Papers

This paper presents a unified error analysis of randomized neural networks (RaNNs) for elliptic interface problems. We first derive an integral representation of Barron functions using the standard $\tanh$ activation, which yields a $C^2$-approximation bound valid for any hidden-parameter distribution supported on a cube with strictly positive density. We then establish a quantitative $\mathcal{O}(n^{-1})$ generalization bound for the composite loss that enforces the partial differential equation, boundary, and interface conditions simultaneously, where $n$ denotes the number of training samples. Combining these results with the optimization guarantees for RaNNs, we obtain an a priori $L^2$ error estimate for the neural network solution in the presence of interface discontinuities. Numerical experiments are presented to validate the theoretical results.

The search for electroweak supersymmetric particles remains an important part of the LHC program since neutralinos and charginos with masses around a few hundred GeV are still compatible with the present constraints in compressed spectra. Run-2 searches for the “golden channel”, $pp\to\widetilde\chi_2^0\widetilde\chi_1^\pm\to\widetilde\chi_1^0 Z^{(*)}\widetilde\chi_1^0 W^{\pm(*)}$, have reported mild excesses in parts of the soft two- and three-lepton data, with the corresponding simplified-model interpretations emphasizing $m_{\widetilde\chi_2^0}\simeq m_{\widetilde\chi_1^\pm}\gtrsim200$~GeV and a neutralino mass difference near $20$~GeV. We study this configuration in the Minimal Supersymmetric Standard Model (MSSM) with the Generalized minimal Supergravity (GmSUGRA) boundary conditions, imposing the Higgs, flavor, collider, relic-density and direct-detection constraints relevant to the spectrum. For both signs of $\mu$, the solutions compatible with the Planck experiment contain an almost pure bino $\widetilde\chi_1^0$ with mass about $260$–$266$~GeV and a nearly degenerate wino-like $\widetilde\chi_2^0/\widetilde\chi_1^\pm$ pair near $280$~GeV. The resulting splitting, $\Delta m_{21}\simeq18.5$–$19.1$~GeV, lies in the mass-difference region probed by the ATLAS and CMS soft-lepton searches and places the $Z^{(*)}/W^{(*)}$ decays below the on-shell gauge-boson thresholds. The same compressed hierarchy keeps the wino states thermally populated during freeze-out, so bino-wino coannihilation yields a neutralino relic abundance consistent with the Planck experiment while the surviving solutions remain compatible with the direct-detection experimental bounds. Thus, the GmSUGRA boundary conditions provide a high-scale realization of the compressed bino-wino spectrum relevant to the LHC soft-lepton channel.

LLM agents often use generative models for bounded decisions, raising the question of when these decisions can be handled more efficiently without reducing task success. We study REFLEX, an agent architecture that uses Jev as a fast, typed decision layer and calls a strong LLM when confidence is low, or generation is required. On a frozen 100-task benchmark, REFLEX achieves 95% success with 72.7% fewer strong-model calls than a strong-only agent, with reductions persisting across three fallback families. Controlled interventions show that reliability depends on action-set size and near-valid alternatives near authorization boundaries. External BFCL and $\tau$-style evaluations reveal limited advantages over a cheap generative cascade when ordinary routing is already highly accurate. These findings identify when selective control with Jev can reduce computation and where its benefits are limited.

The Matching Augmentation Problem (MAP) asks for a minimum-cardinality set of unit-cost edges that, together with a zero-cost matching, forms a 2-edge-connected spanning multigraph. We study the standard cut relaxation. Bamas, Drygala, and Svensson proposed a particularly simple LP-guided algorithm: compute an extreme optimum, run a depth-first search that prioritizes large LP coordinates, and augment the resulting DFS tree optimally. We give a new structural analysis of the Bamas–Drygala–Svensson LP-guided DFS algorithm. The analysis combines an exact primal–dual identity for the residual uplink problem with a rank bound that measures fractional support relative to the unit-valued skeleton. The result is that for every root and every deterministic tie-breaking order consistent with the LP priorities, the algorithm returns a solution of cost at most $\frac{59}{33}c(x^*)-\frac{25}{33}=\left(2-\frac7{33}\right)c(x^*)-\frac{25}{33}\approx1.788c(x^*)-0.758$, where $x^*$ is an optimum of the cut LP. Consequently, the integrality gap of the relaxation is at most $59/33\approx1.788$. No new algorithmic step is required; the improvement is analytical. The exact packing certificate for the residual uplink problem yields a cost identity with a packing-slack term, while a rank theorem bounds fractional support relative to the unit-valued skeleton. A regional classification accounts for the non-tree edges, and a two-cut identity handles self-holes. As a direct corollary, the same $59/33\approx1.788$ bound holds for Forest Augmentation in the minimum-value regime. The proof is self-contained apart from one theorem on the dimension of minimum-cut vectors.

