Papers

Vision-Language-Action (VLA) policies commonly run Vision-Language Model (VLM) backbones with billions of parameters at every policy inference, which costs latency and energy. We revisit a decoupled alternative for multi-task manipulation: separate vision and language encoders whose representations condition a compact action head. We run a standardized comparison that varies the vision encoder, the language encoder, and the action head while holding the demonstrations, the training-step budget, the tasks, the evaluation protocol, and the measurement platform fixed, against seven VLA baselines. The resulting Decoupled Embodiment Model (DEM) combines a fine-tuned DINOv3 vision encoder, a frozen NeoBERT language encoder, and a MeanFlow head that generates an action chunk in one forward pass. On 18 RoboCasa tasks evaluated with held-out instruction paraphrases and randomized scenes, DEM reaches 55.6% mean success against 56.9% for GR00T N1.7 and 54.6% for $\pi_{0.5}$, and on three real-robot tasks it reaches 66.0% against 68.0% for GR00T N1.7. On the same workstation, DEM needs 6.1\,ms per policy forward pass, a maximum throughput of 162.7 policy calls per second, and draws an estimated 2.07\,J of GPU energy per call, eight to seventeen times the throughput and six to fifteen times less energy than these VLM-backbone policies. Within this trained-task regime, DEM sits on the observed success–latency–energy frontier and provides a strong, efficient baseline for language-conditioned robot skills.

The forward-reflected-backward splitting of Malitsky and Tam converges weakly for step sizes $\lambda\in(0,\tfrac{1}{2L})$, where $B$ is monotone and $L$-Lipschitz, and the question whether this bound is tight has been recorded as open \cite{GS}. We show that it is: for the matched-skew instance $A=LJ$, $B=LJ$ ($J$ the counterclockwise rotation by $\pi/2$ in $\R^2$), the iterates fail to converge for every $\lambda\ge\tfrac{1}{2L}$ and diverge for $\lambda>\tfrac{1}{2L}$. More generally, for the skew–rotation family $A=\gamma J$, $B=J$, the exact stability threshold is $\lambda^\star(\gamma)=1/\sqrt{(1+\gamma)(3-\gamma)}$, which attains its minimum $1/2$ at the matched skew $\gamma=1$ and recovers the reflected gradient constant $1/\sqrt3$ at $\gamma=0$. The same instance is a counterexample for the reflected–forward–backward method of Cevher and Vũ, which coincides with forward-reflected-backward on linear operators.

Mapping sequencing reads to a reference genome requires preprocessing and alignment choices that can vary with library type, fragment length, sequencing platform, and reference genome. These considerations are particularly important for ancient and historical DNA, where short and damaged fragments can make the most appropriate mapping strategy difficult to determine a priori. We present PlainMap, a lightweight and restartable mapping pipeline for modern and degraded DNA sequencing data. PlainMap accepts a simple manifest of FASTQ files, automatically identifies single-end and paired-end data from read headers, supports mixed sequencing platforms, and provides alternative mapping strategies for modern and degraded DNA. Deterministic chunking and checkpoint-based execution allow large analyses to resume after interruption, while optional pilot subsampling enables empirical comparison of mapping strategies using identical subsets of raw fragments. PlainMap produces duplicate-filtered BAM files together with fragment-aware mapping and coverage statistics. Evaluation using heterogeneous sequencing data confirmed the expected behaviour of the three mapping modes, while adaptive chunking reduced peak memory use by approximately 25% and allowed an interrupted analysis to resume from completed mapping chunks. PlainMap is implemented as a single Bash script and is freely available at https://github.com/BiodiversityExtinction/PlainMap.

