size of a maximum order scramble, to study the computational complexity of scramble number. We show that there exist graphs with carton number exponential in the size of the graph, proving that scrambles are not valid NP certificates. We characterize families of graphs whose scramble number and gonality can be constant-factor approximated in polynomial time and show that the disjoint version of scramble number is fixed parameter tractable. Lastly, we find that vertex congestion is an upper bound on screewidth and thus scramble number, leading to a new proof of the best known bound on the treewidth of line graphs and a bound on the scramble number of planar graphs with bounded degree.

The control of biopolymer length is mediated by proteins that localize to polymer ends and regulate polymerization dynamics. Several mechanisms have been proposed to achieve end localization. Here, we propose a novel mechanism by which a protein that binds to a shrinking polymer and slows its shrinkage will be spontaneously enriched at the shrinking end through a "herding" effect. We formalize this process using both a lattice-gas model and a continuum description, and we present experimental evidence that the microtubule regulator spastin employs this mechanism. Our findings extend to more general problems involving diffusion within shrinking domains.

In this paper, we study the dynamic properties of a linear array of graphane triangular molecules that transmit a binary signal. The electronic properties of nanoclusters are studied using calculations based on first principles, with hybrid potentials. The dynamic of the system is studied by solving the time-dependent Schrodinger equation. Our results show that a linear array of these nanostructures under clock operations, allow to transmit binary information, with a efficiency close to unity.

This work makes a theoretical study of the dynamics of emergent elemental excitations in artificial spin ice systems with hexagonal geometry during the magnetic reversion of the system. The magnetic and physical parameters of the nanoislands that form the array are considered as variables in the study. The parameters considered are: the energy barrier for the inversion of each nanoisland, the magnetic moment of the nanomagnets and the possible disorder in the sample. Our results show that the reversion dynamic presents two distinct mechanisms of magnetic reversion, with different elemental excitations for each mechanism. The first mechanism presents a reversion with the appearance of magnetic monopoles that do not move in the samples (heavy monopoles) and the absence of Dirac chains. In the other mechanism elemental magnetic excitations (light monopoles) appear that move great distances in the sample, giving rise to extensive Dirac chains during the magnetic reversion.

In this work we study the dynamical properties of a finite array of nanomagnets in artificial kagome spin ice at room temperature. The dynamic response of the array of nanomagnets is studied by implementing a "frustrated celular autómata" (FCA), based in the charge model and dipolar model. The FCA simulations, allow us to study in real-time and deterministic way, the dynamic of the system, with minimal computational resource. The update function is defined according to the coordination number of vertices in the system. Our results show that for a set geometric parameters of the array of nanomagnets, the system exhibits high density of Dirac strings and high density emergent magnetic monopoles. A study of the effect of disorder in the arrangement of nanomagnets is incorporated in this work.

We study the correlated ground states of twisted mono-bilayer graphene with and without proximity-induced spin-orbit coupling (SOC) from a transition-metal dichalcogenide layer placed on top. We perform self-consistent Hartree-Fock calculations that allow the variational space to include multi-$Q$ translational symmetry broken states for all integer and half-integer fillings of the conduction bands, where signatures of correlated, topological states have been reported experimentally. We find interaction-induced insulators that retain moiré translational symmetry at integer fillings, but that break this symmetry at half-integer fillings. We argue that translational symmetry breaking arises from half-filled polarized bands, even when SOC is present. Yet, we find that small SOC can already crucially affect the spin nature of correlated states. Generally, Ising SOC favors out-of-plane spin polarization and spin-valley locking, while Rashba SOC favors in-plane spin order. If only one of these two terms is present, we find that, depending on the type of SOC, it drives a transition from a tetrahedal antiferromagnet to either a coplanar, non-coplanar, or collinear spin-density wave state for half-integer fillings. The frustration associated with the simultaneous presence of both types of SOC can induce chiral, non-coplanar order in parameter ranges where the ground state in the absence of SOC is collinear.