We present time-series spectroscopy of the SU UMa-type dwarf nova V844 Her during quiescence. We discover high-velocity Balmer and He I emission features modulated at a period of 29.3$\pm$0.1 minutes. The spectroscopic periodicity is identical to the photometric period detected only during superoutbursts. Interpreting this as the result of magnetic accretion onto the white dwarf, we identify V844 Her as an intermediate polar (IP). The spin period of the white dwarf is most likely to be 29.3 minutes. In a few IP systems, optical modulation is seen at twice the spin frequency, so we can not rule out that the spin period is 58.6 minutes. The orbital period of V844 Her is only 1.31 hr, meaning that the system has the shortest binary period and one of the smallest orbit-to-spin ratios of the confirmed IPs. We present extensive optical, ultraviolet, and X-ray observations of V844 Her during the 2023 superoutburst. Compared with quiescence, the XRT count rate decreases during superoutburst. While the enhanced mass transfer during the superoutburst likely increases X-ray production, we propose that the drop in the count rate comes from the loss of soft X-rays due to an additional column from the outbursting disk.

Approval mechanisms have become a primary safeguard for consequential actions in LLM-agent software. Yet the action shown for approval is often not the object ultimately consumed: workflow reload, transcript projection, argument rebinding, and durable-state lookup may reconstruct it before execution. Existing fieldflow and check-coverage analyses can establish that expected fields were inspected, but not that the inspected object version reaches the sink or that no replacement intervenes between check and use. Consequently, a locally complete repair may still leave a residual authorization bypass after reconstruction. We address this problem through three designs. (1) We formulate reconstruction-stable authorization (ReSA) over representation transitions, sink dependencies, consumed versions, and grant scope. (2) We derive obligations that judge candidate repairs and expose residual sink suffixes. (3) We implement the analysis in APAS-Finder and freeze predictions before an independent sink oracle observes execution. Predictions agree with all 28 controlled outcomes. Four matched pairs require opposite judgments despite identical field-flow and check coverage; a CodeQL composite recovers all eight when supplied object flow, dominance, interference, and the same grant contract. Two analysts agree on all four model-validation dispositions and 19/20 sink dependencies. On released consumers, five repairs prevent 60/60 tested out-of-scope effects, while three mechanism contrasts expose the predicted residual effects. Repair sufficiency therefore depends on the reconstructed action consumed, not merely on an approval record or earlier checked representation.

We characterize Griffiths positivity of vector bundles on smooth projective varieties by a finite-dimensional convex condition on first jets of sections of positive twists. A nonzero positive matrix-valued measure annihilated by the adjoint Levi operator gives the dual obstruction. We also give an explicit bundle on an abelian surface that satisfies the first-level condition, but whose complete untwisted evaluation has a differential kernel.

When two texts describe the same expression, standard metrics based on lexical overlap or whole-text similarity may fail to detect meaningful differences in how that expression is framed. We propose a framework to evaluate semiotic alignment between texts, where a semiotic profile encompasses both the contextual meaning and the discourse references made salient by a text. Our approach yields two scores, Semiotic Fidelity and Semiotic Coverage, estimating how much of one text's profile is supported by the other and how much of the other's profile it recovers. Experiments show that coverage is typically lower than fidelity, and that alignment between LLMs and human-curated data is highest at low sampling temperatures, while higher temperatures reduce this alignment.