For various reasons, higher-order objects are often studied in mathematical logic via second-order `codes' or `representations'. An important example hailing from real analysis and topology is provided by open sets, which are represented by unions $\cup_{n\in \mathbb{N}}I_{n}$ where each $I_{n}$ is a basic open interval. Now, Montalbán has recently highlighted the importance of robustness of logical systems in Reverse Mathematics (abbreviated RM). It is then a natural RM-question whether basic properties of open sets are robust under slight modifications of the coding of open sets. Here, we study the representation where $I_{n}$ as above is either an open interval or the union of two such intervals but we cannot decide which one. Under this slight variation of the usual coding, basic properties of open and closed sets readily imply the relatively strong system ATR$_{0}$ from RM. Moreover, we obtain equivalences for the former properties and the enumeration principle. The latter states that countable sets can be enumerated and boasts many equivalences from Fourier analysis. Along the way, we investigate the RM-properties of the closure, interior, and boundary of sets of reals, a study interesting in its own right.

We investigate the existence of a one-bubble solution with maximum points escaping to infinity for the energy-critical heat equation in dimension five. The key point of the construction is a refined inner linear theory as in \cite[Section 8]{Wei-Zhang-Zhou2022LLG}.

Let $d>1$ be fixed and let $A_n$ be an $n\times n$ matrix with independent $\Ber(d/n)$ entries. For every $0<r<\sqrt d$, we prove that, with high probability, a positive proportion of the eigenvalues of $A_n$ have modulus larger than $r$. Together with the known upper bound, this implies that the modulus of the second largest eigenvalue converges in probability to $\sqrt d$. Our proof works with the Brown measure $\mu_d$ of the adjacency operator of the directed Poisson–Galton–Watson tree. The convergence theorem of Sah, Sahasrabudhe, and Sawhney, together with the Brown-measure identification following it, gives weak convergence of the empirical spectral measure of $A_n$ to $\mu_d$ in probability. We prove that the outer radius of its support is $\sqrt d$, using a resolvent recursion on Poisson–Galton–Watson trees.

Classical CSI feedback in FDD massive MIMO transmits a compressed reconstruction of the channel, optimizing fidelity to the original signal regardless of the downstream task. We propose a semantic communication perspective: instead of reconstructing the channel, the UE transmits a learned semantic embedding optimized end-to-end for beam selection at the gNB. Comparing reconstruction-oriented feedback (CsiNet) against task-aware semantic feedback across two input domains and three observation scenarios, we show that a semantic embedding of just $d=8$ real values from only 43 NR CSI-RS pilots in the angular-delay domain achieves the highest beam prediction accuracy, outperforming every method with access to the full 512-subcarrier channel. The key insight is that beam-relevant information is intrinsically low-dimensional: the semantic encoder learns to discard reconstruction-irrelevant structure and retain only a compact representation that is relevant to beam selection, realizing the core principle of semantic communication: transmit the intent, not the signal.

We study the minimum adjacency spectral radius in the class $\mathcal{SC}_{m+2}(m)$ of strongly connected digraphs with $m$ vertices and $m+2$ edges. Using generating functions for directed paths, we associate with the relevant digraphs topological polynomials whose smallest positive roots determine the corresponding spectral radii. Based on an ear decomposition, we obtain a complete structural classification of $\mathcal{SC}_{m+2}(m)$ by showing that every digraph in this class can be obtained from a butterfly digraph by attaching a single ear. This reduces the extremal problem to the optimization and comparison of finitely many polynomial families subject to their realizability conditions. We prove that the minimum spectral radius is determined by the polynomial $P_{\min}(z)=1-2z^{m-1}-z^m$. If $R_m\in(0,1)$ denotes its unique root, then $\min_{G\in\mathcal{SC}_{m+2}(m)}\rho(G)=R_m^{-1}$. For $m\geq4$, the minimum is attained, up to isomorphism, uniquely by the cross-chorded cycle $\mathcal{C}_m^\times$. For $m=3$, there are exactly two non-isomorphic minimizers, both with spectral radius $(1+\sqrt5)/2$. Finally, we establish the bounds $2^{1/(m-1)}<\rho\left(\mathcal{C}_m^\times\right)<3^{1/(m-1)}$.