Light Fidelity (LiFi) has emerged as a promising wireless technology that exploits the vast unlicensed optical spectrum to complement radio frequency networks. Recent advances in laser-based transmitters, particularly vertical-cavity surface-emitting laser (VCSEL) arrays, enable LiFi systems with multi-gigabit data rates, fine-grained spatial multiplexing, and high energy efficiency. However, the highly directional nature of laser beams introduces new challenges related to user mobility, alignment, and dynamic environments. This article introduces VCSEL-enabled holographic communication as a system-level paradigm that addresses these challenges by tightly integrating communication, sensing, and positioning within a single LiFi architecture. The proposed approach leverages individually addressable VCSEL arrays to form a dense grid of controllable beams, while a real-time digital twin of the environment enables adaptive beam management, environmental mapping through sensing, and user localization through positioning, including non-line-of-sight operation. By tightly integrating high-speed data transmission with environmental perception and user tracking, the LiFi access point evolves from a static transmitter into an intelligent environmental hub. The article also provides a tutorial overview of the underlying hardware, system architecture, and operational principles of holographic LiFi, and discusses key applications, open challenges, and future research directions toward next-generation intelligent optical wireless networks.

How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is governed by extreme value statistics of first-passage times: a linear spatial disadvantage requires an exponentially larger population to overcome. However, transient superiority cannot stabilize dominance. A non-reciprocal interaction bias is strictly necessary to arrest local fluctuations and drive the system into a robust absorbing state.

We analyse the level crossing rate (LCR) of an uplink single-user (SU) reconfigurable intelligent surface (RIS) aided system. It is assumed that the RIS to base station (RIS-BS) channel is deployed as line-of-sight (LoS), and the user (UE)-RIS and UE-BS channels are correlated Rayleigh. For the optimal RIS reflection matrix, we derive a novel and exact analytical LCR expression for when the direct (UE-BS) channel is blocked, i.e. the RIS-only channel. Also, the existing exact expression for the direct-only channel (equivalent to classical maximal-ratio-combining (MRC)) suffers from extreme numerical precision problems when the BS has many elements. Therefore, we propose a new stable and accurate approximation to the LCR of the direct channel. The approximation is based on replacing any small similar eigenvalues of the channel correlation matrix by their average. We show that increasing the number of elements at the RIS or BS and decreasing channel correlation makes the LCR drop more rapidly for thresholds away from the mean SNR. Crucially, we find that RIS systems do not significantly amplify temporal variations in the channel. This is particularly beneficial for RIS systems considering the difficulty in acquiring channel state information (CSI).

We analyse the Boolean-valued random forcing $B_{M,Ω}$ in bounded arithmetics developed in Krajicek (Forcing with random variables and proof complexity, vol. 382, Cambridge University Press, 2011) from the perspective of the forcing in set theory. We observe that under the assumption that $M$ is a non-standard $ω_1$-saturated model of true arithmetics of size $ω_1$, and $Ω\in M$ is a non-standard number, $B_{M,Ω}$ is isomorphic to the probability (random) algebra corresponding to the product measure space on $2^{ω_1}$ (and hence does not depend on $M$ and $Ω$). Thus, in a well-defined sense, the forcing $B_{M,Ω}$ adds a "random integer" to the model $M$, using a non-separable algebra corresponding to $2^{ω_1}$. If $G$ is a generic filter for $B_{M,Ω}$ over a transitive model of set theory $V$, we naturally define in $V[G]$ two-valued generic extensions $M[G]^{R}$ of $M$ which correspond to Boolean-valued models in Krajicek's book (where $R$ ranges over collections of random variables which function as names for new integers). We study the relationship between the linear order $(M,<)$ and its extensions $(M[G]^R,<)$, proving several results on the extent of the mutual density of new integers in $M[G]^{R}$ and the "ground-model" integers in $M$. At the end, we discuss some advantages and limitations of interpreting forcing in bounded arithmetics (and other weak theories) in the framework of set-theoretic forcing, providing an alternative to an axiomatic approach to forcing in bounded arithmetics formulated by Atserias and Müller in Partially definable forcing and bounded arithmetic, Archive for Mathematical Logic 54 (2015), 1-33.

