We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when $1 \ll ΔH \ll N$, being $ΔH$ the coupling Hamiltonian and $N$ the size of the system. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections and to the correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model.

We study the codegree Turán density of $\mathcal{C}_\ell^r$, the $r$-uniform hypergraph tight cycle of length $\ell$. A result of Han, Lo, and Sanhueza-Matamala states that if $\ell$ is sufficiently large and $r/\gcd(r,\ell)$ is even, then the codegree Turán density of $\mathcal{C}_\ell^r$ is $1/2$. We prove that whenever the latter assumption is not satisfied, there is a significant drop in the codegree Turán density. That is, if $\ell$ is sufficiently large and $r/\gcd(r,\ell)$ is odd, then the codegree Turán density of $\mathcal{C}_\ell^r$ can be at most $1/3$. Moreover, this bound is tight for infinitely many uniformities $r$ and all sufficiently large $\ell$ in the corresponding residue classes modulo $r$. Our proof makes use of a group-theoretic connection between Turán-type theorems for tight cycles and ``oriented colorings'' of the edge set of a hypergraph.

We perform a systematic study of lepton-number-violating (LNV) dimension-9 operators in the Standard Model Effective Field Theory (SMEFT) that can mediate neutrinoless double beta decay ($0νββ$) at tree level, and map them to their possible tree-level ultraviolet completions. Using a diagram-based classification, we enumerate all such completions and isolate minimal two-particle models that avoid generating the dimension-5 Weinberg operator or dimension-7 LNV operators at tree level. We then chart how these minimal models populate the operator landscape and organise them by the loop order at which they radiatively induce lower-dimensional LNV operators, highlighting scenarios in which the tree-level dimension-9 contribution can compete with or dominate loop-suppressed neutrino-mass (dimension-5) effects. Representative one-loop and two-loop classes are matched onto the SMEFT, and their implications for neutrino masses, charged-lepton flavour violation, and the relative size of dimension-9 versus dimension-5 contributions to $0νββ$ are analysed, delineating regions of parameter space where upcoming experiments can be sensitive to genuinely short-range LNV dynamics.

A relation consisting of tuples annotated by an element of a monoid K is called a K-relation. A K-database is a collection of K-relations. In this paper, we study entailment of inclusion dependencies over K-databases, where K is a positive commutative monoid. We establish a dichotomy regarding the axiomatisation of the entailment of inclusion dependencies over K-databases, based on whether the monoid K is weakly absorptive or weakly cancellative. We establish that, if the monoid is weakly cancellative then the standard axioms of inclusion dependencies are sound and complete for the implication problem. If the monoid is not weakly cancellative, it is weakly absorptive and the standard axioms of inclusion dependencies together with the weak symmetry axiom are sound and complete for the implication problem. In addition, we establish that the so-called balance axiom is further required, if one stipulates that the joint weights of each K-relation of a K-database need to be the same; this generalises the notion of a K-relation being a distribution. In conjunction with the balance axiom, weak symmetry axiom boils down to symmetry.

Bateni et al. has recently introduced the weak-strong distance oracle model to study clustering problems in settings with limited distance information. Given query access to the strong-oracle and weak-oracle in the weak-strong oracle model, the authors design approximation algorithms for $k$-means and $k$-center clustering problems. In this work, we design algorithms with improved guarantees for $k$-means and $k$-center clustering problems in the weak-strong oracle model. The $k$-means++ algorithm is routinely used to solve $k$-means in settings where complete distance information is available. One of the main contributions of this work is to show that $k$-means++ algorithm can be adapted to work in the weak-strong oracle model using only a small number of strong-oracle queries, which is the critical resource in this model. In particular, our $k$-means++ based algorithm gives a constant approximation for $k$-means and uses $O(k^2 \log^2{n})$ strong-oracle queries. This improves on the algorithm of Bateni et al. that uses $O(k^2 \log^4n \log^2 \log n)$ strong-oracle queries for a constant factor approximation of $k$-means. For the $k$-center problem, we give a simple ball-carving based $6(1 + ε)$-approximation algorithm that uses $O(k^3 \log^2{n} \log{\frac{\log{n}}ε})$ strong-oracle queries. This is an improvement over the $14(1 + ε)$-approximation algorithm of Bateni et al. that uses $O(k^2 \log^4{n} \log^2{\frac{\log{n}}ε})$ strong-oracle queries. To show the effectiveness of our algorithms, we perform empirical evaluations on real-world datasets and show that our algorithms significantly outperform the algorithms of Bateni et al.

