Papers

The waveform is obtained from one balance of energy and radiation on Helmholtz orbits of the retarded mass kernel, with a spherical-Bessel flux. That balance follows from the Dirac–Maxwell equation with a modified vertex, the single $U(1)$ coupling being replaced by the eight operators of the source interaction. After contact that balance is the energy loss of one packet: a bounded well for a black-hole remnant and the Coulomb ladder of one star for a neutron-star remnant. Ringdown starts from the spherical projection of that end state, which contains its spin. The comparisons use model waveforms at the published parameters. For GW250114, at the Coulomb-radius contact and after a shift of $-16\,\mathrm{ms}$, the noise-weighted norm ratio against the NRSur7dq4 median in $100$–$200\,\mathrm{Hz}$ stays between $1.36$ and $1.94$ across the published distance interval. Stopping at $2.4$ times that radius lowers the ratio to $1.11$, which the same interval moves from $0.94$ to $1.35$. With contact placed on the published merger time and with no time shift, that ratio is $3.32$ at the Coulomb radius and $2.30$ at $2.4$ times that radius. At the larger radius, the unretarded limit of this balance, with unit spherical-Bessel weights, reaches contact at $94\,\mathrm{Hz}$, and in $20$–$100\,\mathrm{Hz}$ the norm ratio to the Helmholtz balance is $1.12$ after a shift of $+27\,\mathrm{ms}$. For GW170817, $|h_{+}|$ near $100\,\mathrm{Hz}$ is $8.0\times10^{-23}$, and the mismatch against the $2.5$PN inspiral is a difference in phasing.

We introduce shadow quantum singular value transformation (Shadow QSVT): given an initial state $|{\psi}\rangle$, a Hermitian matrix $H$, a polynomial $f$, and a set of observables $\{O_1,\dots,O_m\}$, the goal is to estimate $\langle{\psi}|f(H)^{\dagger}O_j f(H)|{\psi}\rangle$ for all $j\in\{1,\dots,m\}$. Shadow QSVT provides a systematic route to reduce the quantum resources required by standard QSVT, which constructs a unitary block-encoding of $f(H)$. It uses structure in the input state and observables, together with the fact that many applications require only observable estimates rather than synthesizing the full unitary. We present three algorithms that exploit structure in the initial state and observables to reduce quantum circuit depth. First, we develop a state-aware QSVT algorithm that prepares the target state with low circuit depth when the Krylov subspace associated with $H$ and $|\psi\rangle$ is low-dimensional or admits an accurate low-dimensional approximation. Second, we introduce an observable-aware Shadow QSVT algorithm that combines a new observable-aware Krylov subspace with history states to further reduce circuit depth and gate complexity. Finally, we develop Classical Shadow QSVT, which constructs a classical representation from $H$, $f$, and $|\psi\rangle$ without prior knowledge of the observables or explicit preparation of the target state proportional to $f(H)|\psi\rangle$. This representation enables estimation of the target quantities for observables specified after the quantum computation. Together, these three algorithms provide tools for reducing the circuit depth of QSVT-based computations across a range of settings.

We study photon superradiant scattering by a Kerr black hole in the presence of an axion-photon coupling and investigate how this coupling modifies the electromagnetic amplification factor. We solve the coupled axion and electromagnetic equations in a fully relativistic framework. We distinguish two regimes according to the relation between the sourced axion frequency and the axion mass. In the radiative regime, the axion can propagate to spatial infinity and carry away energy, thereby suppressing photon amplification. In the subthreshold regime, the axion is confined by the mass barrier and exchanges energy with the black-hole horizon through quasibound-state excitations. In this regime, photon amplification can be either enhanced or suppressed, depending on whether the relevant axion modes satisfy the superradiance condition.

