Papers

Advanced levitation optomechanics in the quantum regime requires sophisticated quantumengineered protocols operating at shorter length and time scales, demanding an increasing control over both optical and electrical potentials. Integrated chip-scale platforms offer a natural route toward such control. Here, we demonstrate optical levitation in vacuum using a miniaturized hybrid electro-optical metalens. Motion control is achieved using a high numerical aperture metalens combined with electrical active feedback using planar electrodes, enabling cooling to low phonon occupations. Reheating measurements enable us to rule out any significant influence from electric field noise; an encouraging result for the future development of on-chip levitation platforms operating close to surfaces. This compact integrated platform facilitates the precise manipulation and control of levitated nanoparticles while laying the ground toward exploiting the full capacity of metaoptics to engineer complex optical potentials, marking a significant step forward in technologies for quantum levitation optomechanics.

PRIMA (PRobe far-Infrared Mission for Astrophysics) is an infrared space observatory designed to operate over the next decade. Equipped with a 1.8 m telescope actively cooled to 4.5 K, the project is currently in the concept study phase as part of the NASA Probe Explorers program. PRIMA will carry two instruments: FIRESS and PRIMAger. PRIMAger will offer two observation modes: hyperspectral imaging and polarimetric imaging. Both channels will use ultra-sensitive kinetic inductance detector (KID) arrays, covering wavelengths from mid-infrared to far-infrared. A European consortium will develop the cold unit of the PRIMAger instrument while the Readout Electronics and Continuous Adiabatic Demagnetization Refrigerator (CADR) will be provided by Goddard Space Flight Center (GSFC) and shared between the 2 instruments. The hyperspectral mode will cover the 24-84 $\mu$m range with a spectral resolution of R $\ge$ 8, ensured by a linear variable filter placed in front of the detector. The polarimetric mode will provide polarimetric imaging in four broad bands from 92 to 235 $\mu$m, using KIDs with three polarization orientations. The main structure of the instrument is the optomechanical assembly, cooled at 1K. It supports at first the two focal plane array assemblies incorporating 0.125K detector stages. In addition, the main structure is providing the interfaces for the 0.125K thermal link, the readout cables and the filters. This paper presents the technical requirements and expected performance of the instrument, as well as the associated design of the sub-systems ensuring compliance. A major challenge will be in-flight performance verification. We will also detail the development strategy, including the planned verification and test program.

We analyzed archival far-infrared to submillimeter Herschel PACS, SPIRE, and HIFI spectroscopic observations of the S140 photon dominated region (PDR) to constrain the water vapor abundance and ortho-para ratio in this region. Toward the high-mass protostar IRS1, 52 spectral lines, including 15 water lines, are detected with the PACS and SPIRE instruments. PDR modeling suggests a UV radiation field G0 ~ 1 x 10^3 Habing units, and a thermal gas pressure of 5 x 10^8 K cm^-3 in this region. The models strongly underestimate intensities of high-J CO lines, which may indicate the presence of hot shocked gas associated with outflows along the line of sight, in addition to the UV irradiated gas. The spectral resolution of the PACS and SPIRE spectrometers is insufficient to separate the PDR and shock contributions. The PDR models further suggest that optically thick ground-state water lines trace primarily surface layers of the PDR. The gas temperature in this region is predicted to be ~ 800 K and the water abundance with respect to hydrogen nuclei reaches ~ 10^-5. However, the bulk of gas-phase water is located in a more shielded region, deeper inside the PDR, with a gas temperature ~ 24 K, and a gas-phase H_2O abundance of ~ 10^-7. A comparison of the observed water line fluxes toward IRS1 with PDR model predictions shows no evidence for departures from the LTE ortho-para ratio at the local gas temperature, which is assumed in the models. The sensitivity of the Herschel instruments was insufficient to measure the water ortho-para ratio toward the externally illuminated edge-on PDR at the surface of the S140 molecular cloud. Such observations will be possible with the next generation far-infrared spectroscopic space missions currently in development.

We give a criterion ensuring that sufficiently high sublevel sets of a discrete Morse function on a $\mathrm{CAT}(0)$ cube complex have polynomial integral homological filling functions. As one application, we verify this criterion for the Stein–Farley complexes of the Higman–Thompson groups $F_{d,r}$, $T_{d,r}$, and $V_{d,r}$. Consequently, these groups have polynomial homological filling functions in every degree $k\geq2$.