Common worst-case analyses for uncertain finite-horizon systems consider quadratic performance metrics based on the strict Bounded Real Lemma. Thus, they assess system performance for bounded inputs, e.g., signals in L2, which exhibit a worst-case shape. Consequently, known disturbance characteristics are left unexploited and uncovered, leading to unnecessarily conservative results. The present paper develops a worst-case analysis covering arbitrarily L2-bounded worst-case signals and partially known disturbances simultaneously. This is achieved by modeling the latter using signal integral-quadratic constraints (IQCs). The resulting analysis condition relies on a dissipation inequality within the IQC framework for finite time horizon problems. This framework also readily allows to incorporate additional system uncertainties in the analysis. The approach's feasibility is demonstrated with the worst-case performance analysis of a small unmanned aerial vehicle in an urban environment.

Tropicalizations of Grassmannians resp. flag varieties parametrizing (flags of) linear spaces have been studied intensely and reveal rich combinatorial structure. Linear degenerations of flag varieties provide ways of interpolating between products of Grassmannians and flag varieties. Tropical versions of these have been introduced recently, but their combinatorial description and computation remains a challenge. We consider a particular case which allows the use of matroidal methods, namely linear degenerate short flag varieties parametrizing tuples of linear spaces such that a projection of one is contained in the other. Their fibers turn out to be linear spaces themselves under mild assumptions, which allows a comprehensive combinatorial description of their tropicalizations, and accordingly, of tropicalizations of linear degenerate short flag varieties.

Fast charging of all-solid-state batteries is limited by solid-state transport in the positive electrode, which can generate substantial concentration nonuniformity under aggressive charging. We formulate fast charging as a minimum-time boundary-control problem for a one-dimensional cathode diffusion model, subject to a terminal average-concentration target and a path constraint on the bulk-to-surface concentration difference. For constant diffusivity, we prove existence of a global minimizer and show that every minimum-time policy is maximal-feasible: the charging rate remains at its upper bound until the transport constraint becomes active and subsequently follows the active boundary. This structure motivates an offline-online strategy in which precomputed PDE responses are combined through low-dimensional algebraic operations, avoiding repeated PDE-constrained optimization. Numerical refinement and perturbation studies verify the predicted control structure and constraint satisfaction. We further investigate concentration-dependent diffusivity, quantify the robustness of the constant-diffusivity policy under model transfer, and introduce a blockwise nonlinear correction that restores admissibility when the transferred policy violates the transport constraint.

In archaeological chronology building, stratigraphic constraints arising from the excavation context are commonly incorporated into Bayesian models through order-constrained priors. However, these models suffer from well-documented artifacts: estimated durations are inflated, and the bias worsens as more samples are dated. First, we prove that this phenomenon is intrinsic to the prior: when all true ages coincide, the posterior duration converges to the prior support's width. We then propose an unconstrained posterior that does not include stratigraphic knowledge and project it onto the space induced by the stratigraphic order. The projected posterior is the Wasserstein-closest constrained distribution; it can be computed via isotonic regression on a directed acyclic graph and corrects duration inflation unlike constrained priors. Simulation studies and two archaeological case studies demonstrate substantial bias reduction and precision gains.

We introduce a new formulation of the Longest Edge Bisection (LEB) of tetrahedra entirely in sextuple space R6, where tetrahedra are represented by the squares of their edge lengths. This representation renders the LEB refinement equations fully linear and eliminates the need for coordinate-based data structures. A central difficulty in three-dimensional LEB arises when a tetrahedron possesses multiple longest edges, making the refinement rule intrinsically multivalued. We formalize this phenomenon through the notion of Multiform Longest Edge Bisection (MLEB), which systematically explores all admissible longest-edge choices. To encode this multivalued behavior, we introduce the concept of bisection patterns, defined as sequences of sextuple permutations governing the refinement process. We prove that the set of sextuples sharing a common LEB pattern forms a convex region in R6. For structurally significant families of tetrahedra, including the R1+ family and the Liu-Joe family, we show that the infinite refinement tree collapses into a finite directed graph with eight states. Remarkably, both families are governed by the same graph, differing only in their initial state. This directed-graph formulation provides a unified combinatorial description of the refinement process and offers an efficient computational framework for deep iterative LEB analysis.