We investigate elliptic fractional equations in the whole space, involving zero order perturbations of the fractional Laplacian $(-Δ)^s$, $0<s<1$. Our main objective is to determine appropriate radiation conditions at infinity that ensure existence and uniqueness of solutions to the fractional type Helmholtz equation. Extending classical scattering theory for the Helmholtz equation, we introduce and analyze suitable Sommerfeld type radiation conditions for fractional orders. A central contribution is the explicit computation of the outgoing free space Greens function for the operator $(-Δ)^s-k^{2s}$, for all $0<s<1$, any dimension and $k>0$, obtained via contour integration and a limiting absorption principle. We show that its asymptotic behavior at infinity coincides with a rescaled version of the classical Helmholtz fundamental solution, thereby justifying the standard Sommerfeld radiation condition for compactly supported sources. In addition, using resolvent estimates and a limiting absorption framework, we establish existence and uniqueness of outgoing solutions for compactly supported data, and for weighted sources. We further derive a convolution representation of the solution in terms of the outgoing fundamental solution. For inhomogeneous media with compactly supported perturbations, we reformulate the problem as a Lippmann Schwinger integral equation of Fredholm type and prove unique solvability away from a discrete set of frequencies. Our analysis provides a rigorous foundation for scattering theory of fractional Helmholtz operators and offers a framework suitable for numerical implementation of these nonlocal wave propagation models.

In this paper, we study the contractivity of nonlinear stochastic differential equations (SDEs) driven by deterministic inputs and Brownian motions. Given a weighted $\ell_2$-norm for the state space, we show that an SDE is incrementally noise- and input-to-state stable if its vector field is uniformly contracting in the state and uniformly Lipschitz in the input. This result is applied to error estimation for time-varying equilibrium tracking in the presence of noise affecting both the system dynamics and the input signals. We consider both Ornstein-Uhlenbeck processes modeling unbounded noise and Jacobi diffusion processes modeling bounded noise. Finally, we turn our attention to the associated Fokker-Planck equation of an SDE. For this context, we prove incremental input-to-state stability with respect to an arbitrary $p$-Wasserstein metric when the drift vector field is uniformly contracting in the state and uniformly Lipschitz in the input with respect to an arbitrary norm.

We prove that computing an $ε$-approximate Nash equilibrium of a win-lose bimatrix game with constant sparsity is PPAD-hard for inverse-polynomial $ε$. Our result holds for 3-sparse games, which is tight given that 2-sparse win-lose bimatrix games can be solved in polynomial time.

In this paper, constrained parameter update laws for adaptive control with convex equality constraint on the parameters are developed, one based on a gradient only update and the other incorporating concurrent learning (CL) update. The update laws are derived by solving a constrained optimization problem with affine equality constraints. This constrained problem is reformulated as an equivalent unconstrained problem in a new variable, thereby eliminating the equality constraints. The resulting update law is integrated with an adaptive trajectory tracking controller, enabling online learning of the unknown system parameters. Lyapunov stability of the closed-loop system with the equality-constrained parameter update law is established. The effectiveness of the proposed equality-constrained adaptive control law is demonstrated through simulations, validating its ability to maintain constraints on the parameter estimates, achieving convergence to the true parameters for CL-based update law, and achieving asymptotic and exponential tracking performance for constrained gradient and constrained CL-based update laws, respectively.

In this work we introduce a new family of symmetric tensors generalizing Killing tensors, that we call magnetic Killing symmetric tensors. We make use of them to construct first integrals for the magnetic flow associated to a given magnetic field. We apply the results to prove integrability of some invariant magnetic flows (either exact or non-exact) on some 2-step nilmanifolds: the Kodaira-Thurston manifold and Heisenberg nilmanifolds of higher dimensions.

In this article, we study the Schrödinger equation posed in the Euclidean space. We prove observability inequalities for measurable sets that are thick with respect to decaying densities. The proof relies on quantitative uncertainty principles adapted to decaying densities, notably those established by Shubin, Vakilian, Wolff, and Kovrijkine.

