Papers

This paper introduces four groups of subspace methods for nonlinear monotone equations, with applications to large-scale machine learning problems. The methods use Jacobian-free subspace (JFS) directions of conjugate-gradient type, combined with either fixed step sizes or variable step sizes generated by the projected method of Solodov and Svaiter. To ensure convergence independently of the specific algebraic form of the subspace directions, we impose an angle condition together with an explicit scaling rule controlling the effective search directions. Under monotonicity and Lipschitz continuity of the operator, we establish global convergence for both the line-search and fixed-step frameworks, as well as a best-iterate residual rate $O(\ell^{-1/2})$. Under a local error bound, the distance to the solution set satisfies the sharper decay $o(\ell^{-1/2})$. If the operator is continuously differentiable and its Jacobian is nonsingular at a solution, the required local error bound and local isolation follow, yielding $R$-linear local convergence. The residual sequence then converges geometrically and hence satisfies the last-iterate rate $o(\ell^{-1})$, without strong monotonicity. We also derive iteration and residual-evaluation complexity bounds: $O(\varepsilon^{-2})$ for the baseline best-iterate guarantee and $O(\log(\varepsilon^{-1}))$ in the local linear regime, together with a uniform bound on backtracking residual evaluations. Under additional asymptotic assumptions, the proposed JFS directions and several classical update directions admit related optimistic gradient descent–ascent (OGDA)-type residual–memory representations. Numerical experiments illustrate the robustness and efficiency of the methods on representative min–max problems.

For a real analytic map germ $G:(\mathbb{R}^m,0)\to(\mathbb{R}^p,0)$, we study Milnor fibrations obtained by replacing the squared Euclidean distance with an analytic control function $\rho$ defining the origin. We formulate the corresponding Milnor set and condition (b), derive criteria for tube and sphere fibrations, and examine their dependence on $\rho$. The family $G_\rho=(xz,\,yz\rho)$ provides explicit changes of regularity under elliptic controls. In particular, the germ $G(x,y,z)=(xz,\,yz(10x^2+y^2+3z^2))$ admits neither the induced tube nor sphere fibration for the Euclidean control, while both fibrations exist for the adapted function $\rho=10x^2+y^2+3z^2$. Thus the control function can be essential to the local fibration structure.

Intermodal freight networks are increasingly exposed to correlated, multi-mode disruptions, yet resilience assessments often rely on historical or uncorrelated scenarios that understate systemic risk. This paper develops a data-driven stress-testing framework integrating generative adversarial networks (GANs) with an intermodal optimization model to evaluate performance under realistic compound disruptions. The case study examines weather-related disruptions in the Tennessee Valley corridor. Each GAN-generated scenario is used as a simulation input, and the resulting routing problem is solved to obtain system costs. Aggregating outcomes enables estimation of expected costs and identification of major risk drivers. Results show that historical disruptions increase total cost by about 3%, whereas GAN-generated scenarios raise costs by over 25%, producing an expected annual cost of $5.11 million. Risk is concentrated in correlated multi-node failures and critical nodes such as the Port of Knoxville. The framework helps identify vulnerabilities and prioritize resilience investments.

A general-purpose robot needs to draw on diverse experience, choose actions, and anticipate how those actions will change the world. We introduce XPACE, a unified embodied world model that serves as both a world action model, jointly predicting executable robot actions and future video, and a world simulator, predicting the visual consequences of prescribed actions. Our key insight is that video prediction can both connect heterogeneous experience to action learning and generate new experience for policy improvement. With a shared video backbone between the policy and simulator, we use action-unlabeled video to learn visual dynamics and action-labeled human and robot demonstrations to jointly learn video and action prediction. Building on this architecture, a coarse-to-fine training curriculum progressively emphasizes robot control while retaining human experience, allowing the policy to learn behaviors beyond those covered by robot demonstrations. Beyond learning from recorded experience, XPACE uses its simulator to create additional recovery supervision for the policy. Specifically, we adapt the simulator to its own generated context, synthesize deviation-recovery trajectories around expert demonstrations, and fine-tune the policy on filtered recovery examples. Experiments on XPENG's IRON humanoid robot show that heterogeneous training improves robustness and enables transfer of human-observed skills to tasks absent from robot demonstrations, while recovery data generated by the model's own simulator further improves real-world task completion. Together, these results demonstrate how joint world and action modeling connects learning from heterogeneous experience with simulation-driven policy self-improvement.

