Papers

We make highly accurate numerical estimates of basic properties of the invariant measure for Liverani-Saussol-Vaienti intermittent maps, an archetypal slowly mixing dynamical system. We solve the challenge of precise and efficient estimation for a map with non-uniform expansion, where the transfer operator does not have a spectral gap. We do this using an Abel function, which solves the neutral dynamics, and which we can compute accurately via an asymptotic expansion. Our work covers both finite and sigma-finite invariant measure cases. In particular, we obtain the first practical estimates for the parameter far from zero, including the sigma-finite case. This opens the door to much deeper numerical study of intermittent dynamics than was previously possible. A driving motivation for this work is the upcoming proof of optimal rates of memory loss which works equally for finite and infinite invariant measure cases. No prior results on rates of memory loss for dynamical systems with infinite invariant measure exist, with a single exception of a recent paper by I.Chevyrev and A.K. on null recurrent Markov chains.

Analogue and digital Hamiltonian simulation represent two distinct approaches to making one quantum system replicate the physical properties of another, with consequences ranging from practical applications to complexity theory and quantum gravity. They are rooted in two distinct regimes of quantum dynamics: time-independent Hamiltonians for the former; fully controllable time-dependent quantum circuits in the latter. Time-periodic Hamiltonians represent an intermediate regime. In this work, we establish a theory of Floquet simulation where we use periodically driven Hamiltonians to synthesise time-independent ones. We show that a set of interactions $S$ can Floquet-simulate every Hamiltonian in the Lie algebra $\mathrm{Lie}(S)$, and consequently we give a complete and constructive characterisation of Floquet-universal Hamiltonians that are able to produce any target Hamiltonian. Notably, our construction uses only $O(1)$ local interaction strengths and ratios thereof, avoiding the impractical multi-scale local interaction strengths often required in analogue simulation via time-independent Hamiltonians. Instead, the construction requires a range of driving frequencies which scales polynomially with system size for important classes such as $k$-local lattice Hamiltonians. This has immediate complexity-theoretic implications, including numerous BQP-completeness and QMA-hardness results for natural physical properties and quantities studied in Floquet physics.

Searches for radiative decays of keV-mass dark matter have been limited by energy resolution. We propose a strategy for the XRISM/Resolve low count rate observations, and search the 3.48-3.56 keV band for a decay line from the Milky Way halo. Despite a lower exposure, our bounds are stronger than those from XRISM observations of galaxy clusters. We also identify a residual at E = 3.5311 keV with ~3sigma local significance, coincident with the previously reported unidentified feature, and having no plausible atomic or instrumental counterpart. These bounds will continue to tighten as additional pointings become available.

A surface photographed under even light presents nearly the same appearance from every angle; the same surface under uneven light does not. Exposure changes between views, illumination varies within a single image, and locally strong light sources leave one region bright and its neighbor in shadow. Multi-view reconstruction methods such as 3D Gaussian Splatting treat these lighting artifacts as if they were properties of the scene, entangling capture-specific illumination with the geometry and color they recover. We present EvenSplat, a framework that separates the two. EvenSplat couples an image-space illumination decomposition with an illumination field carried by the Gaussians, so that the same explanation of the lighting is shared between the two-dimensional and three-dimensional views of the scene; a camera-response network and a local exposure-compensation module absorb the global and residual differences that remain across training images. Through extensive experiments across multiple datasets and diverse forms of uneven illumination (cross-view exposure, spatial illumination variation, and high-contrast lighting) on both real-world captured and simulated benchmarks, EvenSplat generally outperforms state-of-the-art methods, particularly under high-contrast illumination.

We study the focusing one-dimensional cubic nonlinear Schrödinger / Gross–Pitaevskii equation (NLS-GP), where the potential of the underlying linear Schrödinger operator, $H_V=-\partial_x^2+V(x)$, is compactly supported. In \cite{turner2026resonance} the authors proved that purely imaginary zeros (transmission resonances) or purely imaginary poles in the lower half plane (scattering resonances) of a reflection coefficient of $H_V$ seed branches of resonance-induced nonlinear bound states, and that these states bifurcate at a strictly positive $L^2(\mathbb R)$ excitation threshold. This is in contrast to nonlinear bound states which bifurcate at zero $L^2$-norm from point spectra of $H_V$ (corresponding to poles in the upper half plane). In this paper we establish precise criteria for the nonlinear orbital stability and instability of the resonance-induced states near the bifurcation point. A corollary is that resonance-induced nonlinear states are orbitally stable if i) the underlying linear (scattering or transmission) resonance frequency is sufficiently small, and ii) the corresponding linear resonance eigenmode is strictly positive. Numerical simulations are presented to explore regimes not accessible to our theory, and to explore the large time dynamics for initial conditions near stable and unstable resonance-induced nonlinear bound states.