LINE has emerged as one of the most popular communication platforms in many East Asian countries, including Thailand and Japan, with millions of active users. Therefore, it is essential to understand its security guarantees. In this work, we present the first provable security analysis of the LINE version two (LINEv2) messaging protocol, focusing on its cryptographic guarantees in a real-world setting. We capture the architecture and security of the LINE messaging protocol by modifying the Multi-Stage Key Exchange (MSKE) model, a framework for analysing cryptographic protocols under adversarial conditions. While LINEv2 achieves basic security properties such as key indistinguishability and message authentication, we highlight the lack of forward secrecy (FS) and post-compromise security (PCS). To address this, we introduce a stronger version of the LINE protocol, introducing FS and PCS to LINE, analysing and benchmarking our results.

Multimorbidity in older adults is common, heterogeneous, and highly dynamic, and it is strongly associated with disability and increased healthcare utilization. However, existing approaches to studying multimorbidity trajectories are largely descriptive or rely on discrete-time models, which struggle to handle irregular observation intervals and right-censoring. We developed a continuous-time hidden multistate modeling framework to capture transitions among latent multimorbidity patterns while accounting for interval censoring and misclassification. A simulation study compared alternative model specifications under varying sample sizes and follow-up schemes, and the best-performing specification was applied to longitudinal data from the Swedish National study on Aging and Care-Kungsholmen (SNAC-K), including 2,716 multimorbid participants followed for up to 18 years. Simulation results showed that hidden multistate models substantially reduced bias in transition hazard estimates compared to non-hidden models, with fully time-inhomogeneous models outperforming piecewise approximations. Application to SNAC-K confirmed the feasibility and practical utility of this framework, enabling identification of risk factors for accelerated progression toward complex multimorbidity and revealing a gradient of mortality risk across patterns. Continuous-time hidden multistate models provide a robust alternative to traditional approaches, supporting individualized predictions and informing targeted interventions and secondary prevention strategies for multimorbidity in aging populations.

Optimisation problems, which appear in numerous fields of science and industry, are challenging to solve even with modern supercomputers. Many such problems can be mapped onto ground-state searches of spin Hamiltonians, implemented on various physical platforms whose intrinsic dynamics are analogous to spin systems. However, the complex energy landscape of spin Hamiltonians often traps the system in local minima, preventing the system from reaching the ground-state (global minimum). We demonstrate an intrinsic feedback-driven annealing mechanism in class-B semiconductor laser arrays arising from the interplay of internal ($α$) and external ($η$) coupling. The instantaneous phase configuration self-modulates amplitude fluctuations, which act as an effective temperature, dynamically reshaping the potential and enabling the system to escape from local minima. Using a one-dimensional ring laser array, we analyze defect formation in the $α$-$η$ parameter space and identify an optimal regime achieving nearly 100% ground-state probability. Although both $α$ and $η$ are essential for the feedback loop, defect suppression results from modifying two competing timescales: amplitude stabilization (t_amp) and phase locking (t_phase), analogous to the Kibble-Zurek mechanism. These timescales can be tuned independently via $α$ or $η$. Identical timescale ratios yield identical defect probabilities, confirming that relative timescales, not specific parameters, govern defect formation. Our findings establish internal feedback-driven annealing as a practical route to ground-state search in semiconductor laser arrays, providing a foundation for efficient and scalable laser-based spin simulators for tackling hard optimization problems.

Previous numerical simulations have shown that cold clumps can form within hot accretion flows, offering insights into the detailed processes of the state transition in black hole X-ray binaries. However, the evolution of the cold clumps has not been investigated in detail yet. In this paper, we conduct hydrodynamic simulations to investigate the evolution of the cold clumps. In addition to previous result that when the accretion rate is high enough the cold clumps emerge within the hot accretion flow, we found that instead of directly moving toward to the black hole, the clumps moves outward when they initially form. The reason should be the combination of viscous torque and the condensation of hot gas from larger radii, which lead to the slightly super-Keplerian angular momentum of the clumps. After reaching the equilibrium position, the clumps begin to fragment at the inner edge with each fragment moving inward sequentially. Generally, the azimuthal movement of the clumps are quasi-Keplerian, being closer to the outer detached Keplerian cold disk rather than the surrounding sub-Keplerian hot accretion flow, which agrees well with the semi-analytical results for weak coupling case in Wang et al. (2012).