The synergy of ferroicity with altermagnetism offers a novel platform for designing multifunctional altermagnetic-spintronic device technology. In this work, we propose a mechanism to achieve nonvolatile electrical manipulation of spin and layer degrees of freedom in an altermagnetic bilayer via sliding ferroelectricity. Using first-principles calculations, we show that an interlayer translation can induce a switchable out-of-plane ferroelectric polarization in bilayer CuF2, which directly couples to and reverses the d-wave altermagnetic spin splitting. Notably, the altermangetic spin splitting is layer-locked, the sliding ferroelectricity-driven switching thus embodying a nonvolatile spin-layertronics functionality that couples spin-polarized transport and layer degree of freedom in a single platform. We show that in quadrilayer CuF2, four polarization states are identified which may offer multi-state logic device applications. These findings establish sliding ferroelectricity as a versatile tool for designing voltage-controlled, high-speed and energy-efficient spin-layertronic devices based on altermagnets.

Port-Hamiltonian (pH) systems offer a highly structured and energy-based modular framework for control systems. Many pH systems exhibit non-polynomial non-linearities. We consider the problem of immersing such systems into a higher-dimensional polynomial representation. We prove that, along system trajectories, important features of the non-polynomial pH system are preserved such as the internal interconnection geometry, the energy balance relation with passivity supply rate, as well as energy dissipation. We illustrate how the lifted system enables the design of stabilizing feedback laws by combining sum-of-squares optimization with concepts from passivity-based control. We draw upon several examples to illustrate our findings.

Rocky exoplanets are particularly abundant around M-type stars. Their small radii and low luminosities provide favourable conditions for detecting transiting terrestrial planets and probing their atmospheric properties. We report the discovery and statistical validation of TOI-4616 b, an Earth-sized planet transiting a nearby mid-M dwarf observed by the Transiting Exoplanet Survey Satellite (TESS). We confirm the planetary nature of the signal and determine the system parameters by combining TESS photometry with ground-based multi-band transit observations, high-resolution imaging, and optical and near-infrared spectroscopy. The host star lies at a distance of 28.10 +(-) 0.07 pc and has a radius of 0.1889 +(-)0.0096 solar radii, a mass of 0.1881 +(-) 0.0094 solar masses, and an effective temperature of 3150 +(-) 75 K. TOI-4616 b has a radius of 1.22 Earth radii and an orbital period of 1.55 days. The planet receives an incident flux of approximately 40 times that of Earth, corresponding to an equilibrium temperature of about 525 K. This places TOI-4616 b in a regime intermediate between Earth-sized planets orbiting early M dwarfs and those around ultra-cool hosts. Statistical validation with the TRICERATOPS framework, supported by high-resolution imaging and chromatic transit constraints, yields a false-positive probability of 0.0135, below the recommended validation threshold of 0.015, confirming TOI-4616 b as a validated planet. Owing to its proximity to Earth, well-constrained stellar properties, and extensive multi-band follow-up, TOI-4616 b constitutes a valuable benchmark system for comparative studies of terrestrial planets around mid-M dwarfs and for future atmospheric investigations.

The SPEARHEAD (specification, analysis, and re-calibration of high-energy particle data) project, funded by the European Union Horizon Europe programme, enhances the accuracy and usability of high-energy particle measurements. It investigates particle acceleration, release, and transport during solar eruptions by refining instrument response functions and cross-calibrating datasets. We present a comprehensive catalogue of greater than 100 MeV proton events identified from May 1996 to August 2024 using SOHO-ERNE penetrating-particle rates, together with associated solar phenomena derived from multi-instrument observations. The SEP events were detected through a systematic scan of ERNE-HED counter data and cross-calibrated with SOHO-EPHIN to derive peak fluxes and fluences. Each event was associated with its likely parent eruption using X-ray (XR) (GOES-XRS, RHESSI, SolO-STIX), radio (Wind-WAVES, STEREO-WAVES, ground-based observatories), and gamma-ray (Fermi-LAT) observations, CMEs (SOHO-LASCO), and ground-level enhancements (GLEs) (neutron monitors). Timings and physical properties were systematically compared to investigate the relationships between SEP onset, flare evolution, CME kinematics, and radio signatures. Statistical analyses reveal that most SEP releases closely follow flare and CME onsets, with moderate SEP-XR-CME correlations, and a strong SEP-GLE fluence link. These results indicate that high-energy SEP events are typically associated with strong solar activity signatures, with the observed intensities and timings strongly modulated by magnetic connectivity and coronal conditions. This catalogue provides the most extensive reference to date for high-energy SEP events over solar cycles 23-25, establishing a unified framework for future investigations of extreme particle acceleration.

