Papers

We report on the mapping of classical microwave transmission line theory onto the quantum scattering matrix description. By means of a generalized flux formalism a la Devoret, we derive a charge-current vector living on the confining electrodes, to which a Hodge-like decomposition is applied. The presented theory holds equally well for all types of waves traveling within Cartesian and cylindrical guide geometries (the usual Transverse Electric Magnetic, but also Transverse Magnetic and Transverse Electric ones). We then demonstrate how a generic load decomposes into a series of complex coefficients $Z_{load}(\alpha)$, for each mode $\alpha$ propagating along the line. This decomposition leads to a particular classification of traveling waves: gradient-type and curl-type charge-currents. This distinction shines a new light on a broken gauge symmetry exhibited by a class of Transverse Electric modes. Our results provide a universal theoretical framework, which finds a direct usage in microwave-based quantum information transfer.

Temporal action localization (TAL) in wearable sensor streams identifies action classes and temporal boundaries, enabling finer-grained activity understanding than conventional action recognition. However, training typically requires costly start–end annotations for every action instance. To reduce this burden, we study point-supervised TAL, where each instance is labeled with only one timestamp and its class. We propose Progressive Sensor Event Expansion (PSEE), which combines semantic activations, sensor-specific transition evidence, and adaptive temporal ownership to recover point-supervised pseudo segments. These segments supervise standard TAL detectors without modifying their inference procedures. Cross-subject experiments on four inertial-sensing benchmarks demonstrate improved pseudo-boundary quality over adapted point-supervised baselines, compatibility with different TAL detectors, and robustness to point sampling. Code is available at https://github.com/joeeeeyin/PSEE.

Embodied foundation models are constrained by the limited scale and diversity of robot demonstrations, motivating the use of large-scale egocentric human interaction data. However, how to effectively incorporate such data into embodied-model pre-training remains unclear because of substantial embodiment and action-space gaps between humans and robots. We present AtomEgo, a systematic study of ego–robot co-training supported by a curated corpus of approximately 2,659 hours and a scalable data processing pipeline. Across vision–language–action and world–action model architectures, we investigate three representative paradigms: joint co-training with domain-specific action heads, progressive ego-to-robot transfer through embodiment alignment, and joint video–action modeling. We evaluate these paradigms through multi-task real-robot experiments and language-conditioned cross-embodiment representation analysis. Our results reveal a simple principle: Data Scale * Alignment Quality –> Capability Gain; egocentric data can improve generalization, but their value depends on how effectively they are aligned and utilized. This principle can provide practical guidance for scalable ego–robot pre-training.

For a matrix $\gamma\in\mathrm{SL}_2({\mathbb Z})$, we define \[ {\mathcal R}(\gamma)=a_1^2+a_2^2+a_3^2+a_4^2, \qquad \text{where} \ \gamma=\begin{pmatrix}a_1&a_2\\ a_3&a_4\end{pmatrix}, \] and let $S_{\mathrm{sq}}(X)$ count the number of matrices $\gamma$ with $\|\gamma\|_\infty = \max\{|a_1|, |a_2|,|a_3|,|a_4|\} \leq X$ and such that ${\mathcal R}(\gamma)$ is squarefree. We prove that \[ S_{\mathrm{sq}}(X) = {\mathfrak S}_{\mathcal R}^{\mathrm{sq}}N(X) +O(X^{19/10+o(1)}), \quad \text{as}\ X\to \infty, \] where $N(X)=\#\{\gamma\in{\mathrm{SL}}_2({\mathbb{Z}}):\|\gamma\|_\infty\leq X\}$ and ${\mathfrak{S}}_{\mathcal{R}}^{\mathrm{sq}}$ is an explicit positive Euler product of local $p^2$-densities. The proof combines the $\delta$-method for small moduli with a sum-of-two-squares estimate for large square divisors. This complements a result of J. B. Friedlander and H. Iwaniec (2009) on prime values of ${\mathcal R}(\gamma)$, which, however, is conditional on a very strong form of the Elliott–Halberstam conjecture. We also show that ${\mathcal R}(\gamma)$ is squarefree and has at most $9$ prime divisors for at least $cN(X)/\log X$ matrices $\gamma\in\mathrm{SL}_2({\mathbb Z})$ with $\|\gamma\|_\infty\le X$, where $c>0$ is an absolute constant.