Given a uniformly expanding transitive Markov interval map, we show that within the set of ergodic measures the set of nonadapted ergodic measures is residual in with respect to the topology induced by the $\overline{d}$-metric. This set of measures is also shown to be path connected in many cases.

This paper presents a Marginal Reliability Impact (MRI) based resource accreditation framework for capacity market design. Under this framework, a resource is accredited based on its marginal impact on system reliability, thus aligning the resource accreditation value with its reliability contribution. A key feature of the MRI based accreditation is that the accredited capacities supplied by different resources to the capacity market are substitutable in reliability contribution, a desired feature of homogeneous products. Moreover, with MRI based capacity demand, substitutability between supply and demand for capacity is also achieved. As a result, a capacity market with the MRI based capacity product can better characterize the underlying resource adequacy problem and lead to more efficient market outcomes.

Deterministic single photon emission from a Rydberg ensemble coupled to an optical cavity requires high-fidelity preparation of collective single excitations. In such a setup imperfect Rydberg blockade can lead to unwanted double excitations, which degrade photon indistinguishability. In this work we adapt the Derivative Removal by Adiabatic Gate (DRAG) technique, originally developed for superconducting qubits, to shape optical pulses that suppress double excitations in this atomic platform. By combining analytical modeling with numerical optimization, DRAG provides an improvement over conventional sine-squared pulses. Further optimization of pulse duration and atomic ensemble size identifies a parameter regime, distinct from that used in [Nature Photonics 17, 688 (2023)], that enhances the single excitation probability from the previous theoretical benchmark of 77% to 91.9%, approaching the fundamental limits set by decoherence in the system. Benchmarking against GRAPE (Gradient Ascent Pulse Engineering) confirms that DRAG operates close to the optimal control limit, while maintaining smooth, experimentally feasible pulse shapes. These results demonstrate the effectiveness and cross platform adaptability of DRAG for a high-fidelity single photon source.

It has been proved by Boros and Makino that there is no output-polynomial-time algorithm enumerating the minimal redundant sets or the maximal irredundant sets of a hypergraph, unless P=NP. The same question was left open for graphs, with only a few tractable cases known to date. In this paper, we focus on graph classes that capture incidence relations such as bipartite, co-bipartite, and split graphs. Concerning maximal irredundant sets, we show that the problem on co-bipartite graphs is as hard as in general graphs and tractable in split and strongly orderable graphs, the latter being a generalization of chordal bipartite graphs. As for minimal redundant sets enumeration, we first show that the problem is intractable in split and co-bipartite graphs, answering the aforementioned open question, and that it is tractable on $(C_3,C_5,C_6,C_8)$-free graphs, a class of graphs incomparable to strongly orderable graphs, and which also generalizes chordal bipartite graphs.

Quantum relations in the sense of Weaver are $M'$-bimodules, for a von Neumann algebra $M$, these generalising actual relations on a set $X$ when $M=\ell^\infty(X)$. Similarly, relations between two sets can be generalised as bimodules over the commutants of two algebras. We make an explicit study of this idea, developing some tools to check that constructions are well-defined. Motivation comes from Kornell's concept of a Quantum Set (for algebras which are sums of matrix algebras), and we find that $*$-homomorphisms correspond to certain quantum relations, extending unpublished work of Kornell. We find a functor from completely positive maps to quantum relations, related to the idea of taking a noisy communication channel and reducing it to its underlying ``relation''. As with Quantum Graphs, at least in finite-dimensions, quantum relations correspond to ``adjacency operators'', certain CP maps depending on a choices of faithful functional on the algebras. We develop some tools to deal with the non-Schur-idempotent case, and show links with our functor from CP maps, and work of Verdon. We explicitly compute the adjacency operator of a $*$-homomorphism.