The binary perceptron model concerns the set of solutions obtained by intersecting random half-spaces. One of the most striking physics predictions for this model, going back to Krauth and Mézard [KM89] and sharpened in [HWK13, HK14], is strong freezing: typical solutions are at Hamming distance of order $n$ from every other solution. This phenomenon has attracted a lot of attention over the years, partly because of its intricate connections to statistical physics and computational complexity. We prove strong freezing at every positive constraint density for a general class of perceptron models and for any disorder with independent entries of mean zero and unit variance. More precisely, with probability at least $1-e^{-c\sqrt n}$, all but an $e^{-c\sqrt n}$ fraction of the solutions have no other solution within Hamming distance $\delta n$. In particular, our result includes the asymmetric binary perceptron at every margin, for which strong freezing has been a long-standing open problem [KM89,HWK13,HK14], and the symmetric binary perceptron, for which we recover the strong freezing results of Perkins and Xu [PX24] and of Abbe, Li and Sly [ALS21]. Our proof crucially relies on replacing the number of constraints by a Poisson variable, which makes the numbers of constraints cutting out different subsets of the hypercube independent. Since each constraint can only remove solutions, the FKG inequality then decouples the partition function from the event that two nearby configurations are both solutions.

Many agent runtimes give the agent a tool for editing its own configuration. Some of that configuration grants abilities, such as enabling a tool. Other parts set the agent's limits: which directories it may write to, who may send it messages, which network address it listens on, how callers authenticate, and the gate that blocks risky writes. If the agent can edit those limits, a single ordinary request can widen them. We study this in a deployed, model-agnostic runtime. We propose a rule: the agent may change fields that grant abilities, and may never change fields that set its limits. We enforce the rule as a containment floor inside the configuration tool and measure what happens with and without it. Without the floor, a frontier model wrote a protected value on 25 of 72 ordinary requests that gave it permission to change settings, often when the request never named the field. Prohibitions written in the system prompt failed in a predictable way. A prompt that listed the protected field names stopped every request that used those names (0 of 36 saved, against 17 of 36 with no prompt) and did not stop the requests that only described the goal (10 of 36 saved, against 8 of 36). A prompt that described the forbidden effects did the reverse. With the floor, 0 of 167 protected writes were saved, although the models attempted a protected write in 65 of those cases. A search for other routes through the tool found only one, a pinned shell, which the floor's scope statement already excludes. The study covers two models and a single agent. We state what that does and does not support.

Statistically valid estimation of racial and ethnic disparities often requires inferring the probability that an individual belongs to a particular racial or ethnic group given only their name and geographic location. The standard approach, Bayesian Improved Surname Geocoding (BISG), relies on group population frequencies for each name. Although the U.S. Census Bureau provides such information for common names and a limited set of racial categories, comparable data do not exist for many racial and ethnic groups and are rarely available outside the U.S. We propose the list-powered BISG ($\ell$BISG) method, which can be used to derive calibrated group probabilities from group-specific name lists. These lists may be compiled based on expert knowledge or generated synthetically using large language models (LLMs), and thus may be subject to unknown biases. Representing names as embeddings, we treat list membership as a proxy prediction task and apply a correction based on proximal inference to recover the target group probabilities. We validate the method on U.S. voter files with self-reported race, on the full-count 1900 U.S. Census, and on the Lebanese voter registry. We find that LLM-generated name lists yield accurate and well-calibrated probabilities as well as precise disparity estimates comparable to those obtained using methods that require name-race data. Thus, $\ell$BISG substantially broadens the applicability of probabilistic race and ethnicity prediction to settings where name-race data are unavailable.