Future near-infrared (NIR) astronomy missions dedicated to photon-starved science cases, in particular an all-sky astrometric survey extending the legacy of Gaia into the NIR, as identified within the ESA Voyage~2050 programme, require large-format detectors combining sub-electron effective read noise with very low dark current. Linear-mode avalanche photodiodes (LmAPDs) based on HgCdTe meet this need by multiplying the photo-generated charge by an avalanche gain before the readout stage, thereby reducing the relative contribution of the read noise. We report the first electro-optical characterization of an IBEX detector, a $2048\times2048$, \SI{15}{\micro\meter}-pitch HgCdTe LmAPD array developed by Leonardo with the European Space Agency and operated at \SI{80}{\kelvin} on a dedicated bench at CEA-IRFU. We first discuss the central difficulty of characterizing an APD array, the degeneracy between avalanche gain, quantum efficiency (QE), and conversion gain in the measured response, and we then separate the measurements into two categories. Among the quantities that are directly measurable without assumptions, we report a signal-to-noise ratio for a CDS measurement that exceeds that of a Euclid-type H2RG above \SI{8}{\volt} pixel bias under identical low-flux conditions, a photo-response non-uniformity stable at the $\sim$10% level, and a quantum efficiency-to-excess-noise ratio (QEFR) of \num{0.40} at \SI{10.5}{\volt}. Among the quantities derived under an explicit set of assumptions, we obtain a conversion gain corresponding to a sense-node capacitance of \SI{27}{\femto\farad}, a quantum efficiency of $46\pm12\%$ at \SI{2.5}{\volt}, and an excess noise factor $F=1.15\pm0.14$ at \SI{10.5}{\volt}. These results establish IBEX as a promising European large-format detector for future ultra-low-flux NIR instruments.

Motivated by Kawanoue's construction of a basis for the derivation module of the cone of the extended Catalan arrangement of type $B_\ell$, we construct an explicit basis for the derivation module of $\mathbf{c}Shi(B_\ell,m)$. Our construction generalizes the previously known case $m=1$ to $m\geq1$. It also provides a partial answer to a question of Abe and Terao concerning explicit constructions of simple-root bases.

Because it offers exactly-integer topological quantities, the modified Villain discretization offers a route to correct anomaly structure at finite lattice spacing. I will present a 4-dimensional purely-bosonic modified Villain model with an ABJ-type vector-vector-axial anomaly. The model may have a direct continuous phase transition from one SSB phase to another, giving hope of yielding 4D CFT with a VVA anomaly.

Efficient resource use in packing and assembly-line applications requires decisions that jointly account for capacity and precedence constraints. The strongly NP-hard bin packing problem with generalized precedence constraints (BPP-GP) models such decisions by minimizing the number of ordered, capacitated bins required to pack weighted items, even when precedence requirements span multiple bins. Existing exact algorithms primarily focus on classical special cases, whereas general BPP-GP has been addressed only via compact integer models and heuristics, with no efficient open-source exact solver. We present PrecPack, a unified exact solver that extends branch-bound-and-remember (BBR) to arbitrary nonnegative precedence weights and naturally specializes to the classical cases. Generalized states capture restrictions that remain active across future bins, which are addressed through branching, dominance, and conflict-aware lower bounds. Root column generation uses fixed-point arithmetic to compute numerically valid dual bounds for pruning or to prove optimality. To support reuse and verification, we provide common programming and command-line interfaces, independent assignment checking, explicit termination statuses, and reproducible batch execution; the core procedures require no commercial software. In same-machine, single-threaded comparisons on classic assembly-line benchmarks, more instances are proven optimal, and average computing times are substantially reduced relative to leading source-available BBR implementations. Further comparisons with published benchmark results for bin packing with precedence constraints and BPP-GP also show that more instances were proved optimal and that reported average gaps were smaller on most benchmark sets. PrecPack is released under the MIT License at https://github.com/Sunkanghong-Wang/PrecPack.