We study the phase structure of a model containing two flavors of massless staggered fermions interacting through two independent four-fermion couplings, UI and UB, formulated on a three-dimensional Euclidean space-time lattice. At UB = 0, this model is known to exhibit a direct second-order quantum phase transition between a massless fermion (MF) phase and a phase in which fermions acquire masses through the mechanism commonly referred to as symmetric mass generation (SMG). We demonstrate that introducing a small nonzero value of UB qualitatively alters this structure: the single exotic transition at UB = 0 splits into two distinct, conventional transitions, separated by an intermediate phase in which fermion masses arise through the standard mechanism of spontaneous symmetry breaking (SSB). The first of these is a Gross-Neveu transition separating the MF phase from the SSB-induced massive phase, while the second is a three-dimensional XY transition between the SSB phase and the SMG phase. Using the fermion-bag Monte Carlo method, we verify that the critical exponents associated with both transitions are consistent with the literature, thereby yielding a quantitative characterization of the resulting phase structure of the model.

In this article, we characterize the range of $α$ for which the helical maximal function is bounded from $L^p(|x|^α)$ to itself for $3<p<\infty$. Our result is optimal for $4\leq p<\infty,$ except possibly at end-points.

The quality assessment of Artificial Intelligence (AI) systems is a fundamental challenge due to their inherently probabilistic nature. Standards such as ISO/IEC 25059 provide a quality model, but they lack practical and statistically robust methods for assessing functional correctness. This paper proposes and evaluates the Statistical Confidence in Functional Correctness (SCFC) approach, which seeks to fill this gap by connecting business requirements to a measure of statistical confidence that considers both the model's average performance and its variability. The approach consists of four steps: defining quantitative specification limits, performing stratified and probabilistic sampling, applying bootstrapping to estimate a confidence interval for the performance metric, and calculating a capability index as a final indicator. The approach was evaluated through a case study on two real-world AI systems in industry involving interviews with AI experts. Valuable insights were collected from the experts regarding the utility, ease of use, and intention to adopt the methodology in practical scenarios. We conclude that the proposed approach is a feasible and valuable way to operationalize the assessment of functional correctness, moving the evaluation from a point estimate to a statement of statistical confidence.

Terrestrial double-$Λ$ hypernuclear data and astronomical observations of neutron stars provide complementary constraints on the $ΛΛ$ interaction. In this work, we investigate the $ΛΛ$ interaction within a Skyrme energy density functional framework based on the KIDS (Korea-IBS-Daegu-SKKU) models. We employ a Skyrme-type $ΛΛ$ interaction that includes the standard $s$- and $p$-wave terms, as well as a density-dependent term that effectively represents an $NΛΛ$ three-body force. The $s$-wave terms are constrained using data on double-$Λ$ hypernuclei supplemented by pseudodata obtained from core + $2Λ$ three-body model calculations including heavier hypernuclei. We show that the data on heavier systems are essential to simultaneously constrain the two $s$-wave parameters. We further explore the impact of the $p$-wave and $NΛΛ$ components on the neutron-star properties and find that appropriate repulsive contributions of these terms yield consistency with current neutron-star mass-radius observations. These results indicate that the present framework provides phenomenologically acceptable equations of state for dense $(N,Λ)$ matter over a wide range of densities and highlight the importance of future experimental data on heavier double-$Λ$ hypernuclei.

Flow matching and diffusion bridge models have emerged as leading paradigms in generative speech enhancement, modeling stochastic processes between paired noisy and clean speech signals based on principles such as flow matching, score matching, and Schrödinger bridge. In this paper, we present a framework that unifies existing flow and diffusion bridge models by interpreting them as constructions of Gaussian probability paths with varying means and variances between paired data. Furthermore, we investigate the underlying consistency between the training/inference procedures of these generative models and conventional predictive models. Our analysis reveals that each sampling step of a well-trained flow or diffusion bridge model optimized with a data prediction loss is theoretically analogous to executing predictive speech enhancement. Motivated by this insight, we introduce an enhanced bridge model that integrates an effective probability path design with key elements from predictive paradigms, including improved network architecture, tailored loss functions, and optimized training strategies. Experiments on denoising and dereverberation tasks demonstrate that the proposed method outperforms existing flow and diffusion baselines with fewer parameters and reduced computational complexity. The results also highlight that the inherently predictive nature of this generative framework imposes limitations on its achievable upper-bound performance.