We present PrefPI (Preference-Guided Policy Iteration), an iterative framework for steering pretrained generative robot policies using only relative preferences over self-generated trajectories. Unlike prior preference-learning methods that primarily sharpen modes already represented by the policy, we study steering beyond the initial effective support, where desired behaviors are rarely or never observed under the initial policy. Our key idea is to formulate preference learning as preference-conditioned generative modeling: preferred trajectories define a conditional distribution, whose density ratio with the broader behavior prior provides an implicit preference signal amplified by classifier-free guidance (CFG). Repeating this preference-conditioned modeling and guidance step yields a form of preference-guided policy iteration, turning incremental improvements toward previously inaccessible behaviors. Across diffusion policies and the PI0.5 flow- matching VLA in simulation and the real world, PrefPI produces substantial behavioral shifts with limited feedback. In particular, PrefPI increases object transport height from 10.7 cm to 19.8 cm on real hardware with only 150 preference-labeled trajectories.

We determine which representation sectors control the slowest convergence of random Pauli rotations and several local random quantum circuits. For $d=2^n$, the continuous Pauli walk has exact all-representation gaps $$\Delta_{\mathsf{SU}(d)}=\frac{d-8}{8(d-1)}\quad(n\ge4),\qquad \Delta_{\mathsf{PU}(d)}=\frac{d(d-3)}{8(d^2-1)}\quad(n\ge3).$$ The special-unitary gap is attained in $\bigwedge^8\mathbb{C}^d$ and is invisible to balanced moments, while the projective gap is already attained in a balanced fourth-moment representation. We obtain exact discrete and orthogonal Pauli analogues, exact finite-Clifford chain/path gaps, and dimension-independent all-representation Haar brickwork lower bounds; on three qubits every weighted Haar-$\mathsf{SU}(4)$ edge walk reduces to one universal principal-angle constant. For real complete-graph models, the entire ordinary fourth-tensor gap reduces to a quadratic-size occupation operator, is simple for every $n\ge4$, and has an expansion beginning $$\Delta_n^{(4)}=\frac{10}{9n}-\frac{88}{105n^2}+O(n^{-3}),$$ with competing branches separated only beyond all algebraic orders. For the two finite real Clifford complete-graph walks, this fourth-tensor mode is the exact all-representation group gap for every $n\ge144$; in the same range it simultaneously governs every ordinary even tensor degree $k\ge4$. Thus different representation scopes can have genuinely different slow modes.

We prove local well-posedness in the Hadamard sense for the three-dimensional compressible Euler equations governing a liquid with a free surface and no surface tension. Under the Taylor sign condition and the boundary compatibility conditions, we establish existence, uniqueness, and strong continuous dependence in a hybrid Sobolev class for every $s>3$. The velocity and interface have $H^s$ regularity, while the enthalpy and velocity divergence belong to $H^{s+1/2}$ and $H^{s-1/2}$, respectively. This separation reflects the coupling of a nondegenerate acoustic equation with the free-surface and vorticity dynamics. The proof uses regularization operators that smooth the moving domain and extend the nonlinear compatibility hierarchy, together with $L^2$ and partial $H^2$ distance estimates for solutions on different domains. Regular solutions are constructed by a regularized forward Euler scheme. High-order energy estimates and frequency envelopes then yield strong convergence of smooth approximations and continuity of the data-to-solution map. Integer Sobolev indices are treated using a Lions–Magenes endpoint compatibility condition.

We study both the classical and the quantum complexity of the problem of estimating disorder-averaged quench dynamics for all-to-all spin Hamiltonians such as quantum Hopfield, Sherrington–Kirkpatrick (SK) or Dicke-type models. Disorder averaging restores permutation invariance in this setting, so states of $N$ spins can be stored in $\mathcal O(\log N)$ qubits. While logarithmic-space quantum computations are known to be simulatable classically in polynomial time or in polylogarithmic space, whether a single algorithm can achieve both is open, raising the possibility of simultaneous quantum advantage. To this end, we give a quantum algorithm for permutation-invariant $k$-local dynamics without disorder using polynomial time and $\mathcal O(\log N)$ quantum and classical space. We show that any classical algorithm matching these resources would imply $\mathsf{BQL}\subseteq \mathsf{SC}$. For short times, however, we provide such algorithms, including for SK models. For Hopfield models, we discuss how dilating the disorder to ancilla qubits reduces the problem to the disorder-free case on an enlarged system, thus extending both classical and quantum results to them. We give some evidence that their long-time dynamics are non-trivial. They thus emerge as a candidate for a simultaneous time–space advantage in quantum simulation.

