Direct Ink Writing (DIW) has gained attention for its potential to reduce printing time and material waste. However, maintaining precise geometry and consistent print quality remains challenging under dynamically varying operating conditions. This paper presents a control-focused approach using a model reference adaptive control (MRAC) strategy based on a reduced-order model (ROM) of extrusion-based 3D printing for a candidate cementitious material system. The proposed controller actively compensates for uncertainties and disturbances by adjusting process parameters in real time, with the objective of minimizing reference-tracking errors. Stability and convergence are rigorously verified via Lyapunov analysis, demonstrating that tracking errors asymptotically approach zero. Performance evaluation under realistic simulation scenarios confirms the effectiveness of the adaptive control framework in maintaining accurate and robust extrusion behavior.

We develop a variational encrypted model predictive control (VEMPC) protocol whose online execution relies only on encrypted polynomial operations. The proposed approach reformulates the MPC problem into a sampling-based estimator, in which the computation of the quadratic cost is naturally handled by tilting the sampling distribution, thus reducing online encrypted computation. The resulting protocol requires no additional communication rounds or intermediate decryption, and scales efficiently through two complementary levels of parallelism. We analyze the effect of encryption-induced errors on optimality, and simulation results demonstrate the practical applicability of the proposed method.

This paper formulates an optimal control framework for computing cruise airspeeds in predecessor-follower platoons of all-electric aircraft that balance operational cost and airspace complexity. To quantify controller workload and coordination effort, a novel pairwise dynamic workload (PDW) function is developed. Within this framework, the optimal airspeed solution is derived for all-electric aircraft under longitudinal wind disturbances. Moreover, an analytical suboptimal solution for heterogeneous platoons with nonlinear aircraft dynamics is determined, for which a general sufficient condition for string stability is formally established. The methodology is validated through case studies of all-electric aircraft operating in air corridors that are suitable for low-altitude advanced/urban air mobility (AAM/UAM) applications. Results show that the suboptimal solution closely approximates the optimal, while ensuring safe separations, maintaining string stability, and reducing operational cost and airspace complexity. These findings support the development of sustainable and more autonomous air traffic procedures that will enable the implementation of emerging air transportation technologies, such as AAM/UAM, and their integration to the air traffic system environment.

Pulsed Dynamic Nuclear Polarization (DNP) is currently receiving substantial interest as a means to enhance the sensitivity of nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) by orders of magnitude. It has also received much attention as a central ingredient in many modalities of electron spin-involved quantum sensing. Relative to spin engineering associated with NMR, the design of efficient pulsed DNP experiments with a broad experimental scope are challenged by large electron-nuclear spin systems, large electron spin-involved interactions, and instrumental non-idealities and limitations. All of this may challenge traditional NMR-like theoretical and numerical pulse sequence engineering. Exploiting state-of-the-art instrumentation and taking advantage of the high sensitivity of DNP relative to NMR, we here demonstrate the use of combinations of Bayesian machine learning methods and constrained random walk procedures to design pulse sequences \textit{in situ}, by experiments, directly on the spin systems responding to spectrometer instructions. For trityl and nitroxide samples, it is demonstrated that efficient broadband DNP pulse sequences can be designed in situ with experimental protocols benchmarked against in silico analogs.

In the d-Euclidean Distance Matrix Completion (d-EDMC) problem, one aims to determine whether a given partial matrix of pairwise distances can be extended to a full Euclidean distance matrix in d dimensions. This problem is a cornerstone of computational geometry with numerous applications. While classical work on this problem often focuses on exploiting connections to semidefinite programming typically leading to approximation algorithms, we focus on exact algorithms and propose a novel distance-from-triviality parameterization framework to obtain tractability results for d-EDMC. We identify key structural patterns in the input that capture entry density, including chordal substructures and coverability of specified entries by fully specified principal submatrices. We obtain: (1) The first fixed-parameter algorithm (FPT algorithm) for d-EDMC parameterized by d and the maximum number of unspecified entries per row/column. This is achieved through a novel compression algorithm that reduces a given instance to a submatrix on O(1) rows (for fixed values of the parameters). (2) The first FPT algorithm for d-EDMC parameterized by d and the minimum number of fully specified principal submatrices whose entries cover all specified entries of the given matrix. This result is also achieved through a compression algorithm. (3) A polynomial-time algorithm for d-EDMC when both d and the minimum fill-in of a natural graph representing the specified entries are fixed constants. This result is achieved by combining tools from distance geometry and algorithms from real algebraic geometry. Our work identifies interesting parallels between EDM completion and graph problems, with our algorithms exploiting techniques from both domains.