Sharp high-entropy lower bounds for the entropy of a sum were known for identically distributed summands in torsion-free abelian groups and in prime cyclic groups. For arbitrary independent summands, Gavalakis, Goh and Kontoyiannis obtained an additive constant of $1/8$ and conjectured that the sharp constant is $1/2$. We prove that independent discrete random variables $X,Y$ with finite Shannon entropies satisfy $H(X+Y)\ge (H(X)+H(Y))/2+1/2-o(1)$ in every torsion-free abelian group as $\max{H(X),H(Y)}\to\infty$. The same conclusion holds in the prime cyclic group $\mathbb F_p$ when both $\max{H(X),H(Y)}$ and $\log_2 p-\max{H(X),H(Y)}$ tend to infinity. We give explicit error bounds in both settings. The proof extracts a component with paired point probabilities while controlling the entropy of the remainder independently of its support. Discrete rearrangement and uniform perturbation then transfer the continuous entropy power inequality to this component. In prime cyclic groups, an additional estimate controls the entropy lost under modular reduction. Binomial distributions show that the constant $1/2$ is optimal.

Let $L_v=-\Delta-2v\cdot\nabla$ on $L^2(\mathbb R^n,e^{2v\cdot x}\,dx)$, where $v\in\mathbb R^n\setminus\{0\}$ is a constant drift vector. We prove that the full vector Riesz transform $\nabla L_v^{-1/2}$ satisfies a weak-type $(1,1)$ estimate for real-valued functions with constant at most $2$, uniformly in both the dimension and the drift vector. Our proof extends the fractional obstacle method of Ouyang, Spector and Stockdale (https://arxiv.org/abs/2608.18068) to the exponentially weighted setting. Interpolation then yields strong $L^p$ bounds for $1<p\le 2$, with constants depending only on $p$.

Deep neural architectures are widely used for signal processing in automated pain assessment systems. However, architecture design has remained largely a manual task despite the potential efficiency benefits of Neural Architecture Search (NAS). Embedding NAS in a Leave-One-Subject-Out (LOSO) evaluation is computationally demanding because a fully nested implementation requires $N$ independent architecture searches and, assuming approximately linear training cost, scales as $\mathcal{O}(N^2)$. We propose a block-based, leakage-controlled approach that shares NAS runs between subjects, reducing the number of searches from $N$ to $B$, where $B \ll N$, dubbed PainNAS. On the BioVid Heat Pain dataset, PainNAS yields comparable subject-level accuracy with substantially fewer parameters and FLOPs.

We study the large-time behavior of solutions to the aggregation–diffusion equation $$ u_t=\Delta u+\nabla\cdot\bigl(u\,\nabla K*u\bigr) \qquad \text{in } \mathbb{R}^d. $$ Our main results identify a transition, governed by the regularity and singularity of the interaction kernel, between Gaussian and nonlinear self-similar asymptotics. We prove that for regular interaction kernels, as well as for sufficiently mild singular repulsive kernels, the nonlinear drift is asymptotically negligible and solutions exhibit the same Gaussian large-time behavior as solutions of the linear heat equation. In contrast, for the critical logarithmic kernel $ K(x)=-\log |x|, $ the interaction persists at the diffusive scale and leads to genuinely nonlinear asymptotics. More precisely, for every mass \(M>0\), we prove the existence and uniqueness of a self-similar solution of mass \(M\) and show that every solution with mass $M$ and with finite second moment converges in all $L^p$-norms to this self-similar solution as \(t\to\infty\).