Hong Wang has made several tremendous contributions to harmonic analysis and geometric measure theory. On the 23rd of July 2026, she was awarded the Fields Medal. In this short article we shall focus on her work on the Kakeya problem and other problems related to the Fourier transform. We will try to put her work in historical context and present a small selection of her contributions to harmonic analysis.

Galaxies build through infalling gas and galaxy mergers. Tracking the dynamical history of a galaxy from a single snapshot in time is notoriously difficult. We show that the dynamical history of a galaxy can be tracked using oxygen abundances as archeological tracers. We derive the gas-phase oxygen abundances for 4546 spaxels across the face-on spiral galaxy NGC~1365 at a spatial resolution of 175 pc, providing one of the most detailed chemical fossil records of a spiral galaxy outside our Milky Way. We apply IllustrisTNG cosmological simulations to analyse the chemical abundance distribution in a theoretical model for NGC~1365. In the model, the main disk oxygen abundance gradient formed earliest, 11.9-12.5 billion years ago via mergers with multiple dwarf galaxies. A steep inner bar gradient formed slowly over the last 12 billion years through enrichment from star formation triggered by the infall of gas into the nuclear regions. An extended ionized gas disk with flat oxygen abundances was assembled more recently (5.9-8.6 billion years ago) through a minor merger. This work indicates that cosmological simulations and ultra-high spatial resolution oxygen abundances together can provide an archaeological probe of the star formation and merger histories of spiral galaxies.

Sparse triangular solve (SpTRSV) is a fundamental kernel in numerous scientific and engineering applications. However, the data dependencies inherent in sparse triangular matrices significantly limit the available parallelism and make efficient workload distribution challenging. Recent graph transformation techniques address these limitations by modifying the dependency graph of the input matrix to improve parallel execution. Existing graph transformation strategies, however, rely on manually designed heuristics, making their development and adaptation to different optimization objectives challenging. This work proposes a reinforcement learning-guided graph transformation framework for SpTRSV, in which graph transformation is formulated as a sequential decision-making problem and an RL agent learns matrix-dependent transformation policies. Experimental results on real-world sparse matrices demonstrate level reductions of up to 94% and reductions of up to 80% in the coefficient of variation of level costs, while modifying only 1.50% of the rows in the highest case. On average, the RL- guided graph transformation achieves a 23% reduction in the number of levels and a 29% reduction in the coefficient of variation of level costs while rewriting only 0.82% of the matrix rows. Although the heuristic strategies generally achieve more aggressive level reduction(between 31% and 46%), the RL-based approach achieves the largest average reduction in the coefficient of variation of level costs, demonstrating its ability to balance competing graph transformation objectives. The results further show that the learned policies can be transferred to previously unseen matrices through curriculum learning and fine-tuning, while zero-shot experiments provide insights into the limitations of generalizing graph transformation policies across different sparsity patterns.

We focus on legible robot motion generation in social navigation settings. Legibility in human-robot interaction (HRI) is often described as the property of robot motion that enables an observer to confidently infer the robot's intent. While mature frameworks exist for generating legible motion in front of static observers, social robot navigation presents a new challenge: the robot must clearly convey its intent while ensuring human safety in dynamic pedestrian environments where human attention is often divided. With the goal of enabling robots to generate legible motion in dynamic and constrained spaces, we investigate how the choice of representation and the level of human attention shape navigation performance and human impressions. Focusing on the ubiquitous and demanding scenario of hallway navigation, we conduct two controlled user studies involving alternative legibility formulations implemented within a shared model predictive control framework. Study 1 (N = 45) investigates the role of intent representation, showing that passing-side legibility, particularly when adaptively updated, leads to smoother human motion and is perceived as more competent and less mentally and physically demanding than destination-based and non-legible baselines. Study 2 (N = 45) examines the effect of pedestrian attention, demonstrating that legible motion allows for smooth human motion even under distraction, even if this is not consistently reflected in subjective ratings. Together, these findings suggest that effective legible motion in social robot navigation benefits from interaction-level intent representations that support coordination, with some effects persisting even when human attention is divided. Code is available at https://github.com/fluentrobotics/Legible_MPPI.