Reliable agent evaluation is complicated by automatic harness optimization, which repeatedly uses a released benchmark $B_{\mathrm{rel}}$ to guide a Proposer that edits prompts, memory, retrieval, tools, and control code around a fixed foundation model. Task holdout is commonly used to guard against harness overfitting. It varies semantic tasks but leaves the benchmark protocol fixed, so a bad genius Proposer can produce a cheating harness whose improvement over the initial harness on $B_{\mathrm{rel}}$ depends on a benchmark-wide shortcut. We introduce Counterfactual Harness Search and Evolution (CHASE), which casts harness evolution as constraint generation over valid counterfactual benchmarks. After each Proposer update, a Challenger searches for an executable protocol transformation with large gain destruction. A validity firewall checks that task semantics are preserved, while a held-out confirmation set determines whether the counterfactual enters a finite archive. We formalize an ideal shortcut-neutralized benchmark $B_0$ and establish theoretical guarantees linking finite counterfactual archives to $B_0$ and characterizing sequential Challenger search. We evaluate CHASE on Syn-Ledger and OfficeQA, where CHASE retains strong released-benchmark gains while substantially reducing gain destruction under valid protocol transformations.

We present a comprehensive ab-initio study of the elastic properties of the IV-period transition metal nitrides, highlighting the correlation between their mechanical behavior and electronic structure. By analyzing the electronic density of states, we reveal how the occupation of bonding or antibonding orbitals determines the evolution of elastic properties along the period. Furthermore, we examine trends across different crystal structures, specifically comparing rocksalt, zincblende and wurtzite phases, to uncover how variations in crystal symmetry and atomic coordination influence their elastic properties.

Mechanical memristors are systems whose dissipative response depends on the history of previous loading through an evolving internal state. History-dependent forces and dissipation occur in a wide range of materials and devices, including viscoelastic polymers, shape-memory materials, piezoelectrics, granular media and field-responsive fluids. Determining which of these responses admits a mechanical-memristor representation requires a constitutive test, as well as a comparison of scales. In this work, a fractional-order mechanical memristor model is developed and cast into a nondimensional form to identify the governing parameters controlling memory-dependent dissipation. The formulation leads to a set of dimensionless groups that characterise dissipation magnitude, memory-state scale and memory transfer. These quantities are combined into an effective mechanical memristance screening index \(\Mh = \beta\gamma |\mathcal H_\alpha(\Omega)|\), which provides a conditional measure of local damping modulation at matched response amplitude, constitutive slope and reference scales. Illustrative parameter scenarios are then constructed for material classes including shape-memory polymers, shape-memory alloys, hydrogels, nanocellulose, lignin-rich materials, natural fibres, piezoelectric polymers, piezoelectric ceramics, electrorheological fluids, magnetorheological fluids and granular dampers. The framework establishes a common basis for comparing memory-dependent damping within the adopted constitutive description and identifies the calibration required for its application to candidate materials and devices

Online multi camera 3D tracking must maintain scene global identities across synchronized views, yet query-based trackers carry these identities only implicitly in the instance bank, where they fragment upon query interruption. We present an online architecture that recovers association accuracy by predicting IDs explicitly over recurrent sparse queries. An outside-in Sparse4D detector fuses calibrated views into world frame 3D detections while propagating a sparse query bank, and a causal MOTIP ID decoder associates detections against a finite trajectory memory. We adapt MOTIP's relative-ID prediction and recycled slot runtime to globally fused 3D observations, and introduce metric spatial gating and proximity based newborn recovery. On the official 2026 AI City Challenge Track 1 test set, our method raises HOTA from 29.63 with native instance bank identities to 38.01, primarily through an AssA increase from 20.83 to 31.10, and ranks third on the public leaderboard. Full-sequence validation over all 9,000 frames of each scene shows that decoupled ID training improves HOTA over native identities, whereas continuing detector training alongside the detached ID objective produces scene-dependent gains and losses.