While diffusion-based text-to-video (T2V) models have demonstrated impressive capability in generating realistic and temporally coherent videos, they often fail to respect fundamental physical dynamics. Although recent physics-constrained methods incorporate explicit dynamics priors to improve physical plausibility, they remain limited to simple single-type motions, depend on manually specified parameters, and struggle to generalize to unseen physical laws. In this work, we propose CompAdapt, a physics-consistent T2V framework for adaptable generation across complex real-world scenarios. It extends neural dynamics modeling beyond single-type motions to encompass composite physical behaviors, including coupled motions, multi-stage transitions, and multi-object collisions. Furthermore, CompAdapt translates natural language prompts into structured physical semantics, enabling end-to-end specification of motion types, temporal relations, and initial physical parameters. To generalize to novel physical environments, CompAdapt introduces dynamics-aware prior matching, achieving one-shot adaptation without retraining the core dynamics module. In addition, a physics-aware latent feature fusion module improves visual fidelity under fast and complex motion. Experiments on physics-focused T2V benchmarks demonstrate that CompAdapt improves physical consistency over both general T2V models and physics-constrained baselines, while preserving high visual quality and adaptability to unseen dynamics. The project page is available at https://makapic.github.io/CompAdapt/ .

We revisit Breiman's observation that reducing inter-tree correlation without weakening individual trees can improve random forests. Building on this principle, we introduce two variants: Dirichlet-Multinomial Bagging Random Forest (DM) and Dirichlet-Weighted Random Forest (DW). Both modulate sample reweighting via a concentration parameter $\alpha>0$. We provide a simple theoretical criterion that clarifies when these variants behave indistinguishably from standard random forests, and we use it to guide a lightweight tuning strategy. In a controlled evaluation on public classification benchmarks, DM and DW are consistently competitive and often stronger than other random-forest (RF) baselines, with negligible additional runtime.

We study the problem of tiling an $N\times N$ square with axis-aligned squares whose side lengths are integers strictly less than $N$, with the objective of minimizing the number of tiles. The standard placement-based exact-cover MILP contains $\Theta(N^5)$ placement-to-cell nonzero coefficients and is also affected by the dihedral symmetry of the square domain. We introduce a Corner-Difference MILP (CD-MILP) that represents each selected square by at most four signed corner coefficients. Two-dimensional prefix reconstruction shows that the resulting constraints are equivalent to the original cell-cover equations, while reducing the coverage-related nonzero count to $\Theta(N^3)$. We also introduce lightweight corner-ordering constraints that retain at least one representative from every $D_4$ orbit, although ties may leave residual symmetry. Computational experiments on nine prime-size instances compare the baseline, CD-MILP, the baseline with corner ordering, and their combination using Gurobi and COPT. Under the stated experimental settings, the combined formulation solves eight instances with Gurobi and seven with COPT, compared with four and five, respectively, for the baseline. Its average presolved matrixs contain approximately $10^5$ nonzero coefficients on average, compared with approximately $10^7$ for the baseline.

Let $(X,d,p)$ be a noncollapsed pointed Gromov–Hausdorff limit of complete $n$-dimensional Riemannian manifolds with a uniform lower Ricci curvature bound, where $n\ge4$. We assume that, on each bounded ball, the integral of the $3/2$ power of the small-ball volume deficit relative to the hyperbolic comparison volume is $O(r^3)$ as $r\rightarrow0$. We prove that the metric singular set has Hausdorff dimension at most $n-3$ and sigma-finite $(n-3)$-dimensional Hausdorff measure, thus confirming a particular case of codimension-three regularity conjecture \cite[Conjecture 2.4]{Naber2020}.

We establish a global stochastic maximum principle for forward-backward stochastic control systems with an unbounded terminal condition and a generator that has quadratic growth and is convex in $Z$. The control domain need not be convex, and the diffusion coefficient may depend on the control. In this setting, the BMO martingale estimates used for quadratic BSDEs with bounded terminal conditions are no longer directly available. To overcome this difficulty, we work under an equivalent probability measure associated with the optimal trajectory and establish the estimates needed for the variational analysis. In particular, using a representation formula for convex quadratic BSDEs with conditional estimates, we derive estimates for the backward-state perturbations under this fixed measure. These estimates allow us to justify a second-order expansion of the cost functional and obtain the global stochastic maximum principle.