Gauge theories describe fundamental interactions in the standard model of particle physics and build effective theories in condensed matter physics. Being notoriously hard to simulate, these theories are commonly regularized as lattice gauge theories which can be evaluated with high precision through Monte Carlo algorithms or variational methods. However, Monte Carlo algorithms are not applicable in all regimes due to the sign problem; while variational methods, quantum and classical alike, only give upper-bounds on the ground-state energy. Their precision crucially depends on the chosen ansatz. Here, we present a framework based on a hierarchy of semidefinite programs to yield increasingly good lower-bounds on the ground-state energy and propagate these bounds to extended observables like Wilson loops and mesonic strings. We demonstrate the numerical capabilities by applying the algorithm to a (1+1)-dimensional $\mathbb{Z}_2$ theory with dynamic fermionic matter and its pure-gauge version in (2+1)-dimensions. In both cases, we obtain certified intervals for the ground-state energy. For a one-dimensional system with 129 sites, the certified interval has a relative spread of $0.04\%$. For a two-dimensional system with 97 sites (corresponding to a $7 \times 8$ lattice), the relative spread is $2.08\%$. Beyond energy estimates, the proposed method provides rigorous bounds on both short- and long-range observables such as Wilson loops over multiple plaquettes and the magnitude of the mesonic string. The method can be both used as a computational microscope into many-body physics and a way to certify results of quantum simulators.

Adapting vision-language-action (VLA) models to deployment-time distribution shifts is important for reliable robotic operation, but conventional first-order adaptation can exceed the memory budget of inference-oriented deployment platforms. Zeroth-order (ZO) optimization offers a forward-only alternative with inference-level memory, but accurate gradient estimation requires many perturbation queries, making naive ZO prohibitively slow for large VLA models. We present VLA-ZO, a framework for fast ZO adaptation that exploits the structure of VLA computation. By confining adaptation to the action side, VLA-ZO keeps the expensive vision-language prefix frozen and reuses its conditioning states across perturbation queries and optimizer steps, while schedule-aware prefetching hides state-transfer overhead. On LIBERO camera-viewpoint shifts, VLA-ZO reduces end-to-end adaptation time by 25.59$\times$ at $q=16$ and 32.54$\times$ at $q=64$ relative to baseline ZO, while improving average task success from 48.27% without adaptation to 58.17% and 63.58%, respectively. These results show that making ZO faster can make larger query budgets practical, providing a promising path toward resource-efficient VLA adaptation on deployment platforms.

Probabilistic Neurosymbolic Learning (PNL) combines neural predictions with symbolic reasoning, enabling end-to-end learning from final-output supervision without labels for intermediate concepts. A central challenge is probabilistic inference: state-of-the-art approaches often rely on materializing the logical provenance of a query, which can itself become a major computational bottleneck. We introduce Dynamic Probabilistic Neurosymbolic Learning (DPNL), an oracle-guided framework that avoids requiring complete provenance materialization before inference. DPNL lazily explores the space of intermediate assignments, while oracles resolve entire regions that can already be certified to produce or exclude the target output. We establish conditions ensuring soundness and termination. ApproxDPNL extends the same search with early termination while maintaining certified bounds on the exact output probability, providing controlled approximation guarantees. The oracle interface decouples inference from the representation of the symbolic component, enabling problem-specific reasoning within the same framework. Experiments on several neurosymbolic tasks show that DPNL and ApproxDPNL substantially extend the range of problem instances tractable by probabilistic neurosymbolic inference.

Open-ended scientific discovery often requires repeatedly proposing and evaluating candidate solutions. LLM-based systems can support this process by generating and refining executable solutions from verifier feedback. Methods such as TTT-Discover use test-time training (TTT) to update the solution-generating LLM from verifier feedback, adapting its generation policy to improve subsequent proposals on the target problem. However, this becomes expensive when reliable execution requires a large model, since training must maintain gradients, optimizer states, and policy statistics while repeatedly generating long, structured outputs. It also complicates credit assignment: outcome-level verifier feedback must jointly evaluate the high-level strategy and its low-level implementation. In this work, we introduce Guidance-TTT, which separates these roles. A compact guidance model is trained at test time to propose high-level strategic changes, while a frozen execution model implements them as complete executable solutions. At each step, the system selects a promising previously discovered solution, proposes a change, executes and verifies it, and updates only the guidance model using an adaptive group-relative RL objective. This concentrates test-time learning on short strategic decisions while retaining the implementation capability of a substantially stronger model without adapting it. Without web access, Guidance-TTT produces strong solutions across four distinct domains: combinatorial optimization (Polyomino Packing), heuristic programming (AHC058), machine learning (Lasso), and GPU kernel optimization (TriMul). Across these tasks, it outperforms the best solutions reported in prior work while remaining competitive with state-of-the-art results on public online leaderboards. Code is available at https://github.com/Human-Agent-Society/reef/tree/guidance-ttt-support.