Convolutional Neural Networks (CNNs) have proven to be highly effective in solving a broad spectrum of computer vision tasks, such as classification, identification, and segmentation. These methods can be deployed in both centralized and distributed environments, depending on the computational demands of the task. While much of the literature has focused on the explainability of CNNs, which is essential for building trust and confidence in their predictions, there remains a gap in understanding their impact on computational resources, particularly in distributed training contexts. In this study, we analyze how CNN architectures primarily influence model accuracy and investigate additional factors that affect computational efficiency in distributed systems. Our findings contribute valuable insights for optimizing the deployment of CNNs in resource-intensive scenarios, paving the way for further exploration of variables critical to distributed learning.

In this paper, we analyse the performance of a reconfigurable intelligent surface (RIS) aided system where the RIS is divided into subsurfaces. Each subsurface is designed specifically for one user, who is served on their own frequency band. The other subsurfaces (those not designed for this user) provide additional uncontrolled scattering. A new subsurface RIS design is developed based on the optimal single-user design for a pure line-of-sight (LoS) base station (BS) to RIS channel. This is also extended to arbitrary BS-RIS channels. For our method, exact closed form solutions for the mean SNR and a mean rate upper bound are derived for the BS-RIS LoS scenario. For each user, the designed subsurface performs optimally in LoS conditions and is remarkably robust to non-LoS conditions. The system design drives down complexity to extremely low levels, reducing RIS design and receiver processing complexity and reducing the channel estimation requirements. We also quantify the complexity-performance trade-off for the new design relative to multi-user approaches.

The high directionality of hyperbolic phonon polaritons (HPhPs) has opened radically new ways to route and steer the flow of energy at the nanoscale. However, launching HPhPs requires fabricating efficient and precisely aligned polariton launching structures, which remains time-consuming and expensive with conventional nanofabrication approaches. Recently, using optical laser pulses, polariton launching structures have been programmed into the plasmonic phase-change material In3SbTe2. Here, we leverage this approach to reconfigure HPhPs by programming a variety of launching and confining nanostructures through α-MoO3 flakes deposited onto In3SbTe2. Importantly, optical programming after flake deposition enables alignment of launching stripes to the [001]-axis of the flake, essential to control the directional polariton propagation. We showcase these capabilities in a variety of structures: i) an optically programmed disk, showing similar tuning ranges and confinement as focusing by gold disks; and ii) a cavity for in-plane HPhPs created by reconfiguring the single disk to a double disk structure, tailoring the confinement by simply reprogramming the disk distance. Our fabrication scheme offers fast turn-around times, flexible alignment and the opportunity to reconfigure the structures. Thus, it is a fast, efficient and versatile way to tailor propagation and confinement of highly directional polaritons on demand.

We present results on Rydberg atom-based electric field sensing in the range of 1 kHz - 300 MHz, using a three-photon Rydberg excitation scheme and a transverse electromagnetic (TEM) line waveguide to apply low-frequency rf fields to the cell. Measurements of low-frequency screening in quartz and sapphire vapor cells show excellent agreement with a phenomenological model of the effective vapor cell material properties based on an electrical 2-port measurement of the TEM line. We achieve a best noise-equivalent field of 106(4) $\mathrm{\frac{μV}{m \sqrt{Hz}}}$ at 300 MHz and characterize noise-equivalent fields in the ultra-low to very-low frequency (ULF-VLF) band.

