Papers

PEJWAK is introduced as a profile-echoing self-anchored aggregation architecture for multi-criteria decision analysis. Each criterion is coupled geometrically with an endogenous reference derived from the same alternative before final aggregation, so criterion identity is preserved while its expressed contribution is conditioned by the alternative's profile. A general formulation separates the anchor function, anchoring kernel, retention exponents, contribution coefficients, and outer aggregation rule. The canonical member uses a weighted-arithmetic self-anchor, sets each retention exponent equal to the corresponding criterion-importance value, and derives contribution coefficients through a normalized square-root map. Analytical results establish continuity, monotonicity, diagonal calibration, internality, full-domain joint continuity, exact boundary behavior, nonseparability, failure of bisymmetry in the equal-weight binary restriction, and an exact logarithmic retention law. A deterministic MCDA audit provides complete criterion-level decomposition, exact weight-stability intervals and rank transitions, contribution-rule rank phases, set-dependence diagnostics, and exact permutation-based rank-affinity analysis. Canonical PEJWAK handles exact zeros without epsilon regularization: an active zero removes only its own criterion contribution whenever the remaining active scores sustain a positive anchor. The architecture therefore supplies an auditable profile-conditioned aggregation mechanism between direct weighted aggregation and parameter-intensive nonadditive interaction models.

We present a computational framework for robust topology optimization that integrates polygonal finite-element discretizations, spatially correlated non-Gaussian material modeling, and non-intrusive polynomial-chaos surrogates. Spatial uncertainty in Young's modulus is represented as a homogeneous non-Gaussian random field obtained via a memoryless transformation of a truncated Karhunen-Loève expansion, ensuring physical admissibility through positivity of stiffness while preserving the prescribed autocovariance. Polygonal finite elements provide a stable discretization for density-based optimization on unstructured meshes and mitigate checkerboard artefacts and mesh bias, while the sparse polynomial-chaos expansion enables efficient estimation of low-order statistical moments required by the robust objective at a fraction of the cost of intrusive or Monte Carlo approaches. Numerical studies on a cantilever and a curved beam show that introducing non-Gaussian material variability leads to systematic load-path redistribution and a reallocation of 6-12% of the structural volume, together with a reduction in compliance scatter. The non-intrusive surrogate reproduces intrusive reference results within 3% using an order of magnitude fewer full finite-element analyses. These results demonstrate that the proposed framework offers a physically consistent and computationally efficient route to topology-optimized designs that remain reliable under realistic material uncertainty.

We study stochastic approximation of fixed points of a non-expansive operator $T$ when the oracle samples originate from a continuing Markovian trajectory. A direct block-minibatch implementation of Halpern iteration attains an expected last-iterate residual of order $O(\log N/N)$, but accrues a substantive complexity of $\tilde O(\epsilon^{-5})$ Markovian samples. We therefore introduce a variance-reduced Markovian PAGE-Halpern method whose refresh and same-state difference blocks are analyzed through the Poisson equation. In Hilbert spaces, the cocoercivity of $I-T$ results in an $O(\epsilon^{-3})$ sample complexity. Our main result extends this construction to a general finite-dimensional Banach space. A displacement-level Halpern bound replaces the Hilbert-space potential and yields $\tilde O(\epsilon^{-3})$ sample complexity. We also establish a high-probability guarantee with the same leading accuracy dependence by measuring the estimator in an auxiliary smooth norm.

We study optimization problems with noisy zeroth-order objective observations and deterministic nonlinear equality constraints with available derivatives. We propose a constrained variant of the adaptive-sampling trust-region derivative-free optimization algorithm—ASTRO-DF. The method builds quadratic local models from estimated objective values at interpolation points within a moving trust region and promotes feasibility through a Byrd–Omojokun composite-step based on linearized constraints, following an SQP-like framework. We prove almost sure convergence using a new constrained criticality test and present numerical results on an equality-constrained stochastic activity network problem.