We develop a discrete adiabatic framework for Gibbs-state preparation in classical and quantum optimisation algorithms. For finite time-inhomogeneous reversible Markov chains, we derive a tracking theorem that bounds the distance between the evolving distribution and the instantaneous stationary state. The bound combines contraction of accumulated error with the new error generated as the stationary distribution changes. For Gibbs paths, it yields explicit step-complexity bounds and an effective tracking metric determined by the spectral gap and equilibrium energy fluctuations. The associated constant-speed schedule minimizes the metric-energy functional and, in the small-gap regime, takes the form $\dot\beta\propto\delta(\beta)/V(\beta)$, where $V(\beta)=\sqrt{\operatorname{Var}_{\pi_\beta}(E)}$. We then apply the discrete quantum adiabatic theorem to temperature-dependent Szegedy quantum walks, whose eigenphase gap satisfies $\Delta_w=\Theta(\sqrt{\delta_+})$, with $\delta_+$ the underlying Markov kernel's right spectral gap. Under uniform bounds on the discrete operator variation and suitable spectral and path-integral assumptions, gap-adapted schedules give a sufficient fixed-accuracy cost of $O(\delta_{+,\min}^{-1/2})$. This gives a quadratic improvement in gap dependence relative to the classical inverse-gap relaxation scale under the stated assumptions. Numerical tests on a solvable two-state model and Sherrington-Kirkpatrick instances compare tracking and final preparation errors and investigate the transfer of schedules from smaller to larger systems.

In this paper we prove the stability and the continuity of the free boundaries of two-phase and one-phase weak solutions to the Stefan problem in any dimension. Our proof has two main ingredients. The first one is an energy conservation principle for weak solutions that we derive for general domains in both the one-phase and the two-phase settings; this energy conservation principle provides the modulus of continuity for the displacement of the free boundary and is a flexible tool for analyzing long-time behavior of solutions. The second key ingredient for the control of the displacement of the free boundary is a new lower density bound for the melting region at free boundary points that move with maximal velocity. We also discuss some applications, showing a series of qualitative and quantitative results on the asymptotic behavior of weak solutions.

Freeway on-ramp merges are major sources of congestion, causing significant economic and environmental costs. While Deep Reinforcement Learning (DRL) offers a promising solution for ramp metering, existing approaches rely primarily on aggregated macroscopic data. Connected vehicles (CVs) provide vehicle-level observations that can complement aggregate traffic measurements, but their limited penetration produces incomplete microscopic information. This paper proposes a hybrid observation representation combining macroscopic traffic measurements with a two-channel grid encoding observed CV presence and speed. A Dueling Double Deep Q-Network processes these inputs to select ramp-metering green durations. The controller is trained under varying traffic demands and CV penetration rates and evaluated against ALINEA and macroscopic-only DRL variants in SUMO. Across 50 matched evaluation scenarios, the hybrid controller under partial CV visibility reduces the reported total travel time by 11.4 % and mean spillback duration by 84.9 % relative to ALINEA. Evaluating the same trained policy with full CV visibility yields a further travel-time reduction of approximately 1.6 %. Analysis across penetration rates suggests that the performance gap decreases as microscopic observations become more complete. These results support the use of complementary macroscopic and sparse microscopic observations for learning-based ramp metering. The source code implementation of the model is available at: https://github.com/youcefMehamlia/Multimodal-DRL-RMC

Sensor placement for stochastically arriving targets is studied using a void probability objective, defined as the probability that no target remains undetected over a finite horizon. Direct optimization is intractable because it requires an expectation over a random intensity field. A common surrogate based on Jensen's inequality replaces the random field with its mean, yielding a tractable objective but discarding distributional information. The proposed Gamma Laplace surrogate approximates cellwise exposure variables with moment matched Gamma distributions and evaluates the objective using their closed form Laplace transforms. Unlike scalar moment corrections or local expansions, this approach operates at the distribution level and retains a Laplace transform structure under an independent Gamma approximation. A log transformation and constant shift yield an objective shown to be monotone submodular, enabling efficient greedy optimization with performance guarantees. Numerical experiments on real ship traffic data show consistency with the Jensen surrogate in low uncertainty regimes. Under moderate uncertainty, the method improves candidate location rankings, leading to more robust sensor selections and reduced sensitivity to variability in target arrivals.