Authoritative Domain Name System (DNS) response selection defines query-time response selection based on resolver-visible context and per-answer metadata, yielding different observable outcomes for the same query under different conditions. Although such behavior is widely deployed and often described informally as traffic steering, its semantics have not been formalized independently of particular configuration languages or implementations. This paper shows that authoritative DNS response selection inhabits a bounded semantic domain determined directly by DNS protocol constraints. Requirements such as finiteness of responses, RRset atomicity, termination, cacheability, and restriction to resolver-visible inputs jointly limit the expressive power of any query-time selection mechanism. We formalize authoritative response selection as a class of DNS-admissible functions and prove that every such function admits a finite normal form consisting of conditional restriction over observable context followed by selection among a finite candidate set. We further show that this bounded semantic domain carries intrinsic algebraic structure induced by DNS semantics, enabling principled reasoning about composition, expressiveness loss, and semantic collapse. Concrete authoritative systems, configuration models, and serialized encodings are modeled uniformly as semantic restrictions of this domain. This framework supports precise reasoning about equivalence, representability, and approximation across heterogeneous authoritative DNS systems, grounded directly in protocol semantics rather than implementation detail.

We study some properties of the random interlacement model on a transient weighted graph, which was introduced by A. Teixeira in ["Interlacement percolation on transient weighted graphs", Augusto Teixeira, Electronic Journal of Probability (2009)]. We give a simple proof of the FKG-property and discuss the occurrence of several 0-1 laws for non-local events. We show in particular a 0-1 law for some increasing non-local events, without any assumption.

Let $X$ be a smooth cubic fourfold over $\C$ and let $π: \sJ_U \to U$, with $ U \subset (¶^5)^*$, be the Lagrangian fibration whose fibres are the smooth hyperplane sections $Y_ H = X \cap H$, with $H \in U$. There always exists a (not unique) smooth compactification $\bar \sJ \to (¶^5)^*$ which is a hyper-Kälher manifold of OG10 type. Since two different compactifications are birationally equivalent their Chow motives are isomorphic. For a general $X$ a geometrical construction of a smooth compactification $\sJ(X)$ with irreducible fibres has been described in [LSV]. In this note we prove that the Chow motive $h(\sJ(X)) $ is a direct summand of the (twisted) motive of $X^5$ and therefore is is of abelian type if $h(X)$ is of abelian type.We describe a 10 -dimensional family $\sF$ of cubics $X$ such that the compactification $\sJ(X)$ is unique, smooth, with irreducible fibres, and the Chow motive $h( \sJ(X) )$ is of abelian type.

Much of the exotic functionality of prime interest in quantum materials emerges from structural and electronic ground states that can only be accessed at cryogenic temperatures. Understanding device operation therefore requires structural characterization under the same low-temperature conditions at which these functional phases exist, as room-temperature measurements often probe a different structural state. Achieving atomic-resolution in scanning transmission electron microscopy imaging and particularly 4D-STEM electron ptychography at liquid helium temperature has remained extremely challenging because even small amounts of drift, vibration, and thermal instability associated with the cryogen can disrupt the stringent stability requirements of atomic-resolution STEM. In this work we demonstrate atomic-resolution STEM and multislice electron ptychography at temperatures as low as 20 K using a commercial helium cooled holder. We find that rapid scans and a multi-stage registration workflow are critical to reducing artifacts associated with cryogenic instability for atomic-resolution imaging, while for ptychography scan position correction including compensation for coupling between probe aberrations and position refinement is necessary for successful reconstructions. Together these results establish a pathway for reliable atomic-resolution STEM and ptychography at low temperature, enabling direct visualization of structural ground states relevant to quantum technology.