Post-training weight-activation quantization reduces the memory and inference costs of large language models, but aggressive W4A4 quantization remains difficult because activation outliers degrade effective quantization resolution. Although weight optimization, channel-wise scaling, and orthogonal rotation mitigate this problem, the error components they address and their relationship remain unclear. Using an exact decomposition of local weight-activation quantization error into an activation-guided weight compensation term and an orthogonal residual, we bound the residual using persistent channel-wise outlier and regular activation quantities. This decomposition clarifies which error components can be addressed by weight compensation and which require transformation design. We then use the residual bounds to derive practical guidelines for applying randomized Hadamard rotation, sign selection, and channel scaling. In particular, the analysis explains how random signs suppress constructive interference among persistent outlier channels, how sampling multiple sign patterns can improve transformation selection, and how second-moment balancing leads to an $L_2$ scaling rule while a further relaxation recovers SmoothQuant-style $L_\infty$ scaling. We evaluate these guidelines through backpropagation-free configurations across eight Llama and Mistral models, obtaining performance competitive with gradient-trained SpinQuant.

World Action Models bring the predictive capabilities of video models into robot action generation, providing a rich foundation for modeling future visual states. Tactile sensing complements this foundation with direct measurements of physical interaction. Some existing methods use tactile features as conditioning inputs without jointly predicting future tactile states, visual observations, and actions. Our key insight is that tactile signals, like video, provide observations of the evolving world state and should be modeled as future observations alongside video. We present ME-Dex-1.0 (MachEmbodied-Dex-1.0), a unified World Action Tactile Model for joint visual, tactile, and action learning. ME-Dex-1.0 adopts a Mixture-of-Transformers architecture comprising a Video Expert, a Tactile Expert, and an Action Expert, all trained with flow matching. We use shared attention connects the experts in intermediate layers, allowing action generation to draw on learned representations of visual and tactile dynamics during joint denoising. To support multi-source heterogeneous tactile inputs, a Canonical Hand Model and a Unified Tactile Autoencoder map tactile observations from different embodiments and sensing layouts into shared spatial and latent spaces. To address the limited availability of paired visual, tactile, and action data, we develop the Agentic Tactile Data Engine, an agent-based data production platform. It supplements RoboTwin and DexJoCo with tactile data recorded directly from force sensors during trajectory replay in simulation. Experiments on the RoboTwin, DexJoCo, and ManiFeel simulation platforms, together with real robot evaluations, demonstrate improved manipulation performance using both grippers and dexterous hands equipped with tactile sensing.

This work presents Robotic Multiphase Interaction (RMI), a setting in which liquid enters a porous material and interacts mechanically with its deforming solid skeleton. Manipulation can therefore change pore volume, expel or redistribute retained liquid, and alter grasp stability at the same time. Spilled liquid can also create safety risks in domestic and manufacturing settings. This differs from most manipulation of solid objects and from tasks that involve both liquid and solid while keeping the phases spatially separate. We study a sponge filled with water as the first RMI example. We use implicit incompressible porous flow with smoothed particle hydrodynamics as the dynamics engine and enable robotic manipulation by adding Coulomb contact memory, hybrid velocity and force regulation, and a stability gate for lifting. The resulting environment connects robot commands to changes in the coupled liquid and solid state. A world model conditioned on actions predicts how this state evolves under candidate commands, while a temporal UNet generates actions using either Diffusion Policy or rectified flow matching. Our world model reduces retained water prediction error by more than $60\%$ compared with the baseline. The best action sequence selected by the world model from policy proposals further reduces the predicted terminal water error by about half. These improvements show that modelling the coupled liquid and solid state helps the robot predict how its actions affect both the porous object and the liquid held inside.