Topological photonic cavities offer a powerful route to robust optical confinement and enhanced light-matter interactions. Interface states that emerge at the boundary between one-dimensional periodic structures with distinct topological phases, enable cavities with ultra-small mode volumes and intrinsic protection against disorder. Existing implementations typically create the trivial and topological phases by redefining the unit cell on either side of the cavity, so that both periodic structures share the same band structure. This constraint limits design flexibility and the range of accessible devices. Here we introduce a fundamentally different strategy for realizing topological cavities based on combining periodic waveguides with distinct band structures. By exploiting bandgap closing and band inversion in Bragg gratings, we independently control the topological phase and bandgap width of each structure. We experimentally realize silicon topological cavities formed by two different Bragg gratings without period shifting, and observe topological modes despite significant differences between the two gratings. Our results establish a new route to topological photonic cavity design, demonstrating that band inversion between dissimilar Bragg gratings enables cavity formation beyond symmetric constraints and provides a mechanism to engineer optical confinement via mirror asymmetry.

In Digital Negative (DNG) multi-illuminant profiles, characterization matrices and nonlinear rendering payloads share condition-dependent interpolation slots, so adding a slot for rendering capacity also introduces an additional characterization state. We introduce Constrained Color Carrier (CCC), which constructs the three pre-serialization ColorMatrix and ForwardMatrix states from the original dual matrix segments while allowing the same shared slots to carry three HueSatMap rendering bases. Condition-specific HueSatMap payloads are solved as numerical preimages of the target through a fixed serialized downstream rendering operator, and carrier selection enforces a preservation bound on the host-effective interpolated characterization. We evaluate CCC on the Sony ILCE-7RM5 Adobe Standard dual-illuminant profile using a white-balance-dependent Standard ColorCorrect target recovered from Phocus 4.0.1 for the Hasselblad X2D 100C. Using Euclidean Oklab error, CCC yields a worst-temperature 95th-percentile preservation error of 0.003857, below the prescribed tolerance of 0.004, and reduces the worst-condition 95th-percentile target error from 0.08208 for the Dual representation to 0.03508. The synthetic Ordinary Triple yields a preservation error of 0.014802 and exceeds the same tolerance. The serialized DNG Camera Profile (DCP) and Extensible Metadata Platform (XMP) artifacts reproduce the final color-table payloads exactly and yield zero numerical difference from solver-side offline execution, showing that the CCC solution is representable within the evaluated serialized profile format.

The elements of a reconfigurable intelligent surface (RIS) are commonly modeled either as frequency-selective time-invariant reflectors or as instantaneous time-varying reflection coefficients. In practice, however, time-modulated metasurfaces exhibit both frequency selectivity and periodic time variation. We develop a physically consistent linear periodically time-varying (LPTV) model that jointly captures these effects and characterizes their impact on wideband orthogonal frequency-division multiplexing (OFDM) communications. From a canonical equivalent circuit of a generic RIS element, we derive a single-resonance model whose physically meaningful parameters determine both the frequency-selective reflection coefficient and the effective impulse-response duration, i.e., the finite memory of the element. The periodically switched dispersive responses are then represented through harmonic transfer functions, leading to a closed-form per-subcarrier OFDM input-output relation. The resulting coupling is generally non-diagonal: each received subcarrier collects contributions from multiple transmitted subcarriers through the RIS harmonics, each weighted by the element response at the corresponding absolute input frequency. We further derive a generalized cyclic-prefix (CP) condition requiring the guard interval to accommodate both the propagation-channel delay spread and the RIS memory. Under this condition, intersymbol interference and out-of-grid spectral leakage are suppressed, while deterministic on-grid harmonic coupling remains. Full-wave simulations of an OpenRIS unit cell designed for a 5G NR channel validate the proposed resonant model and reveal appreciable in-band dispersion despite nearly ideal binary phase switching. Simulations over 3GPP tapped-delay-line (TDL) channels confirm the generalized CP condition and show its relevance for high-quality-factor RIS elements.