In this paper we study an overdetermined problem which is directly related to the well known torsion problem studied by J. Serrin. A perturbed version of the latter is tackled by using asymptotic series as well as tools borrowed from the celebrated Nekhoroshev Theorem. In a similar fashion to this class of results, we establish the existence of infinitely many approximants for the perturbed problem's solution, whose approximation error is so small which can be regarded as negligible for practical applications. The approach is fully constructive and this feature is demonstrated via an example in the final section.

Concurrent workloads often extract insights from high-throughput, real-time data streams. Existing stream processing engines isolate each query's resources, ensuring robust performance but incurring high infrastructure costs. In contrast, sharing work reduces the amount of necessary resources but introduces inter-query interference, leading to performance degradation for some queries. We introduce FunShare, a stream-processing system that improves resource efficiency without compromising performance by dynamically grouping queries based on their performance characteristics. FunShare strategically relaxes query interdependencies and minimizes redundant computation while preserving individual query performance. It achieves this by using an adaptive optimization framework that monitors execution metrics, accurately estimates computation overlaps, and reconfigures execution plans on the fly in response to changes in the underlying data streams. Our evaluation demonstrates that FunShare minimizes resource consumption compared to isolated execution while maintaining or improving throughput for all queries.

In this paper, we show how to generalize the lazy update regime from dynamic matrix product [Cohen, Lee, Song STOC 2019, JACM 2021] to dynamic kronecker product. We provide an algorithm that uses $n^{ω( \lceil k/2 \rceil, \lfloor k/2 \rfloor, a )-a}$ amortized update time and $ n^{ω( \lceil(k-s)/2 \rceil, \lfloor (k-s)/2 \rfloor,a )}$ worst case query time for dynamic kronecker product problem. Unless tensor MV conjecture is false, there is no algorithm that can use both $n^{ω( \lceil k/2 \rceil, \lfloor k/2 \rfloor, a )-a-Ω(1)}$ amortized update time, and $ n^{ω( \lceil(k-s)/2 \rceil, \lfloor (k-s)/2 \rfloor,a )-Ω(1)}$ worst case query time.

We rigorously prove the existence of interface modes in a sharp interface model, which bifurcate from the double Dirac cone as a consequence of the band inversion induced by super-symmetry breaking. The exact number of interface modes are determined. The proof is based on a discrete version of the layer-potential framework. Moreover, we prove that such interface modes are symmetry-protected against perturbations that respect the reflection symmetry.

We apply novel developments in photoionization modeling and multi-frequency radiation hydrodynamics to the study of line driven AGN disc winds. We use a flux-averaged force multiplier approach to compute the radiation force due to lines for hydrodynamics simulations using 4 frequency bands - infrared (IR), optical (O), ultraviolet (UV) and X-rays. Though line driving is dominated by the UV, contributions from the O and X-ray bands are non-negligible and can lead to enhancements in the wind both in terms of mass flux and outflow velocity. Crucially, these effects are not captured when using a ``grey'' approach to the radiation modeling in the hydrodynamics, where frequency information is averaged over during the photoionization modeling. These results further strengthen the case for frequency dependent radiation dynamics studies for line driven winds.

We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an objective treatment of exterior powers and determinants.

Recent advances in nanoscale fabrication enable atomic-scale manipulation of two-dimensional (2D) materials by introducing engineered pores and perforations. This provides new opportunities to tailor functional properties of 2D materials for applications such as selective ion transport, desalination membranes, and molecular filtration. Despite this progress, the auxetic mechanical behavior of perforated 2D materials has received little attention. In this work, large-scale reactive molecular dynamics (MD) simulations, validated against experimental measurements and first-principles calculations, are employed to investigate the mechanical response of perforated monolayer titanium-based MXene metamaterials. Architectures containing rectangular perforations with straight ligaments and sinusoidally curved ligaments are systematically examined under uniaxial tension and compression over a range of geometric parameters and temperatures, from the onset of deformation to fracture. The results demonstrate that MXene metamaterials exhibit a tunable negative Poisson's ratio (NPR), which can be controlled through the perforation geometry and surface termination. Atomistic stress analysis reveals alternating in-plane shear stresses at the junctions that induce rotational deformation of the ligaments. This rotating-junction mechanism is coupled with out-of-plane deflections arising from the low bending rigidity of atomically thin materials, producing complex three-dimensional deformations. Comparison with graphene metamaterials indicates that the perforation geometry governs qualitative auxetic trends, whereas intrinsic material properties determine quantitative responses. These findings identify MXenes as a versatile candidate for the design of tunable 2D mechanical metamaterials and provide atomistic insight into the interplay between geometry, bending rigidity, and auxetic deformation mechanisms.