Quantum batteries promise revolutionary advantages for energy storage but are fundamentally crippled by environmental decoherence, which induces self-discharge and rapid "aging." Here, we crack this critical bottleneck by exploiting the decoherence-suppression mechanism: the formation of system-environment bound states. We consider a charger-battery system embedded in a three-dimensional anisotropic photonic crystal bath and derive exact non-Markovian dynamics. Strikingly, we reveal a tunable phase diagram where modulating the atomic eigenfrequency and coupling strength switches the system between zero, one, and two bound states. In the presence of two bound states, the battery energy evolves into a persistent periodic oscillation, enabling lossless energy storage and on-demand extraction indefinitely, effectively realizing an aging-free quantum battery. Conversely, the absence of bound states leads to complete energy decay. We also demonstrate that even during self-discharge, a single bound state can stabilize extractable energy. This work establishes bound-state formation as a powerful and feasible strategy for combating decoherence, offering a clear blueprint for designing durable solid-state quantum batteries in non-Markovian photonic platforms.

As technological and social innovations create novel regulatory challenges, legal systems grow in complexity - increasing the need for interfaces that enable effective interactions with legal document collections. Through interviews with legal scholars (n=15), we find that supporting legal work requires going beyond retrieval-centered legal-information-system paradigms. Hence, we propose Lexplorer, a flexible interface for exploring, navigating, and analyzing legal documents, based on a taxonomy capturing user intents. Distinguishing text and data views for one, few, and many documents, Lexplorer enables context-sensitive interactions with evolving collections of interconnected legal texts, facilitating Adaptive Meaning Construction in law. We evaluate Lexplorer with legal scholars (n=20) in the context of European Union law, validating our elicited requirements, intent taxonomy, and prototype design. Resulting from a close collaboration between visual-analytics researchers and legal scholars, our work also provides nuanced insights into the process required to design interactive systems for expert domains driven by implicit methodological knowledge.

Magnetars are young, isolated neutron stars that possess an exceptionally strong magnetic field, with surface dipolar strengths on the order of $10^{15}$ G. One of the plausible scenarios for generating such a strong field is an exponential amplification by a turbulent convective dynamo during the protoneutron star phase. However, the short expected duration of the convection ($\sim 10$ s) imposes a stringent constraint on the dynamo growth rate. We perform an extensive set of 82 three-dimensional convective dynamo simulations in the anelastic approximation and investigate the kinematic phase to quantify the dynamo growth rate $\gamma$. We find that $\gamma$ increases with both the magnetic Prandtl number ${\rm Pm}$ and the Rayleigh number ${\rm Ra}$, with the most unstable mode becoming highly non-axisymmetric and multipolar. We further observe a gradual transition from large-scale to small-scale dynamo as the magnetic Reynolds number ${\rm Rm}$ increases, resulting in a magnetic field that is predominantly concentrated at small scales. The trend remains unchanged when the outer magnetic boundary condition is varied. Since resolving the increasingly small scales becomes numerically impractical, we employ the theoretical small-scale Kazantsev dynamo model to explore the large ${\rm Pm}$ regime characteristic of protoneutron stars. The model qualitatively captures the growth rate behaviour observed in simulations and, upon extrapolation to the large ${\rm Pm}$ limit, indicates that $\gamma$ is only weakly dependent on the resistivity in a PNS. Under conditions relevant to the PNS, this model predicts a magnetic energy growth rate of the order of $\sim 1$ ms$^{-1}$.

The classical Weisfeiler-Leman algorithm (also known as the $2$-dimensional Weisfeiler-Leman algorithm) is a simple combinatorial algorithm that was originally designed as a heuristic for the graph isomorphism problem. However, it has also numerous connections to other areas such as algebraic graph theory, logics, proof complexity, combinatorial optimization and machine learning. We prove that the classical Weisfeiler-Leman algorithm terminates after $5(n-1)$ iterations. This improves over the previous best upper bound of $O(n \log n)$ by Lichter, Ponomarenko and Schweitzer [LICS 2019], and asymptotically matches the known lower bound of $\Omega(n)$ by Fürer [ICALP 2001]. Additionally, building on our results for the $2$-dimensional case, we obtain an improved upper bound of $O(n^{k-1}/(k-2)! + n^{k-2})$ on the number of iterations performed by the $k$-dimensional Weisfeiler-Leman algorithm, for every $k \geq 3$. Our arguments actually hold for a larger class of sequences of colorings of $k$-tuples; in this larger class our upper bounds are essentially tight for all $k \geq 3$.