Generalized morphology control requires a single policy to transform information across limbs with different physical roles, coordinate whole-body motion, and remain efficient as body size grows. Existing communication mechanisms address these requirements only partially. We introduce RecMorph, a topology-guided spatial recurrent architecture that uses recurrent sequence computation to jointly perform cross-limb communication and representation transformation. A depth-first traversal converts the kinematic tree into a morphology-derived sequence, along which shared bidirectional transitions progressively transform limb information before action decoding. Residual preservation, RMS normalization, and input-dependent channel modulation stabilize this repeated spatial transformation, yielding linear token complexity at fixed model width and depth. Across five UNIMAL tasks, RecMorph achieves the strongest mean final training performance among the evaluated generalized morphology controllers and the highest measured inference throughput on FT, while generalizing to unseen variations and bodies with up to 30 limbs. We further migrate representative generalized controllers from UNIMAL benchmarks to a four-platform quadruped setting. RecMorph achieves the best macro-averaged performance under nominal and high friction, reduces nominal velocity RMSE by 43.5% relative to specialist MLPs, and one shared policy completes 40 physical Go1/Go2 trials without falls. These results show that topology-guided recurrent transformation provides an effective and efficient communication mechanism for Generalized Morphology Control and remains effective when transferred from procedural bodies to physical robot platforms. Code and experimental resources are publicly available at https://github.com/quanruirao/RecMorph.

Robot manipulation policies often struggle to generalize beyond their demonstrations, even when new instructions involve familiar objects and behaviors. When language and scenes are strongly correlated during training, a policy can learn a fixed visual-action mapping rather than respond to the requested behavior. We investigate compositional reuse at two levels: within a subtask, combining familiar entities, action types, and action modifiers; and across subtasks, reusing learned subtasks in unseen long-horizon tasks. We introduce CoMani, a benchmark with controlled splits for evaluating both capabilities. Matched initial scenes and controlled changes to a single semantic factor encourage reliance on language rather than visual shortcuts. We further propose GraphPoint, which connects semantic entity graphs to geometric control by predicting future gripper point trajectories and converting them into actions using robot geometry. The framework organizes the gripper and objects by semantic roles and conditions their interactions on action types and modifiers, while predicted progress guides transitions during execution. Experiments and ablations on CoMani validate the effectiveness of our method for instruction-dependent generalization at both levels. Code will be released at GraphPoint.

Large language model (LLM) pricing agents may respond to how market data is presented, even when its numerical values remain unchanged. We introduce market signal injection (MSI), an attack that manipulates numerical formatting, competitor ordering, or qualitative market commentary without issuing explicit instructions. We evaluate nine open-weight models in simulated Bertrand duopoly and triopoly markets and three proprietary models in duopoly markets. Sentiment-based attacks produce the largest behavioral shifts, which propagate to other firms and alter profits and consumer surplus. Susceptibility varies across model families, and larger models are not consistently more robust. Matched neutral-text controls and a rule-based agent support a framing-based account of these shifts under the fixed demand parameters of our simulation. Episode-held-out probes distinguish baseline from attacked activations in all eleven re-evaluated model–condition pairs: linear AUC is 1.00 and MLP AUC ranges from 0.93 to 0.99. This separability does not by itself identify harmful pricing decisions. Input canonicalization removes the tested sentiment attacks, while decision boundary anchoring, which combines prompt constraints with output projection, provides partial mitigation under the tested adaptive attacks. These results identify data presentation as an attack surface for LLM pricing agents and motivate defenses that account for interactions among agents.

It has been over fifty years since Kenneth Wilson had his Nobel-prize-winning ideas on the renormalization group. In this time frame, despite many attempts, no mathematical results have implemented Wilson's vision to a satisfactory degree. Although a number of predictions stemming from the renormalization group framework have been proven to date, these proofs usually rely on alternative ideas and do not cover the full predictive power of Wilson's renormalization group. The discovery of pathologies within rigorous implementations of renormalization group transformations have further reduced the enthusiasm of the mathematics community for this subject. This paper presents a novel framework to implement Wilson's original idea in a rigorous manner based on inverse limits of finite systems. Doing so, one avoids these pathologies and hence obtains a mathematically sound framework for Wilson's renormalization group. This opens up a completely new path to tackle some of the existing problems in rigorous renormalization group theory like the existence of non-trivial fixed points.