In this work, we present a theoretical study of spin transport in a trilayer pseudospin-valve (PSV) heterostructure composed of electrode (L_l)/insulator/electrode (L_r). The insulating layer corrresponds to a semiconductor (SC) with a zinc-blende crystal structure from the III-V (GaSb, InSb, InAs, and GaAs) or the II-VI (ZnSe), while the electrodes are ferromagnetic materials L_j = {FeCr, Fe, Co, NiFe, Ni}. This combination yields 125 possible PSV configurations. The theoretical model implemented is based on the approach proposed by J. C. Slonczewski. In our approach, the exchange splitting in the ferromagnetic materials and the spin-orbit coupling (SOC) of the Dresselhaus and Rashba types in the semiconductors are included, allowing control of the wave vector associated with the spin states. The tunnel magnetoresistance (TMR) is calculated at low temperature as a function of the semiconductor thickness, parameterized with respect to the crystallographic axis that favors the magnetization direction in the ferromagnetic electrodes, within the Landauer--Büttiker formalism in the single-channel regime. The results show that the TMR reaches its maximum value independently of the relative orientation between the magnetization vector and the crystallographic direction. The most efficient configuration corresponds to Fe_{90}Cr_{10}/GaSb/Fe_{90}Cr_{10}, with a TMR value of 83.60%. Furthermore, the Dresselhaus SOC contributes more significantly to the TMR than the Rashba SOC. Finally, the TMR varies when the electrodes L_j are permuted, due to differences in their Fermi energies. The obtained results are compared with previous studies reported in the literature based on alternative theoretical frameworks or assumptions, showing good agreement.

This paper investigates the crucial role of parton distribution functions (PDFs) in high-energy physics, particularly their impact on the extraction of generalized parton distributions (GPDs) at zero skewness. To this aim, we perform six global analyses of GPDs using different modern PDF sets (\texttt{NNPDF40}, \texttt{CT18}, and \texttt{MSHT20}) at three specific factorization scales ($ μ= 2 $, $ 1.3 $, and $ 1 $ GeV) and different perturbative orders. A wide range of elastic electron scattering data is included in the analysis to constrain GPDs in a broad interval in the momentum transfer squared $ t $. The analyses reveal that the best overall description of experimental data is achieved using \texttt{NNPDF40} PDFs at the next-to-leading order (NLO), with moderate sensitivity to the choice of PDF input, especially in the region of low $ t $. The dependence on the perturbative order is relatively mild, indicating stability in the extraction procedure. We also show that different GPD sets become more consistent at larger $ |t| $ values, with down-quark GPDs experiencing greater suppression than up-quark GPDs. The six extracted GPD sets, available at different scales and perturbative orders, provide valuable resources for future theoretical and phenomenological studies, offering flexibility for researchers in exploring the proton's internal structure.

A novel paradigm for sorting is introduced, based upon resetting. Using simple examples, we demonstrate that sorting is achieved by resetting the velocity component(s) or orientation of the particles, rather than position. The objects to be sorted are microparticles, modeled as suspended and spatially extended Brownian particles. This sorting-by-resetting scheme illustrates that stochastic resetting can create non-equilibrium conditions which enable tasks forbidden at thermodynamic equilibrium.

We develop an explicit geometric construction of automorphisms of finite fields arising from isogeny cycles. Let $k$ be a finite field, $E/k$ an elliptic curve, and $\ell$ an integer coprime to $\mathrm{char}(k)$. Let $\mathfrak{h}$ be an ideal of $\mathrm{End}(E)$ dividing $\ell$, and consider the corresponding torsion subgroup $E[\mathfrak{h}]\subseteq E[\ell]$. From the action of End(E) on $E[\mathfrak{h}]$, we construct the splitting field $K$ of the $x$-coordinates of points in $E[\mathfrak{h}]$ and the associated Galois group $\mathrm{Gal}(K/k)$. This yields $(\mathrm{End}(E)/\mathfrak{h})^* \to \mathrm{Gal}(K/k)$ a group homomorphism.