Heavy-ion collisions provide unique access to the properties of QCD matter over a broad range of temperatures and baryon densities. We review recent progress in constraining the high-density phase structure of QCD, with particular emphasis on the microscopic inputs required for reliable transport modeling. We discuss cluster production, strange-particle interactions, collision dynamics at few-GeV energies, and the isospin dependence of the nuclear interaction, together with their impact on the interpretation of flow, yields, fluctuations, and possible critical signatures.

We study multidimensional compressible fluid-particle systems at critical regularity, in which a carrier fluid and a particle phase with Fokker-Planck diffusion are coupled through a drag force. We prove the existence and uniqueness of strong solutions for the Cauchy problems of the Navier-Stokes-Vlasov-Fokker-Planck and Euler-Vlasov-Fokker-Planck systems near equilibrium in their respective critical Besov spaces. Moreover, we establish regularity estimates for the Navier-Stokes-Vlasov-Fokker-Planck system uniform with respect to the common viscosity parameter $\mu=\lambda=\varepsilon$ and justify the global-in-time vanishing-viscosity limit with the convergence rate $\mathcal O(\varepsilon)$. Finally, under an additional lower-order Besov assumption on the initial data, we obtain optimal time-decay estimates for both systems and derive enhanced decay rates for the relative velocity and the microscopic part of the distribution function.

We prove a purely quasi-local positivity theorem for the Wang–Yau mass for a class of initial data whose Jang deformation, after a boundary-preserving conformal reduction to zero scalar curvature, lies in a sufficiently small transverse–traceless (TT) perturbative neighborhood of a strictly convex Euclidean fill-in.We explicitly construct a nontrivial class of physical initial data whose admissible Jang reductions realize this TT-generated sector. The argument reduces the Wang–Yau energy to the Brown–York mass of the resulting scalar-flat compact metric, together with nonnegative bulk terms determined by the Jang deformation, and establishes strict positivity by computing the second variation of the Brown–York functional at the Euclidean metric in transverse–traceless directions. The proof is entirely confined to the compact fill-in and uses neither an asymptotically flat extension nor the positive mass theorem. This gives a partial answer to a question of R. Schoen concerning a genuinely quasi-local proof of positivity for quasi-local mass.

Real-time spoken dialogue systems must distinguish interruptions that require yielding the floor from backchannels that permit continued speaking. Existing benchmarks typically score events independently and may therefore assign high scores to systems with fixed action preferences rather than context-sensitive decision policies. We introduce ECHO, a paired diagnostic benchmark for Chinese turn-taking evaluation. ECHO pairs examples with the same overlap transcript but contrasting preceding multi-turn dialogue contexts, with one requiring Yield and the other Keep. It additionally includes off-talk examples for diagnosing unnecessary yielding. We introduce pair accuracy, which requires correct decisions on both members of a pair and assigns no credit to constant-action policies. Experiments on four speech systems show that three exhibit a severe over-yielding bias: they correctly keep the floor on fewer than 13% of backchannels, resulting in near-zero pairwise success rates equal or less than 4%. While the remaining system remains comparatively balanced across contexts, these findings broadly demonstrate that interruption-only evaluation can severely overestimate practical turn-taking reliability.

We identify a topological constraint on extremal $\mathcal{N}=1$ AdS$_3$ spectra that is not implied by genus-one modular covariance of the three even spin structure partition functions. Assuming the expected topological modular forms divisibility of the Ramond Witten index, we show that for infinitely many odd $n$ at central charge $c=12n$, an extremal holomorphic $\mathcal{N}=1$ superconformal field theory requires an odd number of Neveu–Schwarz primaries at the BTZ threshold. Thus the strict ansatz with no threshold primaries is excluded for this infinite family.