In this paper, we establish a sharp lower bound for the spectrum of the Hodge Laplacian on Kähler hyperbolic manifolds. This bound is expressed explicitly in terms of the supremum norm of the 1-form associated with the Kähler hyperbolic structure. As an application, we obtain explicit spectral lower bounds for bounded symmetric domains.

Qualitative data analysis is labor-intensive, yet the privacy risks associated with commercial Large Language Models (LLMs) often preclude their use in sensitive research. To address this, we introduce ChatQDA, an on-device framework powered by open-source LLMs designed for privacy-preserving open coding. Our mixed-methods user study reveals that while participants rated the system highly for usability and perceived efficiency, they exhibited "conditional trust", valuing the tool for surface-level extraction while questioning its interpretive nuance and consistency. Furthermore, despite the technical security of local deployment, participants reported epistemic uncertainty regarding data protection, suggesting that invisible security measures are insufficient to foster trust. We conclude with design recommendations for local-first analysis tools that prioritize verifiable privacy and methodological rigor.

This study investigates the radial centering of gas bubbles within a buoyant plume of ethanol injected into a co-flowing water sheath flow in a vertical capillary. Bubbles nucleate in the ethanol stream due to CO$_2$ supersaturation and rapidly migrate toward the plume axis via solutocapillary (Marangoni) forces driven by interfacial tension gradients in the ethanol-water mixture. Experiments reveal that bubbles of varying sizes reliably align along the plume centerline, facilitated by steep radial concentration gradients near the plume boundary. A reduced-order model supports robust centering across a wide range of bubble radii. For larger bubbles, axial Marangoni effects modulate ascent velocities and can even induce upstream migration under transient conditions, highlighting the complex feedback between bubble dynamics and plume distortion. The results demonstrate that solutocapillary migration provides a reliable mechanism for contact-free bubble focusing, with implications for bubble manipulation in microfluidics, reactors, and phase-separation processes.

Evaluating the reliability of noisy quantum circuits is essential for implementing quantum algorithms on noisy quantum devices. However, current quantum hardware exhibits diverse noise mechanisms whose compounded effects make accurate and efficient reliability evaluation challenging. While state fidelity is the most faithful indicator of circuit reliability, it is experimentally and computationally prohibitive to obtain. Alternative metrics, although easier to compute, often fail to accurately reflect circuit reliability, lack universality across circuit types, or offer limited interpretability. To address these challenges, we propose a fine-grained, scalable, and interpretable framework for efficient and accurate reliability evaluation of noisy quantum circuits. Our approach performs a state-independent analysis to model how circuit reliability progressively degrades during execution. We introduce the Noise Proxy Circuit (NPC), which removes all logical operations while preserving the complete sequence of noise channels, thereby providing an abstraction of cumulative noise effects. Based on the NPC, we define Proxy Fidelity, a reliability metric that quantifies both qubit-level and circuit-level reliability. We further develop an analytical algorithm to estimate Proxy Fidelity under depolarizing, thermal relaxation, and readout error channels. The proposed framework achieves fidelity-level reliability estimation while remaining execution-free, scalable, and interpretable. Experimental results show that our method accurately estimates circuit fidelity, with an average absolute difference (AAD) ranging from 0.031 to 0.069 across diverse circuits and devices.

The forces that mixtures of motorized and passive crosslinking proteins collectively generate between cytoskeletal filaments within our cells are the key drivers of active cellular mechanics. Despite their importance, a unified theory to describe such crosslinking forces has so far been missing. In this paper, we derive a theory that predicts the forces generated collectively by crosslinking proteins linking two biopolymer filaments from measurable filament and crosslinker properties, using out-of-equilibrium thermodynamics. Our framework allows us to decompose the forces generated by crosslinkers into three separate components: entropic, active, and frictional. In doing so, it offers a clear physical interpretation of the fundamental mechanisms by which crosslinking proteins self-organize and collectively generate forces. We demonstrate the robustness and utility of this framework by applying it to four different experiments that probe the combined roles of passive and motorized crosslinkers. For each experiment, our theoretical approach allows us to disentangle the relative contributions of entropic, active, and frictional forces, clarifying how different physical processes underpin collective force production. In turn, this makes it possible to quantitatively compare and predict how various crosslinker combinations influence force generation between filaments, pattern formation along filaments, and the dynamics of filament pairs.