Frequency crowding, the close spacing of qubit transitions, limits superconducting quantum processors through crosstalk, leakage, and spectator dependent errors. We introduce a Hamiltonian based framework that maps two- and three-body collision mechanisms onto a Max-k-Cut problem on qubit frequency allocation. In order to make larger lattices tractable, we introduce a cluster-stitching protocol that decomposes larger lattices into overlapping subgraphs and reconciles their local frequency assignments into globally consistent configurations. We tested our proposed framework across multiple qubit architectures to suppress dominant collision penalties by revealing a hardware residual crosstalk. We benchmark digitized counterdiabatic QAOA (DC-QAOA), standard QAOA, and simulated annealing. Counterdiabatic terms improve QAOA optimization near steep collision penalties, while simulated annealing achieves the lowest costs on the tested instances. These results indicate that our hardware-aware optimization connects microscopic interaction physics to processor-level frequency planning. These results enable a systematic solver for benchmarking of scalable software hardware co design.

Ultrasound (US)-based auricular vagus nerve stimulation (aVNS) is emerging as a versatile, noninvasive modality for neuromodulation - spanning clinical therapies (e.g., pain management, depression) and general well-being applications. However, most existing US-based aVNS systems remain bulky and require wet coupling media (e.g., ultrasound gel) to achieve both spatially localized stimulation and efficient acoustic transmission. We present a wearable US stimulation system combining a personalized, dry-coupled earpiece with a battery-powered, wireless US probe. The earpiece integrates a 2 MHz piezoelectric transducer fully encapsulated in Humimic material designed for anatomical fit and stable coupling without externally applied gel. Hydrophone measurements of the fully encapsulated earpiece in water give a peak rarefactional pressure of 0.24 MPa at 15 mm for a 15 V unipolar excitation. We further demonstrate in vivo feasibility through fully dry, in-ear 2 MHz pulse-echo acquisitions under realistic wearing conditions, confirming effective US transmission without the need for coupling gel. These results demonstrate the integration of a personalized dry acoustic interface with battery-powered stimulation electronics, providing a wearable platform for investigating US-based aVNS. Future studies will focus on functional outcomes, including heart rate variability and pupillary responses during stimulation.

A single auction can have both a shill-proof equilibrium and a non-shill-proof equilibrium in the model of Komo, Kominers, and Roughgarden. We give an explicit single item example with three bidder positions, publicly observed actions, positive winning prices, and a strictly regular i.i.d.\ value distribution. Real bidders have strict incentives in both equilibria. An initial public action conveys information about whether the final position is real. The resulting belief changes the middle bidder's response and reverses the first shill's strict preference between two actions. We verify both equilibria and compute their expected revenues.

We show that a convex surface in Euclidean 3-space is a sphere if the area cut off from it by a slab of some fixed width depends only on the direction of the slab. This result generalizes theorems of Blaschke and Stamm, which assumed the slab-area property for every width. It holds also for any smooth closed embedded surface, and we obtain analogous results in higher dimensions. The proof is based on an averaging identity, which relates slab areas to the Newtonian potential of the surface, the electrostatic characterization of spheres by Mendez and Reichel, and analytic microlocal properties of the Radon transform, which are used to show that the slab-area property forces real analyticity, via theorems of Kashiwara and Boman.

Diffusion transformers (DiTs) achieve state-of-the-art image generation, but their sampling cost limits deployment. Quantizing both weights and activations to 4 bits reduces this cost, yet existing methods fall short in one of two ways. Calibration-based methods are tied to a specific checkpoint and prompt distribution, whereas data-free Hadamard rotation, effective for LLMs, loses quality on DiTs. We show that this loss has a structural cause. Adaptive layer-norm conditioning adds a per-token mean to the activations, and at the widths of the evaluated DiTs, the Hadamard rotations used by data-free methods cannot spread this mean uniformly across coordinates. A single dominant direction therefore survives the rotation and sets the quantization range. We introduce CentriQ, a calibration-free quantizer that centers each token before rotation and restores the mean exactly through a rank-1 full-precision branch, so that per-token scales follow in closed form without data. Weights are fitted under a robust $\ell_p$ objective that tracks the dense mode of each group and discounts heavy tails. Across three DiTs, CentriQ matches the quality of calibrated SVDQuant at 4 bits, whereas calibration-free weight quantizers with plain per-token activation quantization collapse or degrade substantially. CentriQ outperforms the strongest calibration-free method reported to date at 2-bit weights. It is also the first calibration-free method to retain usable image quality at 2-bit activations.