We analyze a one-evaluation-per-iteration method for $\mathrm{VI}(C,B)$ with monotone $L$-Lipschitz $B$: $x_{k+1}=P_C(x_k-\lambda B(u_k))$, $u_k=x_k+\theta_k(x_k-x_{k-1})+\beta_k(x_k-u_{k-1})$, $\theta_k+\beta_k=1$. For constant step and summable filter ($\sum_k\beta_k<\infty$) we prove weak convergence via a Lyapunov function with exact rational dissipation budgets, including Malitsky's reflected gradient method. It is robust to summable operator errors; if $C$ is bounded, the constant-step range reaches $\lambda<(\sqrt2-1)/L$. For unbounded $C$ this reduces to an a priori boundedness statement, certified to $\lambda L=0.387$ by dissipation trading; for affine $B$ on polyhedral $C$, $\dist(x_n,S)\to0$ with $\sum_n\dist^2(x_n,S)<\infty$, strong convergence for bounded $C$, and $R$-linear rates after face identification. The main result is a safeguarded adaptive step-size rule needing no $L$ and no extra evaluations, proved weakly convergent unconditionally: a data-driven Lyapunov weight removes $L$ from the dissipation budgets. For affine $B$ with $C=\mathcal H$, sharpness of $\lambda L=1/\sqrt3$ via a rotation lower bound; the same constant is sharp for unconstrained nonlinear $B$, with convergence for square-summable operator values. Unconditional convergence below $1/(\sqrt3\,L)$ reduces to a marginal-pole absolute-stability statement; the projected case remains open. Under strong monotonicity we prove $R$-linear convergence with explicit contraction, and certify $\Omega(L)$ speedups over constant steps. Numerics confirm the gains.

EuAgAs is an antiferromagnetic topological material exhibiting intriguing magnetic behavior. We investigate its structural, magnetic, and local electronic properties using X ray diffraction, Mössbauer spectroscopy, dc magnetization, ac susceptibility, and heat capacity measurements. The results confirm antiferromagnetic ordering below $T_\text{N}$ and reveal pronounced magnetic anisotropy and several field induced metamagnetic transitions. We construct the magnetic phase diagram of EuAgAs, identifying several distinct magnetic regions. The field and temperature dependent behavior observed suggests a noncollinear magnetic structure in the low field regime. The sequence of field induced transitions resembles that observed in centrosymmetric rare earth compounds hosting skyrmion phases, suggesting that competing magnetic interactions may play an important role in stabilizing the observed magnetic states.

Context. LHAASO~J2108+5157 is one of the most intriguing Galactic ultra-high-energy $\gamma$-ray sources. It is detected up to hundreds of TeV but lacks a clear counterpart at lower frequencies. Fermi-LAT observations have revealed a compact GeV source spatially coincident with the PeV emission, while VERITAS and LST-1 impose stringent upper limits in the intermediate TeV band, producing a pronounced spectral suppression between the GeV and TeV domains. Aims. We investigate a time-dependent hadronic scenario in which a past episode of microquasar jet activity injected relativistic protons that are now observed in a relic phase. Methods. Energy-dependent diffusion naturally segregates the particle population: Lower-energy protons remain confined near dense molecular gas and account for the GeV emission, whereas higher-energy particles reach more distant material, producing the hard TeV–PeV component. Results. For representative interstellar conditions, the model is simultaneously consistent with the broadband spectral energy distribution, the spatial compact–extended dichotomy, and the lack of detectable radio or X-ray counterparts. Conclusions. The observed bimodal $\gamma$-ray phenomenology thus emerges as a transport effect of a single injected proton population, supporting the interpretation of LHAASO~J2108+5157 as a fossil microquasar remnant observed at an intermediate evolutionary stage and highlighting relic jet systems as a viable class of Galactic PeVatrons.