Geometric quantum machine learning incorporates symmetry into quantum models, but how symmetry shapes their expressivity and guides effective model design remains insufficiently understood. We address this question through the Fourier representation of quantum Fourier models (QFMs). Symmetry organizes the frequency spectrum into orbits and sums the Fourier coefficients within each orbit into a symmetrized coefficient. When QFM trainable layers form independent exact 2-designs, the variance of each symmetrized coefficient equals the sum of the coefficient variances in its orbit. For single-layer QFMs with $\varepsilon$-approximate 2-design trainable layers, we bound the deviation from this identity. The resulting bound for individual Fourier coefficients can be exponentially tighter than an existing bound. The hyperoctahedral group provides an example of orbit growth that can mitigate vanishing expressivity of the symmetrized coefficients. Symmetrization of QFMs over an elementary abelian 2-group also yields pure multivariate Chebyshev polynomial basis functions. We introduce randomized encoding, which implements invariant models without ancilla qubits or the additional circuit depth for quantum twirling. We evaluate the models as quantum physics-informed neural networks (QPINNs) on two-dimensional screened Poisson and stationary viscous Hamilton-Jacobi equations. Under hard boundary constraints, QPINNs using exact symmetrization and randomized encoding achieve the lowest mean errors in the two benchmarks, respectively.

As LLMs take up the role of authoring charts using visualization domain-specific languages (DSLs), the human constraints that shaped those languages may no longer apply, as what is easy for a person is not necessarily easy for a model. To understand how LLMs might work better with DSLs, we explore where and how they fail with current DSL designs. We evaluate 10 JSON-style visualization DSLs with 41 tasks across 3 LLMs, then assess the generated specifications with JSON and rendering checks, and qualitative coding of failed cases. Analyzing how this specification generation process fails, we identify four recurring failure patterns, link each to specific DSL features, and discuss design considerations for future DSL designs.

While the literature on blockchain-assisted intrusion detection and prevention systems (IDS/IPS) for Internet of Things (IoT) and Industrial Internet of Things (IIoT) networks is mature, existing systematic reviews suffer from two critical limitations: they overlook the structural shift toward modern Endpoint Detection and Response (EDR) and Extended Detection and Response (XDR) architectures, and they conflate blockchain's distinct functional roles into a single monolithic category. This Systematization of Knowledge (SoK) addresses these gaps by proposing a three-axis taxonomy that classifies proposals by detection-system class (NIDS, HIDS, EDR/XDR), blockchain functional role, and response-automation maturity. Synthesizing research published in high-impact venues between 2019 and 2026, we provide a rigorous gap analysis exposing why a genuine per-endpoint blockchain-anchored response loop remains nearly nonexistent due to latency, deployment, and community mismatches. Furthermore, we evaluate structural, cross-cutting challenges persisting across the literature, including consensus latency on constrained devices, post-quantum cryptographic vulnerability, smart-contract attack surfaces, and the adversarial vulnerability of evolving LLM-based detection engines. Finally, we outline a comprehensive research agenda centered on hybrid on-chain/off-chain orchestration to bridge the gap between decentralized trust and rapid response automation.

Multimodal Retrieval-Augmented Generation (MRAG) has emerged as a reliable and cost-effective technique of grounding the generative capabilities of Multimodal Large Language Models (MLLMs) into relevant, up-to-date, external knowledge. Despite presenting several benefits, such as reducing hallucinatory behavior, they also introduce new attack surfaces, including leakage of private information and vulnerabilities against data extraction attacks. In this paper, we introduce $\immrag$, an adaptive and automatic data extraction attack procedure operating in a black box setting against image-returning MRAG, a configuration in which the retrieved visual artifact is itself the response. Each query blends an attacker-held shadow image with an image already recovered from the system, and relevance-weighted resampling steers subsequent queries towards regions of the embedding space that still yield novel retrievals. Unlike current extraction attacks that aim to persuade the model towards data leakage by placing a malicious query as a textual prompt, $\immrag$ embeds the malicious instructions inside a user-given input image. We evaluate $\immrag$ on three plausible and distinct real-world scenarios: medical assistant, document-focused helper and general purpose tool. The experiments involve the study of the effectiveness of the attack on multiple CLIP-family retrievers, as well as the impact of various generators. A single 2500-query run reconstructs up to 611 distinct radiology images, 566 document scans and 416 general-purpose images under local-feature correspondence, and reaches up to $5.6\times$ as many distinct datastore items as a non-adaptive baseline. Our results show the urgent need for safeguards specifically designed for multimodal data.