Partial differential equation (PDE) inverse problems are often ill-posed, making fine-scale details difficult to recover. We address this problem by introducing a learned observation-complementary latent representation that preserves reconstruction-relevant information and is combined with the observation to reconstruct the unknown field. Building on this representation, we propose OCL-PDE, a generative framework that encourages the observation to guide large-scale structure and the latent to supply complementary fine-scale details. OCL-PDE is built on a physics-aware autoencoder (AE) and conditional Flow Matching, supporting inverse reconstruction as well as forward PDE prediction. Experiments demonstrate improved reconstruction accuracy and fine-detail recovery compared with the evaluated baselines.

Substantial reduction in launch and manufacturing costs has resulted in the accelerated deployment of small satellite missions, with commercial off-the-shelf (COTS) components becoming the prevailing standard for specific subsystems. However, this modular architecture introduces critical security risks, most notably in the Communication Subsystem (COM), which is continuously exposed by design and implicitly trusted as the entry point for command and control. We construct a tailored threat taxonomy for attacks targeting the COM subsystem and analyze representative COM systems from various vendors. Our findings uncover severe vulnerabilities across firmware, protocols, and architectural designs. This work presents the first in-depth security evaluation of widely deployed COTS COM modules employed in small satellites, identifying vulnerabilities affecting dozens of missions. To assess the real-world impact, we correlate our discoveries with open-source telemetry data, inferring at least 28 vulnerable missions in orbit that are susceptible to hostile takeover. Our work reveals that satellite COM subsystems form an attractive and dangerously neglected attack surface, necessitating urgent attention from the community.

Foundation models can generate scientific code, but authoring a scientific simulator (an executable program encoding hypotheses about how mechanisms generate observable signals) requires iterative refinement. Scientific adequacy rarely admits a unique implementation or exact test, so simulators must instead be judged against limited real observations. We study this setting as scientific simulator authoring under weak empirical feedback, where distributional comparisons between simulated and real signals guide revision, and the target is the simulator itself rather than only its generated samples. We introduce SimAuthor, a persistent authoring harness that retains and revises executable simulators, separates scalar search scores from structured discrepancy feedback, and accumulates reusable implementation mechanisms. We evaluate SimAuthor on six biomedical tasks spanning cardiac and respiratory audio, photoplethysmography (PPG), and electrocardiography (ECG). Under a fixed 100-attempt budget, SimAuthor outperforms PUCT score search on all six tasks, generally outperforms textual-strategy optimization, and achieves the highest endpoint score on five of six. The authored simulators also improve on unseen recordings, transfer to independent pretrained representations, and yield substantial out-of-distribution gains in downstream ECG classification. Finally, 111 of 138 audited revisions alter program structure and account for 86.1% of the signed score improvement. These results suggest that persistent revision can progressively convert foundation-model knowledge into better executable scientific simulators from limited empirical evidence.