We propose a model of the functional architecture of curvature-sensitive cells in the primary visual cortex. The model accounts for the modular and hierarchical organization of the cortex, the horizontal connectivity, and the shape of receptive profiles of these cells as Gabor-type filters. We construct a canonical affine subbundle of the cotangent bundle of the manifold of oriented contact elements of the retina as a geometric model for these cells, and show that this subbundle carries an Engel structure related to that of the Cartan prolongation. On an open submanifold of the Cartan prolongation, we identify generators of the Engel distribution whose iterated Lie brackets span the Lie algebra of SIM(2). The identification of sim(2) as the Lie algebra of these generators determines SIM(2) as the natural symmetry group for curvature-sensitive cells. Finally, we characterize the receptive profiles of curvature-sensitive cells as minima of a SIM(2)-adapted uncertainty principle applied to the generators of the Engel structure.

Nonlinear dynamics clamp the amplitude of mechanical resonators driven into self-oscillation by optomechanical backaction. Here we overcome the conventional limits of self-oscillation amplitude by navigating the nonlinear dynamical landscape of a diamond optomechanical cavity supporting coherent optomechanics at room temperature. By exploiting the bistable phase space of the system, we increase the oscillation amplitude by nearly an order of magnitude. This enhancement arises from deterministic access to a high-energy state in the system's nonlinear attractor, and is accompanied by the generation of an optical frequency comb produced by cascaded phonon scattering that underlies the nonlinear dynamics. Our results establish nonlinear attractor engineering as a route to large amplitude coherent phonon generation and provide a platform for optomechanical frequency combs, spin mechanical interfaces in diamond, and precision sensing in ambient conditions.

We study when a network of coupled oscillators with inertia ceases to follow a time-dependent driving protocol coherently, using a simplified graph-based model motivated by inverter-dominated energy systems. We show that this loss of tracking is diagnosed most clearly in the frequency dynamics, rather than in phase-based observables. Concretely, a tracking ratio built from the frequency-disagreement observable $E_ω(t)$ and normalized by the instantaneous second-order modal decay rate yields a robust protocol-dependent freeze-out time whose relative dispersion decreases with system size. Graph topology matters substantially: the resulting freeze-out time is only partly captured by the algebraic connectivity $λ_2$, while additional structural descriptors, particularly Fiedler-mode localization and low-spectrum structure, improve the explanation of graph-to-graph variation. By contrast, phase-sector observables develop strong non-monotonic and underdamped structure, so simple diagonal low-mode relaxation closures are not quantitatively reliable in the same regime. These results identify the frequency sector as the natural operational sector for nonautonomous tracking loss in second-order oscillator networks and clarify both the usefulness and the limits of reduced spectral descriptions in this setting.

Many real-world optimization models contain exploitable sparsity and block structure, but this structure is often obscured in algebraic form, limiting the effectiveness of modern parallel algorithms. We propose an automatic pipeline that converts a generic multiblock problem into a canonical two-block formulation suitable for parallel Alternating Direction Method of Multipliers (ADMM). The method constructs a coupling graph, applies an edge-subdivision-based bipartization to obtain a bipartite representation, and produces an ADMM-ready decomposition with independent subproblems. Fast graph-traversal heuristics, a new mixed-integer linear program (MILP), and a learning-based graph neural network (GNN) surrogate model are developed to guide edge subdivision. Numerical experiments demonstrate that the resulting reformulations yield strong parallel ADMM performance. The entire pipeline is implemented in the open-source Julia package PDMO.jl.

We study a problem of optimal allocation in a discrete-time multi-period pure-exchange economy, where agents have preferences over stochastic endowment processes that are represented by strongly time-consistent dynamic risk measures. We introduce the notion of dynamic Pareto-optimal allocation processes and show that such processes can be constructed recursively starting with the allocation at the terminal time. We further derive a comonotone improvement theorem for allocation processes, and we provide a recursive approach to constructing comonotone dynamic Pareto optima when the agents' preferences are coherent and satisfy a property that we call equidistribution-preserving. In the special case where each agent's dynamic risk measure is of the distortion type, we provide a closed-form characterization of comonotone dynamic Pareto optima. We illustrate our results in a two-period setting.