Since the release of the ICH E9(R1) addendum on estimands, its application in non-inferiority trials has received far less attention than in superiority settings. A key conclusion from Lynggaard et al. was that the "choice of non-inferiority margin must reflect the chosen estimand." However, current regulatory guidance predates ICH E9(R1) and therefore does not reflect how the estimand influences the historical evidence and constancy assumption (assay sensitivity) used to derive the non-inferiority margin. This paper investigates the degree to which the non-inferiority margin depends on the estimand. Using simulated patient journeys in a weight-management setting, we illustrate how different intercurrent event strategies and variations in the intercurrent event frequency affect the estimand, and consequently the estimated treatment effect. These results emphasize that the historical treatment effect of the reference treatment versus placebo, and thus the margin $M_{1}$, is specific to an estimand and may differ even when trials formally target similar questions. We further illustrate the process of determining the non-inferiority margin using two examples in non-inferiority trials for a new theoretical weight management treatment. In the first example, we focus on the setting where the historical clinical trials use the estimand framework highlighting that even when they include the estimand framework, determining the non-inferiority margin can be challenging in case the historical trials target an estimand different from the one in the planned study. A second example highlights challenges when historical trials did not employ the estimand framework and the targeted estimand cannot be fully reconstructed.

We prove that simplicial volume and dilatation are monotone under ribbon concordance between fibered knots in $S^3$, and that every fibered knot has only finitely many predecessors in the ribbon-concordance partial order, providing evidence for questions raised by Gordon. We also give an algorithm to enumerate, up to symmetries, all minimal compressions of a surface homeomorphism, extending a theorem of Casson--Long. This yields an algorithm to find all knots that are strongly homotopy-ribbon concordant to a given fibered knot in some homotopy $I\times S^3$. Our study of minimal compressions also provides an alternative perspective on results of Miyazaki concerning nonsimple fibered ribbon knots.

Quantum telepathy is the concept of using quantum entanglement to solve real-world problems involving decision coordination between parties with restricted communication. One possible reason for this restriction is a latency constraint: some pairs of parties do not have enough time to communicate with each other before they have to produce their outputs. Example scenarios include high frequency trading and distributed systems. Another reason is isolation: for some pairs of parties, there is an obstacle to communication. Example scenarios include locating a stray traveler by a rescue team and coordination within a network where nodes are owned by competing firms. In this paper we give a concise overview of the different application areas of quantum telepathy. We find that these real-world problems can be modeled as nonlocal games or its generalizations. We also discuss possible physical implementations. Quantum telepathy guarantees a quantum advantage via Bell's theorem and can directly solve real-world problems, such as reducing risk in high frequency trading or balancing data loads efficiently in ad hoc networks. Moreover, this quantum advantage can be physically realized with existing NISQ hardware.

In this paper, we study the Cauchy problem for the four-wave kinetic equation describing the weak turbulence of gravity water waves. The mathematical challenges of this analysis stem primarily from two interrelated aspects: (1) the extreme algebraic complexity of the collision kernel, where controlling its growth in the highly non-local regime constitutes the primary analytical bottleneck, and (2) the construction of strong solutions under the resulting singular integral operators. First, we re-analyze the interaction kernel in this precise regime, where the interacting wave numbers satisfy $|k|, |k_3| \gg |k_1|, |k_2|$. We establish a rigorous upper bound of $\mathcal{O}(|k||k_3|)$, which rigorously verifies the asymptotic smallness of the interaction coefficient anticipated in the physics literature \cite{zakharov2010energy, geogjaev2017numerical, geogjaev2025properties}. Furthermore, this result improves upon the recent $\mathcal{O}\big((|k||k_3|)^{3/2}\big)$ estimate proposed in \cite{waterkernel2024}, demonstrating a strictly milder singularity of wave interactions in this limit. Physically, this regime governs the energy exchange between disparate scales, such as the modulation of short gravity waves by long ocean swells. Second, leveraging this crucial integrability gain alongside a refined structural decomposition of the collision operator, we establish the local-in-time existence of $L^1$ strong solutions to the gravity water kinetic equation for initial data in a suitably weighted $L^2 \cap L^\infty$ space. Specifically, we prove that for any initial data in this class, the resulting $L^1$ strong solution strictly propagates the weighted $L^2 \cap L^\infty$ regularity and conserves the fundamental physical properties of the kinetic model.