We provide in this text a new framework for a family of combinatorial Hopf algebras. We adopt for this the language of species and twisted bialgebras (also known as Hopf monoids). We define the category of combinatorial twisted bialgebras (briefly, CTBs), a class of twisted bialgebras satisfying strong combinatorial conditions of compatibilities of the product and the coproduct with the underlying combinatorial structure. The considered morphisms also have to respect the combinatorial structure, in some sense. Many classical examples fit into this framework, including Hopf algebras of graphs, rooted trees, posets, hypergraphs, symmetric functions, boolean maps, etc. Most of known combinatorial Hopf algebras can be obtained from a CTB by application of a Fock functor, or by duality. A central result is the introduction of a universal CTB denoted by $\mathbf{Exch}$, built from collections of compositions satisfying a certain exchange condition. It has a special character $\epsilon$, such that the pair $(\mathbf{Exch},\epsilon)$ plays a role analogous to that of quasi-symmetric functions for graded and connected Hopf algebras: it is the terminal object in the category of CTBs equipped with combinatorial characters. This leads to universal morphisms that encode important information about the combinatorial structure of coproducts. The natural order on the set of compositions on a fixed set is used to define three important sub-objects $\mathbf{Exch}\_-$, $\mathbf{Exch}\_+$ and $\mathbf{Exch}\_{+\hspace{-2mm}+}$ of $\mathbf{Exch}$. We also studies polynomial invariants associated with CTBs. It establishes a correspondence between characters and polynomial invariants. Well-known invariants such as the chromatic polynomial of graphs and the Ehrhart polynomials of posets arise naturally within this framework. We show that, for a given degree, only finitely many polynomial invariants can occur. We show that these universal polynomial invariants can be used to give cancellation-free formulas for the antipode or the Eulerian idempotent, under conditions on the CTB, and use this for an example based on rooted trees, coming from a Hopf algebra used in linguistics. Results are also obtained for families of polynomial invariants with the alternating sign condition, or satisfying a reciprocity principle. We also extend the theory to combinatorial twisted double bialgebras (briefly, CTDBs), which involve two interacting coproduct structures. These generalize previously known examples arising from graphs, posets, hypergraphs, and rooted trees. The twisted approach preserves the combinatorial richness of these structures while providing a unified algebraic framework. We show that not any CTB can be made a CTDB, leading to the introduction of the notion of quasi-cocommutativity. In particular, we show that $\mathbf{Exch}\_+$ is not a CTDB, and construct a sub-object which is, in a unique way, and maximal for the inclusion. In the cocommutative case, simplifications naturally occur, and we show that in this case, a CTB of hypergraphs plays a central role, especially two sub-objects based on connectedness systems and antichain covers. We also show that, in the cocommutative case, the universal polynomial invariants are always chromatic polynomials of hypergraphs, no matter which CTB is considered. Finally, forgetting the combinatorial underlying structure, we study the algebraic structure of $\mathrm{Exch}$, with the help of a twisted version of Loday and Ronco's rigidity theorem for infinitesimal bialgebras.

Large Language Models are increasingly used in software development processes that rely on defined states, rules, and approvals. This creates a tension between the flexibility of LLMs and the need for reliable and traceable process states. We introduce Controlled Non-Determinism, a process-oriented approach that allows variation without letting it directly determine the authoritative process state. We place LLM-based processing within a controlled variation space that is bounded by a Deterministic Envelope. Before execution, we define the process-relevant properties of the result and the exit conditions. We also record the task configuration. These elements remain fixed during execution. At the end of the variation space, an exit check determines whether the result satisfies the predefined conditions and may become the next authoritative state. Different runs may produce different admissible results while the transition to an authoritative state remains controlled. We illustrate the approach with regulated software development and derive design guidelines for LLM-based changes whose results can be checked before they become part of the authoritative software state.

The ever-growing number of satellites and resident space objects in low Earth orbit keeps increasing the risk of collision between these objects. To mitigate this risk, the development of new space situational awareness tools and a new generation of probabilistic emulators of the thermosphere is increasingly felt by the community of operators and scientists. We previously built a Reduced Order Probabilistic Emulator based on 3 steps: dimensionality reduction, dynamic modeling, and uncertainty quantification. Here we further develop the dynamic modeling side within ROPE using a class of stable and autoregressive nonlinear models inspired by SINDy, a framework for the identification of the nonlinear dynamics. We use this framework, which we call SINDy-AR, to emulate the thermospheric density simulated by TIEGCM. This is also the first time a SINDy-AR framework is applied to such a high dimensional system as the thermospheric emulation because of its complexity. The dynamical emulators are selected on stability and accuracy criteria, so that they can be relied on in operations and space situational awareness applications. Building surrogate models with SINDy-AR can show dynamical differences between the learned emulations. The state-dependent structure of the TIEGCM emulation shows compatibility with the presence of terdiurnal, 27-day linked to solar rotation, semiannual, and annual tidal waves. The execution speedup of the whole SINDy-AR pipeline with respect to TIEGCM 2.0 is about 90,000 times, which makes the new framework capable of being deployed on board a satellite given the low computational constraints it would be subjected to.