We study the plunge and merger of a non-spinning particle falling into a Kerr black hole following an eccentric planar inspiral. The dynamics is driven by an effective-one-body radiation reaction, and the corresponding numerical inspiral-merger-ringdown waveforms are obtained by solving the Teukolsky equation with the 2+1 time-domain code Teukode. We then analyze in detail the plunge and merger phases, modeling the merger-ringdown waveform using closed-form ansätze. Crucially, our modeling starts from a point closely related to the light-ring crossing, rather than from the amplitude peaks. This choice allows us to neglect the impact of the relativistic anomaly at the separatrix-crossing, and to extend the modeling to high spins and high eccentricities. We model all the multipoles with $m\geq 1$ up to $\ell=4$, as well as the $(2,0)$, $(5,5)$, $(5,4)$, and $(5,3)$ modes, including spherical-spheroidal mode-mixing and the beating between co-rotating and counter-rotating quasi-normal modes. The post-merger waveform model is then employed to complete an effective-one-body inspiral-plunge waveform, thus providing a complete description. Our model, built using elliptic-like configurations for the merger-ringdown phase, naturally extends to dynamical capture scenarios without any further modification. Finally, we provide insights into the extension of this framework to generic mass ratios, arguing that a time closely related to the inflection point of the (2,2) waveform frequency could be used as anchoring point for the ringdown modeling.

The Federal Trade Commission has recently filed an administrative complaint against the Big 3 pharmacy benefit managers claiming they engaged in unfair conduct in violation of Section 5 of the FTC Act. They never used the word collusion in the complaint and chose not to sue under The Sherman Act, Section 1. We view this as a novel case of market design collusion rather than a case of price collusion. The Big 3 PBMs are conceptualized as auctioneers soliciting rebate bids off unit list prices in exchange for favored positions on formularies. We will show how the fairness standard of the FTC Act can be made operational by judging fairness against economic theories of good auction design. Discovery is focused on finding explicit communication among the Big 3 PBMs in 2012 to change the so-called winner s determination equation of this auction, adding high gross rebates as a basis for formulary position assignments. On the other hand, we will argue that a case based on a bevy of anecdotes comparing only net unit prices will fail due to complexities in the winners determination equation.

Self-interacting jump processes (SIJPs) describe systems with non-Markovian stochastic dynamics in which transition rates depend on empirical observables of the process, which gives rise to long-range memory and feedback. We derive the ``level-2.5'' large deviation (LD) principle governing the joint fluctuations of empirical occupation measure and the flux matrix for a broad class of SIJPs with general functional dependence on an empirical observable. The derivation is based on an exponential tilting construction and reveals a separation between a faster timescale of the microscopic dynamics and a slower timescale of the memory-driven evolution of transition rates, which is expressed through an exponentially discounted LD rate functional. Using this variational framework, we derive kinetic and thermodynamic uncertainty relations that extend classical Markovian bounds to non-Markovian systems, and illustrate their performance with simple examples.

We consider a status update system consisting of a sampler, a sink, and a controller located at the sink. The controller sends requests to the sampler to generate and transmit status updates. Packet transmissions from the controller to the sampler (reverse link) and from the sampler to the sink (forward link) experience random delays. The reverse and forward links are modeled as servers with geometric service times, referred to as the controller and sampler servers, respectively. Each server is equipped with a single buffer that stores an arriving packet when the server is busy. We adopt a preemption-in-waiting policy on both links, whereby an arriving packet replaces the packet in the buffer whenever the buffer is full. Our main goal is to determine the optimal generation times of request packets at the controller in order to minimize the long-term average age of information (AoI) at the sink. We formulate the problem as a Markov decision process (MDP) and derive the optimal stationary deterministic policy using the relative value iteration (RVI) algorithm. We prove the convergence of the algorithm. Numerical results show that the proposed system consistently outperforms baseline policies from prior work and reveal a threshold-based structure for the optimal policy.