The Wind Farm Layout Optimization problem consists of placing a given number of turbines within a given area so as to maximize energy production. One of its main challenges is the wake effect between turbines, which can strongly affect production and is a cumbersome function to evaluate and to embed in an optimization framework. In this paper we introduce a new endogenous wake model (EndoWake), based on the idea of treating the wind speed at every grid point as a decision variable, linked to its upwind neighbors through linear propagation constraints. This makes it possible to incorporate the wake equations directly into a Mixed-Integer Linear Programming (MILP) model. We then develop such a MILP model and, in particular, introduce a new class of valid "band" inequalities, showing that they substantially strengthen the root bound. Building on this, we design a branch-and-check scheme: the master problem retains only the site variables together with one hypograph variable per cell and scenario, integer solutions are evaluated by an exact linear-time oracle, and the optimality cuts are problem-specific "upwind cuts". Computational results are reported on a ladder of square grids under a four-sector axial wind rose, demonstrating the effectiveness of the proposed improvements.

In many statistical settings, the available data and maintained assumptions do not suffice to uniquely identify the model parameters of interest. In such cases, one can only identify sets which are guaranteed to contain the true parameters. These are often characterized through linear programs that optimize over models compatible with the observed data. These programs can be infinite-dimensional in the optimizer and the number of constraints. We provide a unified way to characterize and solve such optimization problems by phrasing them as optimal transport problems on path spaces. This allows us to regularize the problem with an entropy penalty, recasting it as a multi-marginal entropic optimal transport problem, which can be solved efficiently via Sinkhorn iterations. In addition, it allows us to establish convergence of the regularized value to the sharpest bound, derive consistency rates for a plug-in estimator, and obtain asymptotic distribution for approximate bounds. The method is general and accommodates settings ranging from instrumental variable models with continuous variables to welfare estimation in heterogeneous demand models. We verify the statistical and computational properties in simulations and provide an application to demand estimation.

We study the finite basis problem for flat semirings of the forms \(S_c(W)\), \(M_c(W)\), and \(M(W)\), where \(W\) is a nonempty set of words in a free commutative semigroup, a free commutative monoid, and a free monoid, respectively. We completely classify such flat semirings with respect to the finite basis property, allowing \(W\) to be infinite. We prove that \(S_c(W)\) is finitely based if and only if every word in \(W\) is either a cube of a letter or has length at most two, whereas \(M_c(W)\) and \(M(W)\) are finitely based if and only if \(W\) consists solely of the empty word. As applications, we recover the nonfinite basability of \(\flat(\mathbb{Z})\) and the max-plus semiring \((\mathbb{Z},\max,+)\).

We introduce the quantum Černý complexity $\mathrm{qc}(w)$ of a binary word $w$: the least dimension $d$ for which there exist quantum channels $A_0,A_1$ on $d\times d$ density matrices and a start state $\rho_0$ such that $w$ is the unique shortest word whose associated channel is constant on the reachable set. We show that $2\le\mathrm{qc}(w)\le\lceil\sqrt{|w|+1}\,\rceil$ for every nonempty $w$, a quadratic saving over the classical analogue, and that constant words are extremal: $\mathrm{qc}(0^m)=\lceil\sqrt{m+1}\,\rceil$. In contrast, $\mathrm{qc}(01^n0)=2$ for every $n\ge 1$, realized by a single qubit whose rotation angle acts as a counter; consequently there is no quantum analogue of the Černý function, and $\mathrm{qc}$ is strongly anti-correlated with intuitive notions of descriptive complexity. We further study the variant $\mathrm{qcp}$ in which the synchronization target is required to be a pure state. We prove that in dimension $2$ no word of length at least $2$ can be a unique shortest synchronizing word with pure target, and we exhibit an explicit qutrit instance, combining a coherent rotation with a measure-and-funnel channel, achieving $\mathrm{qcp}(01^n0)=3$ with target a computational basis state and with synchronization holding universally over all input states. Thus purity of the reset state costs exactly one dimension on this family. We also observe that $\mathrm{qc}$ is computable, by reduction to the first-order theory of the reals.