Urban environments are shaped by design choices with long-term implications for health, safety, and quality of life, yet evaluating proposed interventions remains costly, time-consuming, and often impractical. Existing geospatial vision methods largely focus on monitoring urban indicators from aerial and street-view imagery, rather than proposing interventions and estimating their effects on such indicators. Moving beyond recognition, we introduce the problem of discovering interventions that improve target indicators for a given aerial or street-view image. We argue that a black-box indicator model, combined with a generative editing model, can serve as an implicit digital twin for testing intervention hypotheses. We present VIDA-Geo , a multi-agent system that explores this intervention space by coordinating segmentation, diffusion-based inpainting, and indicator scoring models to produce interventions that are both perceptually realistic and aligned with real-world policies. We evaluate our system on 8 indicators across aerial and street-view imagery, measuring changes in factors such as perceived safety and greenery. Our approach outperforms existing baselines in many cases, achieving up to 2X higher perceptual quality and policy alignment scores. Finally, our model provides users with multiple candidate interventions, supporting an expert city-planner-in-the-loop workflow.

We study two three-dimensional quantum superintegrable systems in nonvanishing axially symmetric magnetic fields. For each model the integrals generate a quadratic algebra with a Casimir, and finite-dimensional deformed-oscillator representations yield algebraic spectra. The same spectra are recovered by separation of variables. In circular parabolic coordinates the separated equations are sextic biconfluent-Heun equations with finite polynomial sectors. We formulate them as Sturm eigenvalue problems with the physical energy as a parameter and the separation constant diagonalized. After gauge transformation, each equation admits an $sl(2)$ algebraization and reduces to a finite tridiagonal matrix. We also construct a pre-separation Sturm representation of each complete Hamiltonian, taking the inverse-square coupling as the Sturm eigenvalue. The transformed integrals remain commuting and, after fixing the axial integral, changing variables and gauge rotating, the two-variable Sturm Hamiltonian and its non-central integrals belong to the universal enveloping algebra $U(sl(3))$. We thus obtain three complementary algebraic descriptions: the quadratic-algebra/deformed-oscillator representation of the original Hamiltonian, the $sl(2)$ algebraization after parabolic separation, and the $sl(3)$ algebraization of the complete Sturm problem before separation. Although the two magnetic Hamiltonians are distinct in the original classification, fixing the axial integral reduces them to the same singular 2:1 oscillator normal form with different effective parameter embeddings. This explains the common $sl(3)$ structure without implying equivalence of the original magnetic systems. These results show how distinct hidden algebraic structures and exact or quasi-exact solvability can emerge at different stages of a multiseparable superintegrable system.

The periodically driven Duffing–Holmes oscillator is strongly multistable: for the same forcing amplitude and frequency, periodic, chaotic, and antiperiodic attractors coexist, each with its own basin of attraction. Antiperiodic orbits are periodic orbits invariant under a shift of half a driving period combined with a sign reversal of the coordinates, a symmetry of the equations of motion. Guided by a continuation map of the parameter plane, which locates the regimes but is blind to their coexistence, we explore the space of initial conditions along two one-parameter cuts, at fixed forcing frequency and at fixed forcing amplitude. Stochastic sampling of the full space yields an unbiased estimate of the relative volume of each basin as a function of the control parameter, on the same parameter grids on which single-trajectory bifurcation diagrams are computed by continuation. Basin maps on two-dimensional sections, complemented by maps of the order of the attractor reached from each initial condition, resolve the geometry of the coexisting basins where the competition between attractors is strongest. The relative volumes reveal windows of global antiperiodic dominance, in which the antiperiodic orbit attracts essentially every initial condition, separated by narrow intervals in which two or three qualitatively different attractors share the space in comparable proportions, as well as extended ranges of persistent coexistence; at large forcing amplitude, a single antiperiodic orbit of order one captures the whole space. Compared with the bifurcation diagrams, the abrupt changes of basin volume are the ensemble-level counterpart of the multistability-induced discontinuities of the sweeps, and the gradual shrinking of the antiperiodic basin explains why the branch followed by a sweep depends on the initial state and on the drive phase.