Variational quantum circuits (VQCs) are parameterized quantum circuits optimized classically. We propose a hybrid variational quantum circuit (HVQC) extending VQCs with a classical affine post-measurement layer, enabling vector-valued regression without the linear overhead of independent scalar circuits. Theoretically, we show that elementary one-and two-qubit circuits can approximate quadratic functions and products via data re-uploading and entanglement, providing the foundations of the full architecture. Experimentally, on two synthetic image reconstruction datasets and the Friedman1 benchmark (40,568 test samples), our HVQC matches Gaussian Process Regression and outperforms XGBoost and Random Forest. An ablation study confirms that both quantum and classical components are essential, and results highlight the central role of the feature map in hybrid quantum-classical models.

DBSCAN is an algorithm that denoises and clusters data. In prior work, we implemented the DBSCAN algorithm neuromorphically, introducing two constructions termed “flat” and “systolic”. The “flat” construction prioritizes throughput, while the “systolic” construction trades time for space resulting in a smaller, more hardware-friendly architecture at the cost of throughput. In this work, we offer spatiotemporal extensions of these two constructions to better leverage the spatiotemporal nature of event sensor data. Moreover, as in our prior work, we discuss partial or segmented implementations that further leverage time for space when hardware resources are constrained. All network constructions are provided as open-source implementations.

Let $\Th(\alpha,L)=\sum_{v\in L}e^{-\pi\alpha|v|^2}$ for $\alpha>0$ and $E(L,s)=\sum_{v\in L\setminus\{0\}}|v|^{-2s}$ for $s>3/2$ be the theta and Epstein zeta functions associated to the lattice $L$, respectively. We are particularly interested in physically relevant dimension three. Fix the covolume of the lattice $L$ to $1$. Up to an orthogonal transformation, we prove that \begin{equation}\nonumber \argmin_{|L|=1}\Th(\alpha,L)= \begin{cases} \boldsymbol{\mathrm{FCC}}\;\;\mathrm{lattice},\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;&\text{if}\;\; \alpha>1, \boldsymbol{\mathrm{BCC}}\;\;\mathrm{lattice}, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;&\text{if}\;\; \alpha<1, \boldsymbol{\mathrm{FCC}}\;\;\mathrm{or}\;\; \boldsymbol{\mathrm{BCC}}\;\;\mathrm{lattice},\;\;&\text{if}\;\;\alpha=1, \end{cases} \end{equation} and \begin{equation}\nonumber \argmin_{|L|=1}E(L,s)= \boldsymbol{\mathrm{FCC}}\;\;\mathrm{lattice},\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\text{if}\;\; s>3/2. \end{equation} Therefore, we prove the Sarnak–Strömbergsson conjecture \cite[Inequalities (43)–(44), Section 5]{SS}.

Ambient clinical scribes (ACS) are being rapidly deployed at scale across Global South healthcare settings, aiming to reduce clinician documentation time, especially in overburdened environments like India. These ACS are primarily developed or distilled from models built and validated on Global North speech, languages and consultation styles. Indian clinical encounters are brief, triadic, multilingual, code-mixed with low-resource languages, and conducted in highly resource-constrained, noisy settings – increasing the likelihood of ASR and note-generation errors manyfold. We posit an urgent need to develop a standardized evaluation infrastructure to assess whether these systems are safe, reliable, and well-suited to the Indian healthcare setting. We substantiate our claims through a mixed-methods study – a systematic survey of publicly available patient-clinician conversational datasets, a quantitative comparison of these datasets against conversational and cultural markers drawn from the Indian clinical-communication literature, and semi-structured interviews with five organizations building and deploying ACS in India and Africa. Our survey shows that there are no publicly available, large-scale, real-world benchmarks for ACS in India, with existing datasets being overwhelmingly synthetic. We note that the available Global North datasets diverge significantly from the expected conversational and cultural structures of Indian encounters. Finally, our interviews reveal that deploying organizations have each built proprietary, incomparable evaluation pipelines, creating a fragmented ecosystem with no independent and reliable basis for procurement. We call for the development of a publicly shared, real-world, multilingual benchmark for ACS evaluation and outline the properties and policies such a benchmark would require.