For the weighted Dirac eigenproblem on a compact spin manifold with the chiral boundary condition \begin{equation*} \left\{ \begin{array}{ll} Dφ= λfφ& \text{in } M, \\ \mathbf{B}φ= 0 & \text{on } \partial M, \end{array} \right. \end{equation*} we first give a lower bound of the eigenvalue using the relative Yamabe constant \begin{equation*} λ^2 \geq \frac{n}{4(n-1)} Y(M,\partial M,[g]), \end{equation*} then prove that equality holds if and only if (up to a conformal transformation) $M$ is a hemisphere and $φ$ is a Killing spinor. More generalizations are studied.

We propose a physics-informed neural particle method (PINN--PM) for the spatially homogeneous Landau equation. The method adopts a Lagrangian interacting-particle formulation and jointly parameterizes the time-dependent score and the characteristic flow map with neural networks. Instead of advancing particles through explicit time stepping, the Landau dynamics is enforced via a continuous-time residual defined along particle trajectories. This design removes time-discretization error and yields a mesh-free solver that can be queried at arbitrary times without sequential integration. We establish a rigorous stability analysis in an $L^2_v$ framework. The deviation between learned and exact characteristics is controlled by three interpretable sources: (i) score approximation error, (ii) empirical particle approximation error, and (iii) the physics residual of the neural flow. This trajectory estimate propagates to density reconstruction, where we derive an $L^2_v$ error bound for kernel density estimators combining classical bias--variance terms with a trajectory-induced contribution. Using Hyvarinen's identity, we further relate the oracle score-matching gap to the $L^2_v$ score error and show that the empirical loss concentrates at the Monte Carlo rate, yielding computable a posteriori accuracy certificates. Numerical experiments on analytical benchmarks, including the two- and three-dimensional BKW solutions, as well as reference-free configurations, demonstrate stable transport, preservation of macroscopic invariants, and competitive or improved accuracy compared with time-stepping score-based particle and blob methods while using significantly fewer particles.

We aim to identify the physical mechanism responsible for the observed X-ray emission and polarization of Cyg X-1 in the soft state. We perform a detailed spectral analysis of X-ray data obtained by NICER, NuSTAR, and INTEGRAL during observations simultaneous with IXPE on 2023 June 20, supplemented at higher energies with archival CGRO data. We develop a new model, retBB, that describes thermal disk emission and its returning reflection, and apply it together with accurate models of Comptonization and relativistically broadened reflection. Using the resulting spectral solution, we compute the expected polarization signal and compare it with the IXPE measurements. Our spectropolarimetric modeling shows that the observed polarization is produced by Comptonization in a corona undergoing a semi-relativistic outflow with a velocity of ~0.3c. Our spectral solutions admit either low or high black-hole spin values, depending on the adopted model setup. However, the observed polarization strongly favors a low spin. At high spin, the polarization angle would inevitably rotate significantly across the energy band, which is not consistent with the observations. Apart from this rotation of the polarization angle, general relativistic effects do not play a significant role in producing the observed polarization. In particular, we find that, at most, returning disk radiation contributes only a minor amount.

There is a great need for evaluating screening programs, but analysing data from population screening is often complicated by a delayed screening effect. In cancer screening, only new, not yet clinically diagnosed cases, might benefit from screening through earlier treatment. Hence, mortality data following screening should be analysed based on refined mortality, separating cases based on diagnosis before and after first screening invitation. Historically, refined mortality has been implemented by selecting comparison groups from the available data to disentangle the causal effect. While giving valid estimates, the ignorance of large parts of the available data has limited study precision. In BMJ 2014, Weedon-Fekjær et al. used a new estimation approach applying all the available Norwegian mammography screening data. The estimation uses historic pre-screening data on time from clinical diagnosis to death estimating the proportion of post-screening mortality which is expected to be based on cases incident before first screening invitation, in the absence of a screening effect. Utilizing this expected proportion of post-screening incident cases, Poisson regression offsets are added to align the expected number of cases. The screening effect is then estimated adjusting for relevant covariables. While the method increases study precision, it has not been easily available and widely adopted. We here explain the method in detail, add maximum likelihood estimation, and lay the foundation for widespread use. Applying the method on Norwegian and Danish data, bootstrap confidence intervals are considerably narrower than intervals seen using other refined mortality methods, especially for the gradually introduced Norwegian program.