Video generation models (VGMs) offer strong spatiotemporal priors for embodied observation–action modeling. However, joint-space action vectors lack explicit image-space structure and vary in dimensionality and semantics across embodiments, making it challenging to directly leverage the rich spatiotemporal priors of VGMs. End-effector visualizations provide an alternative but do not specify the full articulated configuration needed for robot execution. We present Dream4ACT, a world model built for joint video-action modeling across embodiments. To unify action representations across embodiments, we introduce a shared visual action interface, called action views, which render target joint configurations from four prescribed virtual cameras using URDF-based forward kinematics. This shared visual representation preserves embodiment-specific articulated geometry while allowing observation and action sequences to share a video autoencoder and diffusion transformer. Through masked flow-matching, our model supports forward dynamics, inverse dynamics, and joint observation–action generation within a single jointly trained model by varying which future sequences are corrupted. To recover executable action sequences from predicted action views, we propose a training-free, URDF-constrained multiview recovery mechanism, without a learned embodiment-specific decoder. Dream4ACT achieves an average success rate of 88.98% on RoboTwin~2.0 and an overall score of 65.66 on TriWorldBench, supporting effective closed-loop manipulation and competitive action-conditioned multiview prediction through the visual action interface.

In this paper, we present a modular proportional-integral-derivative (PID) controller whose computation and mode logic are executed by a higher-level state machine. Inspired by real-time safety-critical applications where computational load, actuator chattering, sensing error and noise are design challenges, the proposed algorithm wraps a standard PID inside a finite state machine with three states (pidInit, ErrorOutRange, ErrorInRange). The goal is to regulate a desired reference within a safe region of operation while reducing actuator chattering and creating a sizable hold band over the range of operation. This design is modular and can be easily integrated into a higher-level state machine with multiple low-level loops and states. The algorithm also has low computational complexity and is suitable for embedded hardware deployment. We demonstrate the effectiveness of the algorithm in simulation on the two test benches of a published event-based PID benchmark. The algorithm computes the control updates significantly less often than the time-triggered PID and less often than both dominant event-driven controllers, while keeping a fairly equivalent control performance profile. Furthermore, we also present some experimental results of the designed algorithm for a real-time flow control.

Dengue virus (DENV) is an enveloped flavivirus of major public health importance. Its envelope (E) protein mediates viral entry through homodimer dissociation and subsequent membrane fusion, making it one of the principal targets for antiviral strategies. To investigate the molecular determinants of this process, we performed steered molecular dynamics (SMD) simulations of the E protein ectodomain (ecE) dimer from DENV-2 and DENV-3 under variable pH and temperature conditions. Force-extension analyses revealed a highly stable interface for both serotypes, with rupture forces exceeding 1000 pN. pH and temperature had modest effects on overall mechanical resistance. However, DENV-3 displayed a distinct sensitivity to thermal stress compared to DENV-2. We identified a robust, asymmetric dissociation pathway across all conditions, characterized by a metastable intermediate state involving partial dimer opening and exposure of the fusion loop (FL). This intermediate exposes an immunodominant epitope and persists under physiological conditions, suggesting it as a viable target for therapeutic intervention. The primary contributions to the interfacial interaction network were found to arise from van der Waals interactions, followed by hydrogen bonds, salt bridges, and pi-cation interactions. DENV-3 exhibited a slightly greater contribution from polar interactions involving domains EDI, EDII, and EDIII. Furthermore, pairwise occupancy analysis identified pH-sensitive contacts that are disrupted under acidic conditions, particularly in DENV-3, providing mechanistic insight into the early stages of ecE dissociation. Together, these findings provide structural insights into the dissociation mechanism, identifying key metastable states and pH-sensitive interactions that could be exploited to develop antivirals that stabilize the dimer and prevent viral fusion.