We study the {\epsilon}-capacity regions of mixed multiple-access channels (MACs) with general mixture and cost constraints by the information spectrum method. The starting point is a general formula for the {\epsilon}-capacity region of general MACs with cost constraint, together with the random-coding and converse lemmas from which it is derived. For the quasi-static fading Gaussian MAC, with random fading coefficients and noise variance, we show that the {\epsilon}-capacity region is the {\epsilon}-outage capacity region, which gives the latter a Shannon-theoretic operational meaning. The direct part follows from the general formula, and the converse part from the strong converse property of the Gaussian MAC, which is stronger than the {\epsilon}-strong converse, applied to each component. The {\epsilon}-capacity regions coincide in all four scenarios of availability of channel state information (CSI), and the results extend to K users. With CSI at both terminals, variable-rate coding enlarges the 0-capacity region to the polymatroid whose rank function is the average of those of the components. For mixed MACs with general components and a countable parameter space, CSI at the receiver alone never enlarges the {\epsilon}-capacity region, and the region with CSI at the transmitters is given by an information spectrum formula; unlike the Gaussian case, the regions with and without CSI at the transmitters may differ. For uncountable parameter spaces, only the formula for the region with CSI at both terminals survives in general. Parts II and III treat finite-alphabet mixed MACs and the strong converse for the K-user Gaussian MAC, respectively.

In this work, we study the connection between the bidomain model of cardiac electrophysiology and the Kirchhoff Network model (KNM), that was recently introduced by Jäger and Tveito. In the KNM, each cell of the cardiac tissue is represented as a node in a discrete network and the dynamics of the electric potentials in the heart are described by a system of ordinary differential equations on the nodes. We first study the well-posedness of the KNM and then prove that, when the nodes are situated on the vertices of a regular lattice and the mesh size $\varepsilon$ tends to zero, the solutions of the KNM system at cell-size $\varepsilon$ converge to the solution of the bidomain model, along appropriate subsequences. Regarding the convergence, we adopt the framework presented by Pennacchio, Savaré, and Colli Franzone in "Multiscale modeling for the electrical activity of the heart", 2005, which is based on (a) the time-discretization of the evolution equations of the bidomain and $\varepsilon$-KNM systems via a semi-implicit Euler scheme, (b) the identification of the time-discrete solutions as extremal points of a Minimizing Movement scheme, and (c) the $\Gamma$-convergence of the Minimizing Movements functionals.

We demonstrate the emergence of quantum-chaotic dynamics in a quasiperiodically driven impact oscillator near the grazing condition. While previous studies of the quantum impact oscillator under periodic driving reported strange nonchaotic dynamics, we show that quasiperiodic driving produces robust signatures of chaos. The corresponding classical system undergoes a sharp grazing-induced transition from quasiperiodic motion to chaos, as established by bifurcation analysis, Lyapunov exponents, Fourier spectra, and the 0-1 test. In the quantum system, Shannon-entropy time series exhibit broadband spectra, 0-1 test values close to unity, and predominantly positive finite-time Lyapunov exponents for both rational and irrational driving-frequency ratios. Independent quantum diagnostics reinforce this result: the out-of-time-order correlator (OTOC) displays early-time exponential growth with nearly identical rates, while the golden-ratio drive leads to a substantially faster saturation of the OTOC. Fidelity exhibits an exponential decay regime that is approximately independent of perturbation strength. These results establish quasiperiodic driving near grazing as a mechanism for generating quantum-chaotic behavior and reveal that, although the initial onset of scrambling is largely insensitive to frequency-ratio rationality, the subsequent development of global scrambling is strongly influenced by the degree of irrationality of the drive.