Humanoid locomotion over complex terrain requires anticipating footholds that may no longer be visible at touchdown. Limited camera coverage and self-occlusion make it necessary to retrieve relevant terrain information from earlier observations. We present FootQuery, a perceptive locomotion framework that queries depth history using each foot's predicted next touchdown. The policy predicts touchdown locations and uncertainty from proprioception and uses these distributions, together with per-foot features, to query sparsely sampled historical depth frames. During training, realized contacts are projected into historical images to supervise retrieval at the regions where those contacts were visible. The retrieved per-foot features are fused with global visual memory to generate control actions. A progressive force-assistance curriculum supports early exploration, while event-consistent tread-midline shaping encourages coordinated stair contacts. Deployment requires only proprioception and onboard depth images. In simulation, the complete framework outperforms its component ablations on the most challenging tested stairs, gaps, and platforms. Real-world experiments on a Unitree G1 demonstrate continuous traversal with a single policy across outdoor stairs and indoor routes combining stair ascent and descent, platforms, and gaps. These results support organizing visual history around anticipated contacts for perceptive humanoid locomotion.

We extend a recent physics-based matrix model for calculating PEM fuel cell impedance (doi:10.1149/2754-2734/ad6ce8) to cases of low air flow stoichiometry and functionally graded cathode catalyst layers (CCLs). We demonstrate that the matrix model produces accurate spectra and is almost three orders of magnitude faster than a model based on the standard boundary-value problem solver. The physics-based matrix model can compete with equivalent circuit models for fitting experimental EIS spectra, particularly those measured from cells with functionally graded CCL.

We prove that the optimal expected mistake bound of online learning a function class $\mathcal{H}$ by a randomized proper learning algorithm is $O(\mathtt{L}(\mathcal{H}) \log T)$, where $\mathtt{L}(\mathcal{H})$ is the Littlestone dimension of $\mathcal{H}$ and $T$ is the time horizon. Our result improves upon the previously best known bound of $O(\mathtt{L}(\mathcal{H}) \log^6 T)$ given by Daskalakis and Golowich (STOC 2022), and is optimal up to a universal constant for worst-case classes.

The interpretation of high-energy nuclear recoil events in direct-detection experiments can depend sensitively on the poorly understood high-speed tail of the Galactic dark matter velocity distribution. This fact has been brought into sharper focus recently by an anomalous nuclear-recoil event at $E_R\approx248~\mathrm{keV}$ observed by the LZ experiment. If interpreted as caused by a dark-matter-induced recoil, kinematic constraints on many models imply this particle would have to emerge from the high-speed tail. Here, we re-assess this astrophysical uncertainty using Milky Way analogues from the IllustrisTNG and FIRE simulations. We find that the maximum laboratory-frame DM speed on June 16, when the event was observed, is $792.7^{+82.9}_{-95.6}\, \mathrm{km/s}$ (median and 95% containment across simulations), with a median very close to the fiducial SHM value. Modelling the tail of the velocity distribution in three dimensions is complicated by the fact that these simulated dark matter halos are anisotropic and are generically seen to spin in the same direction as the baryonic disk. However, we find that this does not reduce the maximum laboratory-frame DM speed because the approximately Gaussian azimuthal velocity distribution is negatively skewed by this co-rotation, rather than shifted by it. We illustrate these results in the context of an inelastic dark matter interpretation of the LZ event.

A central conjecture in the regularity theory of harmonic maps asserts that the singular set of a stationary harmonic map has codimension at least three. In this paper, we construct counterexamples to this folklore conjecture. We construct stationary harmonic maps whose singular sets $S$ satisfies $\dim S=n-2$ and $\mathcal{H}^{n-2}(S)=0$ . The target is a smooth compact manifold diffeomorphic to $\mathbb{S}^2 \times \mathbb{T}^3$, with metric arbitrarily close in $C^\infty$ to the standard product metric.