Facial reduction (FR) is a preprocessing technique used to restore Slater's condition in semidefinite programming (SDP), but each step generally requires solving an auxiliary SDP. Factor-width-\(k\) partial FR restricts the class of exposing matrices. Increasing \(k\) enlarges this class, but, for \(k\geq3\), the auxiliary problem remains an SDP involving positive semidefinite blocks of order \(k\). For SDP relaxations of binary programs, we replace this auxiliary SDP by an LP-based face-identification method. We construct a polyhedron in subset-indexed moment variables that has polynomial size for fixed \(k\). The resulting face contains every feasible binary lift and is contained in every face exposed by a factor-width-\(k\) exposing matrix from the same auxiliary system. Thus, linear programming identifies a face no larger than those obtained from the factor-width-\(k\) auxiliary SDP while preserving all feasible binary points. To iterate the construction, we represent each identified face by linear equations in the original matrix variable, thereby retaining the moment-matrix indexing and the factor-width comparison at every iteration.

We study continuous-time multi-asset portfolio choice and consumption under smooth pointwise constraints, including state-dependent feasible sets. The method separates dynamic information acquisition from local constrained recovery. A pointwise-feasible neural actor generates reference rollouts; after training, its realized latent outputs are frozen and first- and second-order adjoints are harvested from a fixed-latent open-loop backpropagation-through-time graph. Feedback therefore generates the reference trajectory without restricting the adjoint formulation to Markov controls. Conditional on the harvested adjoints, deployment solves a local generalized Pontryagin-Hamiltonian problem: quadratic-affine portfolio blocks are recovered exactly by a quadratic program, while a log barrier approximates more general regular KKT branches. We establish local chart representations, an OL-BPTT-to-adjoint correspondence retaining orthogonal martingale residuals, and an end-to-end bound from reference value loss and numerical errors to recovered-policy and local QP-gap errors. Analytical constant- and predictable-opportunity benchmarks validate the adjoints. Common-input experiments show that recovery reduces residual PMP/KKT error left by finite-budget direct policy optimization, including under a state-dependent consumption cap and with up to 100 risky assets. Scalability concerns the constrained action block rather than dimension-free state-space complexity.

A small n-gon is a planar n-gon whose diameter is at most one. For odd n, Reinhardt proved that the regular polygon is optimal. For even n, the maximizer is nonregular, and only a few low orders were known exactly. We prove that for every even n >= 8 the maximum-area small n-gon is unique up to Euclidean isometry and reflection. Foster and Szabo's description of the diameter graph reduces a maximizer to an (n-1)-cycle of unit distances together with one pendant diameter. We determine the compatible boundary order, interpret the cycle as the centers of a Reuleaux (n-1)-gon, and eliminate the pendant vertex by a one-variable area calculation. The remaining first-order equations have conserved translation and rotation quantities. In the resulting radial variables they become the critical-point equations of an explicit function on a convex domain. We prove that this function is strictly concave by factoring the relevant principal minors of its local Hessian. Compactness gives existence, while strict concavity gives uniqueness. The proof is analytic. The symbolic scripts supplied with the paper check algebraic identities but are not used as part of the proof. Combined with the classical odd-order and low-order results, this determines the maximal area for every n >= 3.

We prove that, on a smooth manifold $M$ equipped with a constant rank horizontal distribution $H$ and a smooth inner product $g_H$ on $H$, any horizontal vector field can be written as a linear combination of, at most, $3N$ Lie brackets of horizontal gradient fields of depth-$(1)$, where $N$ is the minimal immersion dimension of $M$, recovering the Riemannian case trivially when $H$ is the entire tangent bundle. When $H$ is also bracket-generating with a uniformly bounded step, we show that any vector field can be written as a linear combination of a uniformly bounded number of iterated Lie brackets of horizontal gradient fields with uniformly bounded depth, both bounds depending solely on the immersion dimension $N$ and the uniform upper bound on the step of $H$. Utilizing this, in conjunction with the Trotter property, we show that, if the manifold is compact, connected, and without boundary, the group generated by flows of horizontal gradient fields is dense in the identity component of the diffeomorphism group. When the manifold is also Riemannian, we show that the same density statement holds for the group generated by diffeomorphic optimal mass transport maps.