We describe adapol, a Python package for fitting Matsubara Green's functions, self-energies, and hybridization functions by a compact sum of simple poles with real pole locations and matrix-valued residues. This pole-fitting step arises in many contexts, including hybridization fitting for quantum impurity solvers based on exact diagonalization, perturbation theory, and tensor networks, the compression of existing pole expansions such as the discrete Lehmann representation, diagrammatic methods based on discrete pole representations, and the analytic continuation of Matsubara Green's functions. adapol uses a modified version of the AAA rational approximation algorithm to estimate pole locations, and non-convex optimization to refine them. This procedure yields accurate and compact fits in a black-box and noise-robust manner. adapol provides a simple, self-contained interface with extensive documentation and examples, as well as an interface to the TRIQS package.

Policy regularization in offline reinforcement learning balances policy improvement against reliance on uncertain value estimates. This balance can differ between selecting actions for execution and supplying actions for critic bootstrapping, yet methods such as TD3+BC couple these roles through a shared policy. We propose Role-Adaptive Policy Optimization (RAPO), which adapts policy-update coefficients according to their roles in value learning and execution. RAPO learns these coefficients by differentiating through candidate policy updates formed using the base algorithm's actor objective. For TD3+BC, RAPO separates bootstrap and execution actors and adapts their coefficients independently: the bootstrap objective penalizes policy-induced changes in target values, while the execution objective evaluates a local policy-improvement surrogate. For IQL, whose value learning is already independent of the execution actor, RAPO preserves the original value updates and adapts only the inverse temperature in advantage-weighted policy extraction. Experiments on D4RL locomotion and AntMaze tasks show improvements over both base algorithms, with larger gains for TD3+BC, whose RAPO instantiation outperforms baselines on average.

Power-law learning curves are often treated as fixed properties of a model and its data, although learning-rate and batch-size schedules can change the observed loss. We study this dependence in noisy online SGD with linear random features. Conditional on the representation, an exact Volterra equation separates two response components: a forcing term that propagates unresolved target error and a memory kernel that propagates stochastic-error injections. We prove that either component follows a power law if and only if its cumulative weighted spectral mass has the corresponding low-spectrum scaling; individual eigenvalues and target coefficients need not obey coordinatewise power laws. Under a joint schedule, intrinsic time $T_t=\sum_{s<t}\eta_s$ controls optimization progress, while $r_t=B_t/\eta_t$ controls noise injection. Their interaction yields sharp conditions under which a schedule preserves, changes, or destroys the clean power law, together with a memory ceiling on noise reduction. The power-law random-feature model realizes this mechanism in $3+3(+2)$ propagation regimes with phase-dependent compute rates. Controlled nanoGPT experiments show that (1) learning-rate and batch-size schedules with matched $B/\eta$ paths are nearly equivalent in intrinsic time, (2) a forcing-memory surrogate accurately predicts loss across schedules, and (3) its fitted exponents across real-world datasets identify the regime of LLMs in $3+3(+2)$ map. The source code for reproducing our experiments is available on https://github.com/yichenblue/spectra-to-schedules-in-pretraining.

We establish exponential iteration lower bounds in the number of states for Howard's policy iteration on deterministic discounted and average-reward Markov decision processes (MDPs), with a constant number of actions per state. This rules out strong polynomiality of Howard's policy iteration in both settings. We further prove that a Dantzig counterpart of Howard's policy iteration runs in strongly polynomial time on deterministic average-reward MDPs. Together with the known strongly polynomial bound for Dantzig's rule on deterministic discounted MDPs, these results establish an exponential separation between the two algorithms in both settings. This separation between Howard's decentralized and simultaneous selfish improvements and Dantzig's coordinated selection of a single action with the largest improvement across all states reveals a “price” of algorithmic anarchy.