Inferring network structure from dynamical observations is a fundamental inverse problem in complex systems. Existing approaches have largely focused on single-layer or pairwise interaction networks, leaving the reconstructability of multiplex systems with higher-order interactions poorly understood. Here, we show that structural identifiability in such systems is jointly governed by cross-layer spreading couplings and network heterogeneity. Building on coupled awareness-behavior dynamics, we develop a multiscale inference framework that disentangles interacting spreading processes and enables the simultaneous reconstruction of microscopic simplicial interactions and macroscopic metapopulation organization. Numerical experiments on synthetic and empirical networks demonstrate high reconstruction performance, particularly in non-absorbing dynamical regimes sustained by weak inhibitory and strong facilitatory couplings. Results reveal the mechanisms governing structural identifiability in higher-order multiplex networks and provide a general route for inverse inference in multiscale complex systems.

Prefix-free parsing provides an efficient way to construct compressed representations of large and repetitive pangenomes and naturally induces a graph representation known as a prefix-free graph. In this work, we initiate a theoretical study of the problem of constructing prefix-free graphs of minimum size, where the size accounts for both the total length of distinct segment labels and the paths representing the input sequences. We show that selecting an optimal set of trigger words is NP-hard, already when triggers consist of single characters. Using a synchronized-code reduction, we extend this hardness result to every fixed trigger length and further show that the problem remains NP-hard over an alphabet of size three. We then establish a structural connection between prefix-free graphs and de Bruijn graphs. In particular, we show that every compacted de Bruijn graph can be realized as a prefix-free graph and derive a hierarchy relating the sizes of minimum pangenomic graphs, minimum prefix-free graphs, compacted de Bruijn graphs, and de Bruijn graphs. Finally, we give an exact fixed-parameter algorithm running in $O(2^q n)$ time, where $q$ is the number of distinct candidate trigger words and $n$ is the total pangenome length. Our results characterize both the computational limitations and the structural properties of optimizing prefix-free graph representations and provide a theoretical foundation for the design of compact graph representations of repetitive pangenomic data.

Loading multiple quantum states in parallel into a quantum machine learning (QML) model can unlock learning tasks where key information resides in the relations between states rather than in individual states. We introduce an adaptive relational learning framework for such multi-instance quantum data that accesses pairwise and higher-order relations. Our model combines global measurements via SWAP or CYCLE tests for evaluating an $n$-state Bargmann invariant with shallow trainable transformations applied locally to each input state. We demonstrate the approach for continuous-variable (CV) photonic systems, which naturally provide access to quantum data and necessary computing operations. We solve tasks involving hidden relationship detection, geometric phase classification, and sensing in the presence of an unknown shared nuisance interaction. We benchmark the adaptive model against a non-adaptive “measure-first” approach based on continuous-variable classical shadows, and show that the cost of shadow estimation grows rapidly with $n$, while our model avoids this dependence. Already for $n=2$, we achieve perfect test accuracy $A=1.0$ with $500$ inference shots, improving average test accuracy over the shadow-based method by $\Delta A=0.15$ while using $100$ times fewer shots per data point. Our work opens routes to sensing and quantum-data applications where adaptive photonic QML can access relational features that are costly to recover with non-adaptive, measure-first models.

We construct singular weak solutions to scalar, linear, uniformly parabolic equations with complex coefficients in one space dimension. Our examples show that the space-time integrability provided by the energy estimates is sharp: for every $p>6$, there exists such an equation admitting an energy solution that fails to be $p$-integrable on a compact subset of the space-time domain. In particular, the local boundedness of weak solutions from the De Giorgi–Nash–Moser theory fails for complex coefficients already in one space dimension.