Reusable-rocket powered landing under strong aerodynamics couples variable mass, free final time, and bounded aerodynamic controls through nonlinear velocity-frame dynamics. This paper develops a condensed proportional–integral projected-gradient (PIPG) sequential-convex method whose principal contribution is an exact reduced-space inner architecture. Because the problem contains only six terminal hard equalities and no state path constraints, 217 nodal-state variables and 210 trapezoidal dynamics equalities are eliminated from the 31-node convex subproblem, leaving 101 primal variables and six terminal equalities. Row-orthogonal preconditioning, fixed-size matrix–vector products, and nodewise circular-epigraph projections then yield a customized PIPG kernel. Physical consistency of the angle-dependent axial force is maintained by gradually releasing drag sensitivity between the reference squared angle and an epigraph variable $A$, together with a convex tightness term. A pointwise Hamiltonian argument shows that the fully released limiting subproblem admits a tight optimum satisfying $A=\alpha^2+\beta^2$. Deterministic annealing, two-stage inner accuracy, and a rejected-on-failure threefold extrapolation are secondary outer-loop accelerators.

This paper addresses the challenging problem of output feedback stabilization for nonlinear nonminimum phase (NMP) systems in the presence of parametric uncertainties and external disturbances. The proposed framework integrates three distinct observers: a reduced-order observer for reconstructing the unmeasured states of the internal (zero) dynamics, a high-gain observer for estimating output derivatives, and an observer for estimating the aggregated effect of parametric uncertainties and disturbances. Leveraging these estimates, a sliding mode control law is synthesized to ensure global asymptotic stability of the entire system using only output measurements. The control design requires only partial model knowledge, significantly relaxing the restrictive assumptions common in existing literature. Numerical simulations illustrate the effectiveness of the proposed output-feedback strategy and corroborate the theoretical developments.

A real symmetric matrix is called $d$-locally positive semidefinite if all of its $d \times d$ principal submatrices are positive semidefinite. We investigate the spectral geometry of $d$-locally positive semidefinite matrices. The set of vectors of eigenvalues of $d$-locally positive semidefinite matrices of size $n \times n$ is fully understood and known to be convex when $d \in \{1,n-1,n\}$ \cite{blekherman2022hyperbolic}. In the smallest remaining case $n=4, d=2$, non-convexity of the set of vectors of eigenvalues was proved in \cite{kozhasov2023eigenvalues}, but even in this case the full description was unknown. We provide a basic semialgebraic description of the set of vectors of eigenvalues for $n=4, d=2$ by establishing a Fischer-type inequality for $2$-locally positive semidefinite matrices of size $4 \times 4$ and prove non-convexity for $n \geq 4$ and $d \in \{2, n-2\}$. Non-convexity is established via solving certain non-smooth and non-convex min-max point configuration problems in the complex plane, which could be interesting in themselves. Similar problems were considered in \cite{nesterenko2024submatrices,sengupta2026submatrices} in the context of matrix decomposition and approximation.

While recent advances in minimax dual control have led to exact solutions for uncertain general linear time-invariant systems as well as (sub)optimal dual controllers, corresponding results for linear positive systems are still lacking. This paper aims to fill this gap and thereby pave the way toward scalable dual control algorithms. We study the general minimax optimal dual control problem for positive linear systems with unknown dynamics and reformulate it as a standard zero-sum dynamic game. By allowing randomized control inputs, we solve the corresponding Bellman equation exactly for the scalar case with sign uncertainty in the input. This yields an implicit dual control policy that is optimal both in terms of cost and $\ell_1$-gain. The optimal dual policy uses exploration in a specific region of the hyperstate space to conduct optimal probing. Outside this exploration regime, the controller reduces to a deterministic certainty equivalence policy, indicating that sufficient information has been obtained to identify the correct input direction. In addition, these results allow us to analyze fundamental limitations of minimax dual control for positive systems and provide a foundation for more general dual control problems for positive systems for future work.

Control barrier functions (CBFs) provide a systematic framework for enforcing safety constraints in nonlinear control systems. However, their implementation typically relies on accurate system models, which can limit their applicability in the presence of significant modeling uncertainties or unknown dynamics. This paper proposes a model-free framework for the computation of recursive control barrier functions based on the ultra-local model approach that leverages online estimation of the unknown system dynamics to construct CBF constraints. This approach does not require an explicit model of the system dynamics and enhances robustness with respect to disturbances and model mismatch. The resulting control architecture enables the enforcement as well as the anticipation of safety constraints for systems with higher relative degree. The effectiveness of the proposed approach is illustrated on the adaptive cruise control benchmark.