Battery Energy Storage Systems (BESS) operators face significant challenges when participating in multiple electricity markets due to the complex coupling of price volatility and stochastic reserve activation. Traditional deterministic dispatch models neglect the "tail risks" associated with extreme market realizations, potentially leading to technical infeasibility or severe economic losses. This paper proposes a risk-aware stochastic optimization framework for the co-optimization of BESS participation in the Day-Ahead (DA) energy market and the manual Frequency Restoration Reserve (mFRR) market. The model explicitly captures multi-dimensional uncertainties by utilizing non-parametric Kernel Density Estimation (KDE) to generate joint price scenarios that preserve the empirical characteristics of European balancing markets. A two-stage stochastic programming approach is employed.To manage the financial exposure to high-impact price events, the Conditional Value-at-Risk (CVaR) metric is integrated into a Mean-CVaR objective function. This allows decision-makers to tune their risk-aversion levels and identify an efficient frontier between profitability and robustness. Simulation results demonstrate that the proposed joint CVaR approach significantly enhances revenue stability compared to deterministic benchmarks.

We show that the norm-closed linear span of products of two Dunford-Pettis operators on $L^1(0,1)$ lies strictly between the representable and the Dunford-Pettis operators. This gives an additional proper large closed ideal in $\mathcal{B}(L^1(0,1))$, answering the existence question of Johnson, Pisier and Schechtman. The quotient of the Dunford-Pettis ideal by this square ideal contains a contractively complemented isometric copy of $L^1(0,1)$. We also prove that the Dunford-Pettis ideal has no right approximate identity, answering a question of Johnson and Schechtman. More precisely, a positive norm-one convolution operator $R$ satisfies $\|R-RT\|\geq1$ and $\|R-TR\|\geq1$ for every Dunford-Pettis operator $T$. The proofs combine translation averaging, Rajchman measures supported on a strongly independent set, and two atomless disintegrations of positive operators. The approximate-identity obstruction extends to every finite measure space with a nonzero atomless part. Finally, we prove that quantitative multiplication estimates for an ideal pass to all its closed power ideals.

Under the label of optical quantum computing, there are a variety of protocols and experiments that use the quantum properties of light to achieve a computational advantage over classical computing machines. In this review, we describe some of the main implementations, which differ in the type of encoding and in how the computation is performed, whether using gates or cluster states. For each protocol, we describe advantages and challenges with an overview of the experimental results obtained, summarized in tables. Because of the great relevance achieved in this field, there is a section dedicated to non-universal quantum computation with photons, where boson sampling, variational quantum eigensolvers, and quantum machine learning applications are described. The aim is to give the reader the broadest overview of the applications where photons and their quantum properties play a key role in computation.

Large language models (LLM) deployed as autonomous pricing agents may sustain supracompetitive prices through tacit coordination. We develop a causal graph divergence framework that separately measures structural faithfulness and intent faithfulness of LLM pricing agents in Bertrand competition. Across nine LLMs under duopoly and triopoly conditions, collusive behavior and chain-of-thought (CoT) faithfulness dissociate along both dimensions: the most collusive model accurately reports cooperative intent yet reasons structurally unfaithfully, while the most structurally faithful model sustains supra-Nash pricing under both market structures. These findings establish that CoT monitoring alone cannot serve as a standalone safeguard against algorithmic collusion.

Large vision-language models (LVLMs) are commonly prompted with text alone or together with an image. In this paper, we find a new aspect of LVLM vulnerability in its response robustness: adding an image can unexpectedly affect responses even when text prompts ask about a concept rather than the instance of the concept depicted in the image. For example, adding an image of an animal can change the generated attribute descriptions of its breed, and framing of the image further affects those changes. We study this new problem on seven LVLMs with image sets covering 30 animal breeds and eight food categories, using two types of framings that focus on the subject (subject-focused) or place it in a broader context (subject-in-situation). We draw the following main findings: (1) adding images increases physical-term proportions for animals (16.7% $\to$ 32.8%) and decreases sensory-term proportions for food (83.6% $\to$ 73.2%) among the most frequent terms, averaged over seven models and two framings on correctly recognized images. (2) attribute-term distributions differ significantly between the two framing types for 41.4% of animal and 71.4% of food model–concept pairs, with generally higher physical-term proportions for animals and sensory-term proportions for food under subject-focused than subject-in-situation framing.