Chronic Obstructive Pulmonary Disease (COPD) remains a major global health challenge, emphasizing the need for accessible and non-invasive detection. Since speech production is fundamentally linked to respiratory physiology, its disruptions can serve as indirect indicators of pulmonary impairment. This study introduces SpiroPhonia, a machine learning framework that leverages spontaneous speech for respiratory health assessment. We evaluated SpiroPhonia on a new dataset of 201 speakers (102 with COPD, 99 healthy controls). By integrating statistical analysis with recursive feature selection, we identified a compact set of discriminative speech markers. Our best model achieved 78% accuracy, 80% F1-score, and 87% AUC. This performance on spontaneous speech is competitive with methods using controlled laboratory recordings. Findings demonstrate that everyday speech encodes robust respiratory biomarkers, paving the way for continuous health monitoring via voice-enabled technologies.

In embodied cyber-physical systems, active cyberattacks pose an immediate threat not just to data, but to physical integrity and human safety. While existing security approaches excel at detection, they lack the runtime mechanisms to determine whether a disruption is tolerable or if performance degradation remains within safe operational bounds. This gap leaves autonomous systems vulnerable to graceful failure paralysis, where they cannot distinguish between a safe, degraded state and a catastrophic hazard during an ongoing attack. This paper presents RobResilience, an implementation of a formal resilience framework for embodied cyber-physical systems in a Webots simulation environment, using a PR2 robot and ROS2. The framework evaluates three predicates at runtime: tolerable disruption ($\delta$), tolerable degradation ($\gamma$), and mitigation feasibility ($\mu$), over a compromised device set derived from IDS confidence scores. When resilience is lost, the framework triggers available mitigation strategies. We evaluate our implementation through eight attack scenarios that systematically cover all possible combinations of the predicate state space, varying attack targets, degradation rates, and mitigation availability. Results confirm that the runtime behaviour of the implementation is consistent with the theoretical definitions.

Independently at every vertex $x$ of a large core graph $\mathbb G$, we draw a random graph and connect $x$ to a subset of its vertices. This model of a randomly sprinkled graph captures qualitative features of commonly observed graphs; it can also be regarded as a model of quantum disorder, where disorder arises from local perturbations to the graph geometry. We show that it is naturally connected both to the Anderson model and to site percolation on $\mathbb G$ by deriving an Anderson-percolation representation for its spectrum. We characterize the support of the spectrum and derive quantitative bounds on the integrated density of states. We also analyse in detail the regime of sparse sprinkling, in particular investigating the behaviour of the density of states in the vicinity of atoms.

Collision avoidance constraints for autonomous systems are typically formulated in position or velocity space, implicitly reacting to geometric proximity. We propose an alternative paradigm based on the adversarial time-to-collision (aTTC): the minimum time in which an adversary could achieve a collision given its dynamical constraints. By defining a control barrier function (CBF) directly in the time domain, the resulting controller is inherently anticipatory. The evading agent responds not only to whether a pursuer is on a collision course, but to how quickly it could reach one. This formulation enables velocity modulation that exploits the pursuers dynamic limits as an evasive strategy, a behavior not captured by standard distance-based CBFs. Since exact aTTC computation requires integrating the full system dynamics, we employ a lightweight neural network surrogate that admits a real-time quadratic program-based control law. We validate the approach in a 2D comparative study and a 3D multi-agent pursuit-evasion scenario, where the aTTC-based CBF outperforms a higher-order distance-based baseline by more effectively buying time against superior pursuers with a significant speed advantage.

To answer questions outside of their pre-training data, large language models (LLMs) need access to new information, which can be presented in the context window as documents, encoded into the model's parameters, or injected as latent representations. However, each of these methods comes with different efficiency, cost, and performance trade-offs, with no single winner. We present a controlled comparison of representation-based (KV-cache based) and parametric (fine-tuning-based) adaptation methods on five knowledge-intensive benchmarks. We show that in the oracle setting, Cartridges (KV) are the most accurate injection method at nearly every storage budget, outperforming parametric methods by 10 points. Compaction (KV) matches Cartridges only at low compression rates, lagging behind the parametric methods by 10 points at rates higher than $50\times$. In the more realistic multi-document retrieval scenario, Cartridges are the only method that matches in-context learning (ICL), leading the parametric methods by 29 points and Compaction by 15 points. Nonetheless, Cartridges are also the only method, besides full fine-tuning and large MLP adapters, that suffers from catastrophic forgetting, i.e., a 6% performance degradation on control benchmarks, with 13% in coding.