We propose a family of control variate estimators for variance reduction in design-based survey sampling and causal inference, with and without interference. In these settings, inverse probability weighting (IPW) estimators are widely used, but may have large variance when sampling, treatment, or exposure probabilities are small. Building on the observation that several common estimators, including the Hajek estimator, the normalized estimator, the augmented inverse probability weighting (AIPW) estimator, and the targeted maximum likelihood estimator (TMLE), all correct the Horvitz-Thompson estimator by canceling part of its randomness, we provide a unified interpretation of these estimators as special cases of a general control variate estimator. We then construct optimal control variates that can reduce the finite sample variance compared to these common estimators. We parameterize the proposed control variates by their bases and characterize the optimal bases through a stochastic optimization formulation. In survey sampling and causal inference without interference, the optimal bases are characterized by leading eigenvectors of matrices that depend on both the design-based sampling structure and the model-based outcome uncertainty. In causal inference under network interference, the optimal bases solve a nonconvex quadratic optimization problem; we provide a $\frac{1}{2}$-approximate solution and an alternating local search heuristic. We apply the control variate estimators to the Swiss Environmental Panel survey data and the Chinese social network data, and conduct extensive simulations to show that the proposed control variate estimators can achieve substantial variance reduction.

This paper presents an iterative model predictive control algorithm that stabilizes constrained nonlinear systems without evaluating a single plant derivative. By factoring the exact nonlinear dynamics into a pseudo-linear form using state- and control-dependent coefficients (SCDCs), we replace the standard nonconvex optimization with a sequence of constrained linear-quadratic programs. Refreezing the coefficient matrices along the previously predicted trajectory drives the iteration. Near the origin, we prove this sequence contracts to a unique fixed point. We explicitly bound the number of iterations required to reach any stopping tolerance, and we quantify the distance from the fixed point to a true Karush-Kuhn-Tucker point, showing this optimality gap vanishes quadratically as the state approaches the origin. Inflating the discrete algebraic Riccati equation generates terminal ingredients that guarantee recursive feasibility and asymptotic stability, even when the solver terminates early. We adapt the terminal penalty online, proving it remains uniformly bounded, and we secure output feedback through the block-observable canonical form, which extracts the exact system state directly from past inputs and outputs. Retaining the block-banded structure of the subproblem forces the computational cost to scale linearly with the horizon length $\ell$. This $O(\ell)$ complexity matches the iterative linear quadratic regulator (iLQR) but sharply undercuts the $O(\ell^3)$ scaling of dense sequential quadratic programming (SQP). Numerical studies on a saturated quadrotor, a nonholonomic integrator, and a nonminimum-phase plant illustrate the theoretical bounds and map how the algorithm compares with iLQR, SQP, and linear-parameter-varying MPC.

Dimension reduction removes variables, but a reliable reduction should not erase their dynamical influence. We study this principle for linear block evolution systems on resolved and unresolved Hilbert spaces. Exact elimination of the unresolved component yields a Volterra equation with a memory kernel and an effective forcing term carrying hidden initial data and forcing; in the Laplace domain the same operation is a dynamic Schur complement. We introduce finite-horizon trajectory-stable reduction and derive perturbation estimates for operator-valued kernels, then lift them to perturbations of the hidden propagator, couplings, hidden initial state, and hidden forcing. For passive skew-adjoint couplings, the reduced memory operator has positive type and an exact storage identity, and norm-convergent passive realisations preserve both trajectories and the storage–dissipation functional. Compatible finite spectral truncations provide structure-preserving internal-variable reductions. Two elementary examples separate positive type from instantaneous $L^2$-coercivity and show that small hidden amplitude need not imply small long-time influence. The framework isolates the controlled approximation of unresolved influence, rather than elimination alone, as the central reduction problem.