As LLMs grow in size, compression becomes increasingly important for efficient deployment. SVD-based low-rank compression reduces parameter counts but can degrade downstream performance. To improve performance after compression, we introduce QuLoC, a photonic quantum-assisted LLM compression algorithm that uses quantum circuit outputs to gate the retained low-rank components during training. Model performance is recovered through local functional reconstruction followed by end-to-end knowledge distillation. After training, the gating coefficients are absorbed into the low-rank factors, allowing the compressed model to run on classical hardware without executing quantum circuits during inference. Experiments on Qwen3.5-4B show that QuLoC achieves a 9.73% relative improvement in average accuracy over state-of-the-art baselines across multiple downstream tasks, demonstrating its effectiveness. We further evaluate QuLoC on LLaMA-7B at different parameter compression ratios. It achieves comparable or higher average downstream accuracy than state-of-the-art baselines, supporting its applicability to a larger model across different compression settings. These results motivate further exploration of photonic quantum-assisted compression for larger models and more complex agentic tasks.

We consider the functional $I_{\delta,\Psi_1,\Psi_2}:X \to \mathbb{R}$ defined for any $z=(u,v) \in X$ as \begin{align*} I_{\delta,\Psi_1,\Psi_2}(z) & = \int_{\Omega} \Psi_1(\nabla u) \, dx + \int_{\Omega} \Psi_2(\nabla v ) \, dx & - \int_{\Omega} H(\delta,x,u(x),v(x)) \,dx, \end{align*} where $\Omega$ is a smooth bounded domain of $\mathbb{R}^N$, $\Psi_1, \Psi_2: \mathbb{R}^N \to \mathbb{R}$ are convex functions satisfying suitable conditions for $1 < p, q < N$, and the nonlinearity $H$ is allowed to exhibit both subcritical and critical growth and may depend on a parameter $\delta \in I \subseteq \mathbb{R}$. Here, the functional space setting is given by the product space $X :=W_0^{1,p}(\Omega)\times W_0^{1,q}(\Omega)$ equipped with the norm $\|z\|= \|u\|_{1,p} + \|v\|_{1,q}$ for any $z=(u,v)\in X$, where $\| \cdot \|_{1,s}$ is the usual norm in $W^{1,s}_0(\Omega)$. In this paper we prove that $I_{\delta,\Psi_1,\Psi_2}'$ is of class $(S)_+$ and we infer that each isolated critical point of $I_{\delta,\Psi_1,\Psi_2}$ has critical groups of finite type and a Poincaré-Hopf formula holds.

Additional qubits can reduce the depth of a quantum circuit by providing workspace for parallel computation, but standard constructions assume that this workspace is initialized in a known state. In this work we study catalytic implementations, i.e. asking whether dirty qubits can instead be used provided that their joint state including any entanglement with other registers is restored exactly at the end of the computation. We show that every $n$-qubit Clifford circuit has a catalytic implementation of depth $O(\log n)$ using $O(n^2/\log^2 n)$ catalytic qubits and no clean qubits, matching the asymptotic depth achievable when clean workspace is available. We extend this approach to diagonal elements of any fixed level $C_k$ of the Clifford hierarchy, which admit catalytic implementations of depth $O(\log(n+1))$ with $O(n^k/\log(n))$ gates and $O(n^k/\log^2(n))$ catalytic qubits, as well as to semi-Clifford Gates.

Compact regulatory DNA can free up space in vector payloads, reduce synthesis and assay burden, and expose which sequence features drive predicted activity. Yet most model-based nucleic-acid designers optimize fixed-length sequences through substitutions; they do not ask which bases of an existing functional element can be removed while retaining predicted activity. We define the task of sequence slimming as selecting an exact-length, order-preserving subsequence while retaining activity. Modeled on the design benchmark NucleoBench, we propose a quantitative evaluation for slimming that balances sequence reduction with maintaining function. Each slimmer must return both the subsequence and its source indices, which can be used to verify that the slimmer obeyed task requirements. To our knowledge, this is the first dedicated benchmark of this deletion-only problem. The coding agent Empirical Research Assistant (ERA) then searched over executable designer programs. ERA received the task prompt and a successful substitution-only designer GrAdaBeam as a starting program, and it modified the designer to produce GRADASLIM. We report held-out evaluations for five transcription-factor binding targets, comparing random, greedy, and ERA-guided slimming at 400 and 100 bp. ERA has the highest mean in 9/10 settings. Paired bootstrap intervals for ERA minus greedy are above zero in all five 400-bp settings, below zero in one 100-bp setting, and overlap zero in the remaining four.