We consider moving-average iteration for fixed complex matrices and place the theory in the general context of Krasnoselskii and Mann iteration. Necessary and sufficient spectral conditions for the asymptotic stability of moving-average iteration are presented in dependence on the fixed window width. For the corresponding region of stability in the complex plane explicit formulas are derived and it is shown that the region is open, convex and semi-algebraic. The regions are shown to be strictly increasing in the window length and the limiting stability region is determined as the window size tends to infinity.

Cross-border FM spectrum coordination involves protecting foreign broadcasting services while preserving domestic coverage, amid increasingly large radio-planning datasets containing thousands of transmitters and millions of transmitter-pixel relationships. In such scenarios, conventional optimisation approaches become computationally demanding due to the high dimensionality of the associated power-control problem. This paper proposes an interference-driven clustered optimisation framework for large-scale FM spectrum coordination. The proposed method exploits the observation that violations of foreign-service protection are typically dominated by a limited subset of transmitters. Protected services are therefore analysed to identify dominant interferers and quantify their impact on interference. These relationships are represented through an interference graph from which optimisation-oriented transmitter clusters are extracted. The clusters decompose the global power-control problem into smaller optimisation tasks solved with clustered simulated annealing, followed by a global refinement that captures residual inter-cluster interactions. Coverage and interference are evaluated using frequency-dependent protection criteria and a dynamic strongest-service assignment model. To enable operational-scale planning, the framework uses sparse matrices and GPU-accelerated computations. Tests on realistic cross-border FM coordination scenarios show that the clustering strategy greatly reduces optimisation complexity and runtime while maintaining foreign-service protection and domestic coverage. The method also yields an interpretable ranking of transmitters that contribute most to harmful interference, supporting optimisation and spectrum planning.

Synthetic frequency dimensions provide a powerful and highly reconfigurable platform for topological photonics. However, experimentally identifying their topological phases remains challenging because these systems do not naturally provide well-defined boundaries or readily accessible edge-state signatures. Here, we realize a reconfigurable Su-Schrieffer-Heeger (SSH) lattice in a synthetic frequency dimension using an integrated thin-film lithium-niobate photonic molecule and directly measure its topology. Electro-optic coupling between staggered resonator supermodes enables independent control of the effective intra-cell and inter-cell hopping strengths, enabling dynamic switching between trivial and non-trivial topological phases on the same chip. We validate the transition through two independently derived bulk topological invariants: direct retrieval of Zak phase from time-resolved synthetic-dimension band-structure spectroscopy; and extraction of the winding number using mean-chiral-displacement method from site-resolved steady-state measurements. Both approaches consistently identify the topological transition and agree closely with theoretical predictions. Our results demonstrate experimentally accessible, boundary-independent methods for characterizing topology in synthetic-frequency lattices. More broadly, the integrated and dynamically reconfigurable photonic platform provides a scalable framework for bulk topological characterization and programmable topological photonic systems.

People increasingly compete against AI agents, and organisations decide what to tell them about these opponents. We distinguish an opponent effect, specific to the system faced, from an information effect, a property of the disclosure. In a preregistered, deception-free experiment (N = 1,395), we crossed what participants were told about their opponent with whom they faced in a live all-pay auction in which escalation arises from the incentives. Holding the opponent fixed, being told a human was or might be the opponent raised the median price by 6.7% of the prize value, and being told an optimising machine might be lowered it by 8.8%. Facing an AI agent lowered prices and made it rarer that both players finished with positive earnings. Exploratory analyses indicate that the labels changed how often people raised again while already ahead, not how often they responded when behind. Describing an AI competitor is not behaviourally neutral.

We introduce a new model for a system of interacting bosons placed in an array of sites. At its core is a nonlinear, nonlocal evolution equation, which we have dubbed the Schrödinger-Dirichlet equation. The construction is closely related to the Bose-Hubbard model and to a specific type of generalized bosons. In contrast to conventional mean-field closures, the resulting nonlinear dynamics need not preserve product structure and can generate entanglement from initially separable states. The relevant methods of analysis are based on harmonic analysis for the multiplicative group of positive rationals.