In this work, we demonstrate the first single-crystal aluminum nitride (AlN) wafer-based thickness-extensional (TE) mode bulk acoustic resonator for piezoelectric power conversion. The device exhibits a high series resonance 3-dB quality factor ($Q$) of 1677 and an electromechanical coupling coefficient ($k^2$) of 6.1%, highlighting the strong potential of AlN resonators for efficient power conversion. To suppress in-band spurious modes, a grounded ring structure is proposed and experimentally validated. The measured frequency-domain impedance response shows a spurious suppression of the spectrum above the resonance at 13.52 MHz. A comparative analysis with prior PZT, LN, and LT-based resonators indicates that AlN achieves a competitive figure of merit and $f \cdot Q$ product, while its material thermal conductivity is orders of magnitude higher than that of the incumbent piezoelectric power-converter resonators. The power-handling capability is expected to be superior in AlN single-crystal wafers and will be demonstrated in ongoing experiments. These results suggest that AlN offers a promising platform for compact, robust piezoelectric power converters and next-generation power electronic systems.

We propose a simple and flexible mechanism by which sterile neutrinos with masses below the electroweak scale can simultaneously account for the observed baryon asymmetry of the Universe and the dark matter abundance. Crucially, neutrinos in this mass range behave as Dirac particles at high temperatures, allowing connections to Dirac leptogenesis, while at low temperatures, they can serve as viable warm dark matter candidates. We first perform a general analysis, assuming that unspecified ultraviolet dynamics generate both symmetric and asymmetric sterile-neutrino abundances before decoupling. Treating these abundances as initial conditions for the subsequent evolution allows us to systematically explore the phenomenologically viable regions of the low-energy parameter space, taking into account cosmological and astrophysical constraints, as well as implications for light-neutrino mass generation. Finally, we illustrate the model-building opportunities enabled by this minimal setup by studying two specific ultraviolet completions.

In this paper, we observe that if the initial data of pseudo Calabi flow has volume form $C^0$ close to a smooth one, then the flow is immediately smooth for $t>0$. As an application, we show that if the initial data has volume form $C^0$ close to that of a cscK metric, then the pseudo Calabi flow exists for $t\in (0,+\infty)$. We also prove similar improvement of regularity and long time existence result for pseudo Calabi flow on a Fano manifold when the volume form is bounded and the class is close to $c_1(M)$.

Memory is a foundational concept across disciplines, from neurobiology and electronics to artificial intelligence and quantum gravity. In materials, memory effects typically arise from ferroic orders, such as ferroelectricity and ferromagnetism, where information is stored in charge or spin degrees of freedom. Here, we report a surprising discovery of a nonvolatile superlattice memory effect in monolayer TaIrTe4, a dual quantum spin Hall insulator, where information is encoded through sharply contrasting lattice periodicities. In particular, in a pristine monolayer, we observe the spontaneous emergence of a long-period superlattice that can be programmed ON and OFF in a nonvolatile manner by electrostatic tuning of low-energy electronic states. This switching toggles the system between two structural configurations with unit cell areas differing by nearly two orders of magnitude. Mechanistically, our results reveal two independent and distinct instabilities, one in the lattice and the other in the QSH electrons, which are coupled, leading to electrostatic control of lattice configurations with nonvolatile memory. This finding is enabled by combining linear and nonlinear transport measurements, Raman spectroscopy, and scanning tunneling microscopy, which probe complementary aspects of the underlying orders. Remarkably, this nonvolatile memory effect stabilizes a spontaneous superlattice with a periodicity on the few-nanometer scale that remains robust across a wide doping range, persists over days, and survives above 70 K. Combined with the QSH topology, this stability offers a promising route to nonvolatile memory control of topological flat bands and their filling enabled quantum states. Our preliminary data indeed show the emergence of new insulating states at fractional superlattice fillings, which can be clearly switched ON and OFF together with the superlattice.

Candidate binary endpoints are often considered as surrogates for time-to-event (TTE) clinical endpoints, primarily because they can be assessed at earlier time points. To be submitted for regulatory approval candidate binary endpoints need to validated. The most well-known method for performing such validation employs a meta-analytic framework to estimate individual-level and trial-level association. However, the performance of these association estimates in the context of a binary surrogate has not yet been examined through a comprehensive simulation study. This research aims to systematically investigate the performance of association estimates at the trial-level and at the individual-level under various trial design choices, using both simulation studies and clinical trial data, where available.