In this article, we explore how transport at a solid–electrolyte interface is affected by the internal fluctuations of the solid and quantify the role of solid excitations on ionic friction. Combining molecular dynamics simulations with theoretical modeling, we show that the presence of ions enhances the dynamical response of the electrolyte compared to pure water. This leads to an ionic contribution to the fluctuation-induced interfacial friction. We show that collective ionic modes dominate the dissipation, such that ionic friction arises from many-body effects rather than from individual drag forces. Furthermore, high-frequency molecular modes are found to be ion-specific, suggesting possible routes toward spectral separation of ions, with implications for desalination, filtration, and energy conversion.

Deriving a safe upper bound on the worst-case execution time (WCET) of a real-time task is essential for hard real-time systems. Many WCET analysers exist, but they are either (i) closed source or (ii) do not provide a WCET for an existing microcontroller. Hence, it is difficult to obtain a trustworthy WCET bound for the binary that is flashed to an available embedded hardware platform and to observe whether the bound is safe. To solve this, we present LLTA, an open-source WCET analyser for Commercial-Off-The-Shelf (COTS) microcontrollers. LLTA is designed based on the following goals: it is simple (G1), runs on real COTS hardware (G2), reports results that are unsound due to programming or device constraints (G3), and is available open-source without licensing complications (G4). LLTA generates WCETs for the ESP32-C6 and the MSP430(FR5994), which are broadly available. This paper systematically lays out our design decisions for LLTA with those goals in mind. To demonstrate its ease of use, we propose scenarios where LLTA can be used for lab exercises of real-time systems.

Extreme heat is where urban adaptation needs kilometer-scale data the most, but the simulations training a downscaler can cost more than they save, and how much is needed has not been identified. We measured it with CASPER, a U-Net with a structure-preserving loss downscaling 32 km reanalysis to 1 km temperature, humidity and wind, across 24 configurations of one to eight months. Held-out error grows linearly with climatological distance to the training data, RMSE = 0.83 + 2.95 d, explaining 90% of its variance against 7% for volume and predicting unseen months in advance. On held-out extreme summer weeks CASPER preserves the fine-scale structure and cross-variable physics that matched-budget baselines degrade, and matches station observations during documented heat waves to within 1.8 K. Transfer to a new region degrades geographically; 11 days of local simulation cuts Vancouver's held-out error from 3.8 to 1.3 K. Training periods should span the target climate: the same accuracy for four times less simulation, putting kilometer-scale downscaling of extreme heat within reach of groups without large computing facilities.

The emergence of high-$T_c$ superconductivity in pressurized La$_3$Ni$_2$O$_7$ is intimately linked to a structural transition that suppresses the tilts of the NiO$_6$ octahedra, yet its impact on the electronic structure remains poorly understood. Here, we probe the electronic response across this tilt-free transition at $T_{st}\simeq 544$ K using broadband infrared-to-visible reflectivity at ambient pressure, covering photon energies from 15 meV to 3.2 eV. We observe a pronounced redistribution of spectral weight over an exceptionally broad energy range, with spectral weight transferred from excitations between 1 and 3 eV toward low-energy excitations below 1 eV. Most strikingly, two low-energy interband excitations progressively converge and merge upon entering the tilt-free phase, revealing a substantial reconstruction of the finite-energy electronic structure. These changes point to a reconstruction of the bilayer Ni $3d_{z^2}$-derived electronic states, whose interlayer coupling is central to proposed mechanisms of superconductivity in La$_3$Ni$_2$O$_7$. Our results establish the tilt-free transition as a direct route to reorganizing the electronic degrees of freedom implicated in high-$T_c$ superconductivity and provide an ambient-pressure reference for the electronic structure of the superconducting state.