We construct an irrational one-point Seshadri constant on the blow-up $X_9$ of $\mathbb{P}^2$ at nine very general points. The divisor $L=9H-3(E_1+\cdots+E_5)-2(E_6+\cdots+E_9)$ is ample and satisfies $\varepsilon(L;x)=2\sqrt{5}$ at a very general point $x\in X_9$. To prove this, we establish that the Seshadri constant of $\mathcal{O}_{\mathbb{P}^1\times\mathbb{P}^1}(1,1)$ at ten very general points is $1/\sqrt{5}$, completing the reflection approach proposed by Dionne and Roth for the ten-point case. We also prove that the same equality holds at a very general free orbit of a fixed dihedral group of order ten. This yields an irrational one-point Seshadri constant on the singular quotient surface. A plane model of its minimal resolution and a deformation of the blow-up centers then give the result on $X_9$.

Humanoid robots require diverse embodied experiences to acquire complex loco-manipulation and collaborative skills. However, existing humanoid data pipelines primarily focus on individual agents, while physical multi-robot collaboration remains difficult to scale due to costly hardware, dedicated spaces, and repeated resets. In this work, we introduce MATE, a Multi-Agent virtual TEleoperation platform for humanoid collaboration data collection that enables multiple geographically distributed operators to simultaneously control whole-body humanoids in a shared physics-based environment. MATE removes the need for multiple physical robots and co-located operation while preserving physically coupled interactions among humanoids, objects, and environments. Using MATE, we construct a multi-humanoid collaboration dataset comprising 24.1 hours of coordinated behavior across 2,500 joint episodes and five long-horizon tasks, including object handover, relay delivery, environment interaction, and cooperative transport. To improve learning from these interaction-rich demonstrations, we introduce EAIS, an Execution-Aligned Interaction Sampling strategy that computes sampling signals within an execution-aligned prefix and prioritizes task-progressing and interaction-critical behaviors. We evaluate MATE with representative imitation learning and vision-language-action policies across diverse collaboration tasks. Experiments demonstrate efficient data collection, effective policy learning, and zero-shot transfer from virtual demonstrations to a physical humanoid without real-world fine-tuning. Project page: https://yerik-yu.github.io/MATE/

Given three normed spaces $X\_0 , X\_1 , \tilde{X\_1}$, with $\tilde{X\_1}$ a closed subspace of $X\_1$ with same norm, how does $[X\_0 , X\_1 ]\_\theta$ compare to $[X\_0 , X\_1 ]\_\theta\,? This classical problem of interpolation theory has been mostly considered in the case of finite codimensional subspaces. We show here that quotient J norms are a useful tool which allows to tackle several relevant cases.

We study the high-temperature derivation of $\Phi^4_d$ measures from grand-canonical Bose gases on two- and three-dimensional tori. Building on the upper-symbol variational approach of the author's earlier work, we use relative entropy to give a simple, unified proof of relative free-energy convergence and Hilbert–Schmidt convergence of all fixed-order rescaled reduced density matrices to their Hartree counterparts. For interaction ranges $\varepsilon=\lambda^\eta$, where $\lambda$ is the inverse temperature, these results hold for every fixed $0<\eta<1/2$ in two dimensions and $0<\eta<1/26$ in three. In two dimensions, we improve the result of Jougla and Rougerie (2026) and the local $\Phi^4_2$ derivation of Fröhlich, Knowles, Schlein and Sohinger (2025). Combined with classical approximation, the two-dimensional result gives the first local $\Phi^4_2$ derivation valid for every fixed exponent $0<\eta<1/2$, allowing polynomial exponents arbitrarily close to the diluteness threshold from below. In three dimensions, we use the identification of the local measure and the stationary SPDE estimates of Nam, R.~Zhu and X.~Zhu (2025). From these estimates we strengthen their classical correlation convergence to the Hilbert–Schmidt norm. This yields the local limit at every fixed order in the same polynomial range.