We propose LoG-VGGT, a memory-efficient framework for long-sequence 3D reconstruction that balances local temporal modeling with global camera consistency. Instead of relying on full global attention, our method introduces cross-window attention at a small subset of transformer blocks, enabling effective information propagation across adjacent temporal windows while keeping memory usage bounded. To mitigate long-term pose drift, we further design a global camera consistency refinement module, where camera tokens interact with compact register tokens via cross-attention to enforce scene-level constraints across the entire sequence. This design enables joint optimization of camera representations and significantly improves long-horizon pose stability without incurring the high cost of sequence-wide attention. Extensive experiments demonstrate that LoG-VGGT achieves improved depth accuracy and robust camera pose estimation across multiple long-sequence benchmarks, while delivering competitive streaming reconstruction performance.

Silent speech interfaces (SSIs) enable private communication without audible speech and may support people with post-stroke dysarthria. Everyday reuse requires articulation-related representations that generalize across days despite sensor repositioning and physiological changes. We present AESSI, an around-ear SSI using masked-context representation pretraining (MCRP): a student predicts teacher representations from masked time-frequency inputs to encourage robustness to recording variability. We collected 44 electrophysiological recordings from 24 participants for 25 everyday Mandarin sentences. With six participants' complete final recordings held out, AESSI achieved 92.24 percent mean accuracy without test-day calibration. AESSI exceeded the best adapted baseline by 50.57 percentage points. At least 21 days after each participant's last recording, five participants each completed 50 independently randomized online tests without calibration, achieving 98.0 percent overall accuracy. Median preprocessing and inference time in CPU replay was 31.70 ms. These results demonstrate end-to-end system operation and support online reuse without test-day calibration. Demo is included with the paper.

The growing integration of DERs underscores the importance of unified coordination across TSO, DSO, and aggregator levels. This paper proposes a coordination method between TSO, DSOs and DER aggregators, based on a transparent, well-scalable, and decentralized single-loop iterative mechanism with limited information sharing. The approach enables iterative price-based coordination between adjacent levels, where the higher-level entities provide price signals and the lower-level ones respond with desired power schedules. The proposed method uses the proximal-gradient-based iterative co-optimization algorithm extended to a three-level case, which enjoys convergence characteristic of proximal algorithms. The performance of the proposed approach is compared with both a centralized formulation and a sequential reference formulation based on fixed transmission-level energy prices. The results demonstrate that the proposed coordination achieves outcomes very close to those obtained with the centralized formulation, while significantly improving performance relative to the sequential reference, particularly at higher levels of DER flexibility.

Some products are, by nature, designed to operate under stress conditions that repeatedly cycle between two levels, such as batteries undergoing repeated charge and discharge, or components exposed to recurring thermal or pressure cycles. When such products are tested under accelerated conditions, the applied stress is naturally elevated in the same cyclic manner rather than held constant or increased in a single step. Cyclic-stress accelerated life testing (CyALT) reflects this by alternating the applied stress between specified levels. Units are often inspected only at fixed times, so the data consist of interval failure counts rather than exact lifetimes. Hypothesis testing plays a crucial role in this setting. It can assess whether the applied stress significantly affects lifetime, or validate the parameter values used to design the experiment. Classical tests rely on the maximum likelihood estimator, which is highly sensitive to contamination. Since interval probabilities are estimated jointly across stress conditions, a single anomalous failure count can distort the entire parameter vector and severely affect the test's significance level and power. This paper develops Wald-type and Rao-type test statistics for log-normal CyALT lifetimes under interval monitoring, based on the weighted minimum density power divergence estimator. Both tests are derived for simple and composite null hypotheses. A Monte Carlo study shows that classical tests lose control of the significance level rapidly under contamination, while the robust tests stay close to nominal with only a modest loss of power under clean data. An application to air-conditioner evaporator lifetime data further illustrates the proposed tests.