We investigate long-time learning in ergodic, potential, monotone mean-field games (MFGs) via a self-fictitious-play (SFP) dynamics coupling an optimally controlled diffusion with a slowly evolving belief. At each time, the state follows the optimal feedback associated with the current belief, while the belief is updated using the player's own empirical occupation measure rather than the population distribution. For ergodic monotone potential MFGs on the torus, we prove that the SFP dynamics is contractive and admits a unique invariant law. Moreover, we show that this invariant law is quantitatively close to the MFG Nash equilibrium, with an error of order equal to the square root of the belief-update rate. The proof combines uniform-in-time regularity estimates for the ergodic Hamilton-Jacobi-Bellman equation with an energy argument based on the Lasry-Lions divergence. The linear-quadratic example shows that this rate is sharp, and the numerical experiments illustrate the predicted scaling.

In this article, we introduce a novel approach to solving the ergodic stochastic optimal control problem whose dynamics is driven by a controlled stochastic differential equation. The coefficients of this stochastic differential equation are non-autonomous but periodic in time. We first prove that the infinite horizon average stochastic optimal control problem is ergodic, i.e., the value function equals a constant $\rho$ which is independent of the initial conditions. Based on the result of ergodicity, we construct an auxiliary function $w(t,x)$ that is well-defined and periodic in time. We can prove that the pair $(w,\rho)$ satisfies the dynamic programming principle and is a viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Finally, we apply our results to the study of ergodic backward stochastic differential equations. Our method is even new in the homogeneous case.

We consider the gain of entrainment (GOE)–the difference between the average steady-state output under a periodic input and the steady-state output under a constant input with the same mean–for an $n$-stage feedforward cascade of stable first-order filters interleaved with static nonlinearities. The main result is an exact decomposition of GOE as a weighted sum of local Jensen gaps, where each gap quantifies the mean shift generated by a nonlinearity, and each weight is a product of downstream incremental gains divided by linear time constants. We provide a Bregman-divergence interpretation of the decomposition, and a second-order small-amplitude of GOE separating local curvature, fluctuation energy, and differential gains. We demonstrate the theoretical results using a Michaelis-Menten cascade showing that any nonconstant periodic feeding strictly reduces the average terminal product relative to constant feeding with the same mean.

In apparel retail and other applications, when a customer's preferred size is unavailable, demand may shift to nearby sizes. This substitution creates new assortment and inventory optimization challenges by coupling product availability and demand across sizes. We introduce the consider-fit-then-choose (CFTC) model to capture such size-dependent choice behavior. Products may be offered in multiple sizes, which affect customer preferences and consideration sets through fit, measured by distance from the customer's ideal size. We study assortment optimization and show-all inventory selection, in which the retailer chooses initial inventory and subsequently offers every in-stock product. We show that assortment optimization under the CFTC model is NP-hard and develop a PTAS when customers deviate by at most $O(1)$ sizes from their ideal size. Combined with the recent black-box framework of Fu et al. (2026), this yields a nearly $0.272$-approximation for show-all inventory selection. We next exploit the specific choice dynamics of the CFTC model. By stocking only every other size, we decouple demand across stocked sizes and reduce CFTC to a special class of mixed multinomial logit models that we prove satisfies the convex chain decomposition (CCD) property of Goyal et al. (2023). For the fluid problem, we develop a polynomial-time $(1/2-\epsilon)$-approximation under adjacent-size substitution and a mild condition on preference weights. For the stochastic problem, we establish an asymptotic $1/2$-approximation using a new coupling argument connecting the stochastic inventory process to its fluid counterpart. Numerical experiments calibrated using footwear data show small optimality gaps across a broad range of substitution patterns and problem settings.

The consensus of continuous-time multi-agent systems with unbounded and heterogeneous constant delays is investigated by combining frequency-domain analysis and algebraic graph theory. Several types of signed Laplacians are constructed to characterize consensusability under delays. The core results are established based on the defined delay-embedded signed Laplacian, where a small-delay link creates a cooperative interaction and a possibly unbounded large-delay link creates an antagonistic interaction between the agents. The dividing line between small and large delays is given by $\tau_{ij}=\pi/2\lambda_{\max}(L_0)$, where $\lambda_{\max}(L_0)$ refers to the maximum eigenvalue of the conventional graph Laplacian. It is proved that the consensusability is preserved if the delay-embedded signed Laplacian is positive semi-definite with a simple zero eigenvalue. Moreover, we derived some consensus conditions in terms of the extended effective resistance which measures the overall coupling between two sets of agents. The obtained results provide new insights into the mechanism of delayed consensus from the interplay between the small-delay-induced cooperativeness and large-delay-induced antagonism in the underlying network topology.