The second data release of the Dark Energy Spectroscopic Instrument (DESI), based on more than fourteen million galaxies and quasars, prefers a dark energy component whose equation of state is dynamical. In the simplest two-parameter description of this behavior, the Chevallier–Polarski–Linder (CPL) parametrization, the data favor the quadrant $w_0>-1$, $w_a<0$, which implies that the equation of state crosses the phantom divide $w=-1$ at a redshift $z\simeq0.4$. We show that the local limit of nonlocal gravity, a teleparallel extension of general relativity governed by a scalar function called gravitational susceptibility $S(x)$, offers a natural explanation. In this model a cosmological constant is not allowed; dark energy is necessarily dynamical. The phantom crossing seen by an observer is an effective phenomenon generated by the time evolution of $S(z)$. We establish a correspondence: to every general-relativistic dark energy model with equation of state $w(z)$, there corresponds a modified TEGR cosmology with $w=-1$ and a suitable susceptibility $S(z)$ that are indistinguishable at the level of the background expansion. We construct the susceptibility functions that reproduce the CPL behavior favored by DESI data, and we confront the model with the combined CMB,BAO, and SNe data using Boltzmann solver codes. The recovered susceptibility displays a characteristic low-redshift dip with depth $\beta = -0.025 \pm 0.007$ at $z\simeq 0.4 $, and its derivative changes sign at a redshift equal to the phantom-crossing epoch.

Dynamic circuits, which incorporate mid-circuit measurements and classically controlled operations, extend the expressive power of quantum programs and are central to applications such as quantum error correction, state preparation, and distributed quantum algorithms. However, their classical simulation is challenging due to the exponential growth of execution branches induced by mid-circuit measurements. In this work, we develop a tensor network approach for simulating dynamic circuits by extending a DMRG-based method for quantum circuit simulation to support dynamic circuit operations. To address the exponential proliferation of execution branches, we introduce and compare two strategies: a single-path stochastic approach that samples individual measurement outcomes, and a multi-path approach that maintains an ensemble of branches. We benchmark these methods on standard dynamic circuits, including the teleportation protocol and GHZ state preparation, as well as on random dynamic circuits. Our analysis explores the trade-offs between simulation accuracy and computational efficiency. These results provide a practical and scalable framework for the classical simulation of dynamic circuits.

Liu and Ruan showed that a separable operator space has the completely bounded approximation property if and only if it admits a completely bounded frame. We show that, even for Hilbertian operator spaces, such a frame need not give rise to a completely bounded basis. More precisely, we construct a separable Hilbertian operator space with the $1$-CBAP but with no completely bounded basis. Our construction relies on a theorem of Oikhberg that provides a structural description of the completely bounded maps on a suitable operator space.

This paper proposes the design of a single linear parameter-varying (LPV) controller for the combined control and smooth transition between two modes in a spacecraft mission. Current industry practice for transitioning between different controller modes is to use a discrete switching approach. When predefined criteria are satisfied, the controller of one mode is turned off and the controller of the other is initialised, resulting in an undesirable transient behaviour. In addition, each controller must individually undergo a rigorous verification and validation (V&V) process. A single controller synthesised using LPV methods streamlines the V&V process and improves the transient behaviour. The proposed design follows a mixed-sensitivity control scheme with LPV weights that are derived from the performance and robustness requirements of the individual modes. The controller is synthesised by minimising the induced $\mathcal{L}_2$-norm of the closed-loop interconnections between the controller and weighted plant. The performance and robustness of the controller is demonstrated on an acquisition and pointing task of a flexible satellite through a Monte-Carlo campaign.

Multimodal language models traditionally rely on dedicated perceptual encoders to construct task-usable representations. More integrated architectures have recently emerged, which instead expose the shared transformer to lightly projected patches, audio frames, or discrete visual tokens. Where does this encoding happen when such representations are not provided? We find that the transformer can internalize this missing computation, constructing task-usable perceptual representations within its own early-to-middle layers before the downstream language model. We call this computational structure a Virtual Encoder. Across linear probing, similarities to perceptual encoders, and causal analyses, we identify signatures of this structure in models that receive perceptual tokens without continuous encoder-derived features. These analyses also suggest that the boundary between perception and language processing need not coincide within an architectural module. Instead, encoder-like computation can emerge as a functional regime within a shared transformer, providing a new perspective for understanding where and how multimodal models process perception.