Hard carbon self-supported electrodes (HC SSEs) have gained significant interest as an alternative to classical binder-based anode materials for sodium-ion batteries (SIBs), eliminating the need for binders, solvents, conductive carbon, and current collectors. In this work, we investigate the impact of HC thickness and macroporosity, as well as the presence/absence of an electrolyte additive, on the formation of the solid electrolyte interphase (SEI) and electrochemical performance. Three cellulose-based filter paper (FP) precursors with different thicknesses were used to prepare HC SSEs through a pyrolysis process at 1500 {\textdegree}C, and then these were compared with an HC SSE obtained from commercial carbon fabric. The results highlight the importance of appropriate structural, morphological, porosity, and surface chemical properties of the materials to achieve high initial Coulombic efficiency (up to 93%) and high reversible capacity (up to 328 mAh g -1 at 37.2 mA g -1 ). However, the cycle stability was greatly impacted by the electrode thickness/macroporosity and the electrolyte additive. In NaPF6 without fluoroethylene carbonate (FEC) additive, the maximum number of cycles (50) was obtained for the thinnest electrode (79 $\mu$m), while rapid fading (after $\approx$1-5 cycles) was observed for electrode thicknesses >185 $\mu$m. By using the FEC additive, the fading is mitigated and cycling stability (100 cycles) is reached for all the electrodes, except the commercial one (5 cycles), due to its highest thickness (1042 $\mu$m). The improvement in stability could be explained by the buildup of a thin homogeneous inorganic-rich SEI containing more NaF in the presence of FEC, which is more stable, protective, and electronically conductive.

The Lipschitz property of a deep neural network provides a direct measure of its sensitivity to input perturbations and, when explicitly controlled, offers a principled way to limit the propagation of errors and improve robustness. Over the past decade, Lipschitz-bounded layers have been incorporated into increasingly expressive and high-performing deep models, narrowing the gap between empirical robustness and formal, by-design guarantees of stability. This article introduces the fundamental concepts underlying Lipschitz-bounded neural networks, explaining the principles behind Lipschitz-constrained layers, the mechanisms used to enforce their bounds, and how they yield robustness certificates at the cost of a single forward pass. The tutorial concludes by discussing emerging and open directions, highlighting Lipschitz control as a general framework for offering guaranteed, by-design stability.

Language-model systems batch questions for throughput, but unrelated questions should not change a target's answer when its input and numerical execution are fixed. We study compression of the key and value cache, which stores attention representations reused during generation. With request-local groups, Transformers' Half-Quadratic Quantization (HQQ) backend updates compression parameters separately but uses a shared average error to decide when all updates stop. Replacing only the question batched with the target changes four-bit HQQ answers in 170/384 test comparisons across two models. Replaying the other execution's update counts reproduces its complete answer and cache fingerprints in every changed pair, in both directions. Computing the stopping mean in FP32 reduces cache differences but leaves answer changes. Native HQQ also changes confirmed numerical correctness in eight arithmetic pairs. Fixed iterations and request-local stopping remove observed companion dependence under matched controls. Request-local stopping remains sensitive to synthetic padding changes at the tensor level. Fixing the original iteration budget removes this decision path without tuning. Neither repair has an established quality advantage, and natural rebatching still changes answers. Request-independence audits must cover stopping decisions as well as quantization groups.

World models, which learn how environments respond to actions, are emerging as a powerful paradigm for planning through imagined futures, transforming decision-making across games, robotics and autonomous driving. Bringing this capability to manufacturing could enable process decisions on timescales inaccessible to high-fidelity simulation. Here we introduce a generative world model for localized highly dynamic laser melt pool that predicts evolution from histories of temperature and phase morphology under candidate actions. Its generative latent dynamics capture the effects of unresolved melt flow, enabling more accurate recursive rollouts than deterministic regressors under transient laser inputs. Because the learned dynamics are differentiable, the model can serve directly as a predictive control plant. Gradients through imagined futures optimize laser schedules that regulate melt-pool depth over previously unseen geometry, path, initialization. We further distil this optimization into an amortized policy that produces control actions in a single forward pass, providing a proof of concept for real deployment on machines.