In contextual optimization, the decision-maker seeks optimal decisions to minimize a cost function, that varies based on observed features. This context is common in many business applications ranging from on-demand delivery and retail operations to portfolio optimization and inventory management. In this paper, we study the learning and optimization approach, which first learns how outcomes result from the features, and then selects optimal decisions based on these outcomes. We focus on the integrated learning and optimization literature, and identify that a lack of control for prediction accuracy can lead to overfitting and a loss of decision effectiveness against simple separate learning and optimization models. Instead, we propose a bi-objective formulation that balances prediction accuracy and cost minimization, termed decision-driven regularization. It also addresses ambiguity in the definition of the cost function via a surrogate that depends on a new hyperparameter. We additionally show that alternative perspectives for formulating the problem, namely robust optimization and regret minimization, lead to models that are closely related to our proposed model. As a consequence, our framework generalizes models such as SPO+. Our model is shown to be numerically superior to other benchmarks, such as OLS, Random Forest, XGBoost, SPO+, Perturbation Gradient, and Learning and Rank, in our synthetic studies.

We revisit the problem of computing mean-field equilibria (MFEs) in discrete-time, monotone, finite-horizon mean-field games (MFGs). We show that, when the transition kernel is independent of the state-measure term and the reward function satisfies the usual weak monotonicity condition and is Lipschitz continuous, anchored proximal gradient descent methods can be used to compute a monotone MFE. We also establish last-iterate convergence results for these methods. Our approach relies on formulating the computation problem as an optimization problem over the space of occupation measures. Using this formulation, we show that the problem is equivalent to a class of constrained Lipschitz monotone inclusion problems. We then apply iterative methods for this monotone inclusion formulation to derive a tractable algorithm. The resulting algorithm achieves a convergence rate of \(O(1/\sqrt{T})\) after \(T\) iterations, without requiring any regularization. This rate holds even in the absence of a uniqueness assumption for the corresponding MFE.

Andy is an autonomous mathematical research agent that turns a mathematical problem into a traceable proof. It solves or verifies a submitted problem, formulates a literature-grounded new problem through a research-value gate, and carries it through proof construction and final verification. It organizes proof steps in an executable DAG, verifies each step independently and binds the result to a certificate, retains verified work whose interfaces remain unchanged during local repair, and records the full path from problem formulation to final proof. The system separates proof generation from correctness evaluation and can acquire, retain, retrieve, and reuse knowledge from existing results. Starting from a self-triggered impulsive consensus result, Andy formulates a global exponential leader-follower synchronization problem for delayed heterogeneous networks with switching communication topologies. The proposed hybrid control combines self-triggered impulses with execution delay and continuous feedback over a recovery window. After each delayed impulse, the feedback cancels the delayed error channel until the pre-impulse history leaves the active delay interval. Sufficient conditions for global exponential synchronization are established, Zeno behavior is excluded for both timing sequences, and a numerical example illustrates the result.

Structured nonconstant large stepsizes can improve the convergence of gradient descent in the deterministic setting. However, in stochastic optimization, aggressive stepsizes can amplify oracle noise and hinder the convergence of stochastic gradient methods. We characterize the globally optimal two-step stepsize schedule for stochastic gradient methods applied to strongly convex and smooth functions, assuming access only to unbiased stochastic gradient estimates with finite support and bounded variance. The optimal schedule depends on the ratio of the initial optimality gap to the noise level and exhibits several distinct regimes. As the influence of stochastic noise diminishes, the optimal two-step stepsizes become larger, reflecting a balance between the benefits of faster iterate convergence and the perturbations induced by stochastic noise.