Convolutional neural networks (CNNs) and vision transformers are both used to model the human visual system, but whether the two architectures diverge at a specific point in network depth is unclear. We compared six CNNs and two vision transformers by computing the Pearson correlation (r) between each model's predicted and measured EEG response at every layer or block, in ten participants viewing 200 natural images. For the transformer models, we also tested four token representations, from the classification (CLS) token alone to CLS combined with all patch tokens. CNNs showed strongest correspondence at the earliest layers, weakening at deeper layers, particularly later in the post-stimulus response. Transformers instead sustained strong correspondence at their deepest blocks, though not at their earliest ones. This advantage depended on token representation: pooled representations gave weaker peak correlations (r approx 0.48-0.51) than representations retaining all patch tokens (r=0.640 for CLIP-ViT-B/32, r=0.656 for DINOv2-ViT-B/14). Controlled comparisons showed architecture, not training objective, drove this effect: MoCo-v1 and ResNet-50 (matched architecture) performed nearly identically (r=0.673, 0.670), whereas CLIP-RN50 and CLIP-ViT-B/32 (matched objective) diverged until patch tokens were preserved. We propose that CNN training's classification bottleneck compresses brain-relevant information at depth, unlike transformers' self-attention and non-classification objectives. A spatial topography analysis showed a common occipital-dominant pattern across all models, indicating these differences reflect signal strength and persistence rather than distinct brain regions. Patch-preserving transformer representations sustain brain-predictive correspondence where CNNs collapse.

This paper investigates dynamical properties of the Nonlinear Walecka Model (NLWM), also known as Quantum Hadrodynamics (QHD), which provides a relativistic framework for describing nuclear matter through nucleon-meson interactions. While the original linear model successfully captures qualitative features of nuclear matter, it overestimates nuclear compressibility; consequently, nonlinear extensions incorporating cubic and quartic self-interaction terms in the scalar field $(\sigma)$ are employed to achieve better agreement with experimental data. By treating the self consistent effective-mass equation as an iterative mapping, the study explores the emergence of complex behaviors such as periodic orbits and chaotic regimes. Using tools from nonlinear dynamics, including return maps and bifurcation diagrams, we characterize routes to chaos via period doubling cascades and identify the presence of "shrimps" stable isoperiodic islands within chaotic regions of the parameter space. Furthermore, we discusses the physical implications of these findings, suggesting that crisis phenomena and structural convergence may serve as dynamical signatures of macroscopic rearrangements in the scalar mean field, potentially influencing the stability and equation of state (EOS) of dense nuclear matter in extreme environments like neutron stars.

This paper presents a new approach to the derivation of decentralized plug-and-play stability certificates that can be calculated using black-box admittance spectra, without requiring white-box models of devices. The method is based on analysing the properties of the nodal admittance matrix. The certificates ensure that the devices can be connected at any node of a network of any topology as long as the R/X ratio is within a specified range. The approach is related to the passivity concept, but uses frequency-dependent transformation matrices to check if a device, which is non-passive in a certain frequency range, can still satisfy a plug-and-play stability criterion. We illustrate the method using Grid Forming Inverters (GFMs) connected to IEEE 39 node test-case.

We will use consistency properties to characterize strongly compact cardinals, first showing an adequate Model Existence Theorem for larger fragments.

Streaming principal component analysis (PCA) seeks to recover a leading spectral subspace in a single pass over a data stream. We give a new analysis of the ubiquitous Oja's algorithm [Oja82] for the most general, gap-free variant of this problem, where no eigengap assumptions are made on the underlying mean matrix, complemented by a nearly-matching lower bound. Prior works achieving near-optimal rates for streaming PCA either required gap assumptions [JJK+16, HNWW21], or were limited to rank-one updates [AZL17, Lia23]. Our proof only uses a second moment bound on the individual stochastic updates, bypassing the almost sure bounds needed by prior near-optimal analyses, and the analogous offline matrix Bernstein bound. We also extend our result to a Rayleigh quotient notion of approximate PCA, addressing an open question of [JJK+16]. As our main application, we give gap-free differentially private PCA guarantees for sub-Gaussian data, settling Conjecture 1.1 of [Bro26] up to logarithmic factors.