Extreme weather leaves power systems exposed to residual outage risk even after physical resilience investments. Parametric insurance can provide pre-agreed contingent liquidity, but its physical value depends on how trigger thresholds and payout levels are designed. This paper proposes a resilience oriented parametric insurance framework that couples a three tier wind-index contract with post-event network restoration. Insurance payout expands the budget available to activate emergency resources, so the contract changes the physical restoration feasible set rather than merely offsetting accounting losses. Trigger thresholds and payout levels are jointly designed to balance actuarial premium, expected post-event system cost, and the conditional value-at-risk (CVaR) of scenario energy not supplied (ENS). A response-library method precomputes the restoration mixed-integer linear program for each scenario-payout pair and then evaluates admissible contracts efficiently. On the IEEE RTS-24 with 80 extreme-wind scenarios, the optimized contract reduces expected EENS and CVaR0.90 of ENS by 21.1% and 21.4%, respectively, relative to no insurance, while requiring 48.8% less premium than a fixed parametric contract with comparable resilience. The results show that insurance design should target the nonlinear liquidity-to-resilience response rather than loss compensation alone.

Spacecraft attitude control becomes challenging when light-sensitive instruments must avoid bright objects. This work proposes a path-planning-based spacecraft attitude reorientation maneuver considering these constraints to reach the desired attitude. Constraint-compliant attitude trajectories are computed using a fuzzy enhanced potential field approach in the attitude space. Based on the path-planning output, the control input is determined by considering the dynamics and kinematics of the spacecraft to satisfy dynamic constraints in the time domain. Numerical simulation results demonstrate successful reorientation maneuvers without violating the constraints.

Pathological neuronal synchrony provides one practical motivation for studying sparse desynchronisation control in networked oscillatory systems, particularly in applications where actuation and communication are resource constrained, as in deep brain stimulation. Motivated by this challenge, we study how to stabilise desynchronisation in coupled oscillatory dynamical systems without continuously updated control, even when the oscillators' phase is unavailable. We develop a general event-triggered control framework for stabilising the desynchronised state of coupled limit-cycle oscillatory dynamical systems. Our analysis establishes a unified theoretical result showing that desynchronisation can be achieved by various feedback controllers that act sparsely and depend only on an order parameter observable. The proposed controllers admit a gradient-descent interpretation and stabilise the desynchronisation state of general phase-reduced oscillator networks. We further prove the controlled systems under event-triggered mechanisms possess a strictly positive lower bound of the inter-event dwell-time, excluding Zeno behaviour. To address the practical unavailability of exact phase reductions, we introduce a pseudo-phase construction that yields a computable order parameter from state measurements alone. Numerical studies on representative oscillator networks demonstrate the effectiveness and robustness of the proposed framework.

Making language models solve constraint problems reliably often means having them translate the problem into a formal specification and delegating the search to a sound solver. But the translation is itself a language-model task, and an unfaithful translation makes the solver faithfully solve the wrong problem. Existing pipelines repair only translations that crash, returning the solver's error message and falling silent when the program runs but is wrong. We replace the error message with a proof: when the generated program is unsatisfiable, we extract a minimal unsatisfiable core over the model's own constraints and hand it back the exact set that cannot hold together, a leakage-free signal that localizes the fault. On a new benchmark of 77 problems with an exact oracle, translation to Answer Set Programming is faithful on six of seven domains and fails only on aggregate coverage scheduling, which concentrates the translation tax in one diagnosable pattern. A minimal core, rather than a bare error, is what stops a weaker model from fabricating solutions to infeasible problems, cutting fabrication from 79% to 7%. A strong chain-of-thought baseline meanwhile matches the symbolic route on accuracy, so the route's value is not accuracy but certificates and its refusal to fabricate.

In this paper, a general principle for coercivity in optimal control problems is investigated. Utilizing regularity properties of solutions to second-order elliptic PDEs on Lipschitz domains, we provide quantitative sufficient second-order optimality condition for control-constrained semilinear elliptic optimal control problems. The main property of the investigated optimal control problems is the absence of a Tikhonov regularization term on the objective function. For these problems, the second variation is a quadratic form in the linearized state, and its curvature function may vanish or change sign. The quantitative condition we introduce implies coercivity with respect to the $L^2$-norm of the linearized-states. As a consequence, the stability of the sufficient second-order condition under perturbations of the states and the tracking data is shown.