Deep learning systems now mediate military decisions to use force, yet their internal logic resists inspection, their evaluation practices are gameable, and their deployment fractures accountability across dispersed stakeholders. The ethical challenge posed by these systems is fundamentally epistemic: not just whether autonomous weapons should be permitted to kill, but whether the conditions for responsible human judgment can survive when critical functions are delegated to opaque algorithms. We show that this epistemic condition produces a concrete accountability gap: responsibility diffuses across designers, operators, and policymakers while International Humanitarian Law presupposes capacities for judgment that current AI systems lack. To address this gap, we propose a governance framework that proceduralizes ethical constraints through named accountability roles, adversarial auditing with undisclosed benchmarks, tiered deployment thresholds, and a proposed NATO evaluation standard. Counterfactual analysis of eight documented cases (1988-2025) shows that each governance mechanism addresses a documented class of failure, but no single safeguard suffices in isolation: effective governance of military AI requires not only technical constraints but the institutional infrastructure to keep human judgment meaningful.

The Fitness-Fatigue model (FFM) was initially designed to gain a better physiological understanding of the impact of training loads on sports performance. For almost 50 years, simulations have been compared with the observed response of sports performance to training loads. Understanding the relationship between training load and performance should have answered some fundamental questions for the physical trainer or sports coach: 1/ how to define the best training to achieve a performance without exhausting an athlete or how to achieve a performance in a limited time; 2/ how to assess the athlete's fatigue and fitness reliably to better understand his performance; 3/ how to prevent the risk of injury. But this was not the case. Studies dedicated to the FFM have been limited to improving somewhat on Banister's initial model without really taking the necessary step back to take advantage of the mathematical framework offered by the state representation, the implicit formalism underlying the FFM. The idea behind this research strategy is that having a valid and accurate model makes it easy to address previous questions through simulation: multiple training scenarios can be simulated until the ideal scenario for a given training question is identified. The main drawback to this approach is the combinatorial nature of the exercise. This paper is not discussing the relevance of the model, but how to use it. The state representation makes it possible to study the controllability, observability and diagnosability of a system (i.e, the athlete) and thus to formally answer the three previous practical questions. It can be considered that sports science studies have missed the richness of the FFM model. Artificial learning approaches are increasingly preferred to the FFM model because they are supposed to better capture observation. However, in the light of the state representation, the FFM model could still be extended naturally while remaining mathematically interpretable, offering mathematical tools to estimate the state of the athlete, and to define the most adequate training and prevent the risk of injury. This article does not aim to solve the question of optimal training in practice, for that it would need to be validated by specialists in physiology and sports science, it just proposes to take a fresh look at training issues and to demystify the mathematical formalism adopted by Banister.

Retraining visual perception pipelines in High-Mix, Low-Volume (HMLV) automotive manufacturing must be carried out under tight annotation, energy, and time budgets, yet most Synthetic Data Generation (SDG) strategies still operate in the thousands of images. This work evaluates Semantically-Guided Domain Randomization (S-GDR), an annotation-free adaptation pipeline that couples Vision-Language Model (VLM)-based semantic captioning of a small unannotated real reference set with diffusion-based background synthesis (Stable Diffusion XL (SDXL) conditioned by ControlNet and IP-Adapter) and mask-based object composition. On an automotive multi-object detection benchmark and with a fixed budget of 200 synthetic training images, S-GDR reaches mAP50-95 = 0.739 on a real held-out test set, outperforming a domain-randomized render baseline (mAP50-95 = 0.697) as well as brightness filtering, perceptual hashing, CycleGAN style transfer, and unguided diffusion variants sharing the same 200-image budget. These initial observations position S-GDR as a promising annotation- free alternative for extreme data-scarcity regimes.