Low-precision inference is widely adopted in edge AI to reduce computational cost and memory footprint. However, existing open-source accelerator platforms provide limited end-to-end support for CNNs following the standard TensorFlow Lite integer inference scheme. This paper presents ZTA-Q, an open-source RISC-V-based platform that enables accurate deployment of TensorFlow Lite INT8 models. In addition to extending operator support, ZTA-Q provides a configurable post-processing datapath for studying how circuit-level approximations, including reduced multiplier precision, shared shift scaling, and simplified rounding, affect model accuracy. The proposed system is implemented on a Digilent Arty A7-100T FPGA and operates at 83.3 MHz. Evaluations on representative CNN models show that with LUT, register, and DSP overheads of 26.3%, 12.6%, and 150%, respectively, ZTA-Q limits the degradation in both top-1 and top-5 accuracy to within 0.25 percentage points.

Motivated by Kawanoue's construction with the finite-sum formulas, we construct an explicit homogeneous basis for the derivation module of the cone of the extended Catalan arrangement of type Dl. We further show that the restriction of this basis at infinity coincides, up to a nonzero constant, with the integral basis constructed by Feigin-Wang-Yoshinaga. This identifies the geometric motivation behind the parameter choices.

hyprfine is an analytic simulation of the sky-averaged 21-cm signal from $z=1100 - 6$ written using JAX and Python for native GPU capabilities. It models the average temperature of the 21-cm signal over cosmic time as a function of the $\Lambda$-CDM cosmology parameters and the astrophysics of the first stars and galaxies. As far as we are aware, the code is the first analytic GPU native simulation of the 21-cm signal. It runs in a fraction of a second, parallelises efficiently across a GPU and is differentiable through the Dark Ages ($z \geq 35$). The code is publicly available at https://www.github.com/htjb/hyprfine.

How can we understand what a music foundation model has learned internally? Most interpretability approaches, such as probing and Sparse Autoencoders (SAEs), focus on identifying individual features with minimal structural assumptions. We argue that many concepts are better understood as structured relations rather than isolated features. This is especially prominent in music, where tonal structures are organized in the space of pitch and time. For example, concepts such as chords or keys are naturally expressed as structured sets (e.g., the 12 transpositions of a chord or the diatonic system within a key), rather than isolated features. In this study, we shift from feature identification to structure-based analysis, asking whether the learned inner representations of music foundation model emerge as organized structures over features. To this end, we introduce a framework that uses pitch transposition as an inductive bias to induce ordered orbits via multi-view SAE alignment. Concretely, we generate pitch-shifted input pairs and align their SAE representations to discover structured groups of pitch-related features. Experimental results show that this approach recovers orbit structures corresponding to chords, keys, and melodic patterns across two state-of-the-art music foundation models, while requiring only minimal grounding (e.g., a few anchor examples) to interpret entire concept families.

We present LiteReality-Agent, an agentic system for reconstructing real indoor environments as realistic, articulated, and simulation-ready 3D scenes from RGB-D scans. At its core, LiteReality-Agent formulates 3D reconstruction as a coding problem, in which a coding agent gathers evidence using specialised tools and iteratively edits a Python script, Room.py, which can be executed to produce a 3D digital twin of the room. With this formulation, we develop a robust observe-edit-verify harness that supports evidence gathering, measurement, verification, layout optimisation, simulation readiness, and quality control throughout the reconstruction process. LiteReality-Agent produces high-quality reconstructions suitable for simulation and downstream embodied AI tasks. Furthermore, as agent capabilities continue to improve rapidly, the system introduced by LiteReality-Agent remains a strong orchestration framework for future agents: it equips them with specialised tools, structured workflows, and robust verification mechanisms that substantially improve reconstruction quality and reliability. We demonstrate that LiteReality-Agent produces reconstructions that are more geometrically accurate, visually realistic, and simulation-compatible than those generated by recent frontier models, such as Astra and Fable. We therefore view LiteReality-Agent as a practical and important building block for robust real-to-sim systems. Both the source code and the data-capture application are publicly available. Code:https://github.com/LiteReality/LiteReality-Agent/

We study coherent release from a finite serial Krylov sector into an exact conformal tail with asymptotically linear Lanczos coefficients. We derive the cumulative occupation up to a cut that moves to greater Krylov depth with time, tracking the probability accumulated behind the propagating front. This quantity separates the release dynamics of the finite sector from subsequent propagation through the tail. The tail sets the logarithmic transit scale, while the finite sector shapes the resulting distribution. The early edge records the number of serial steps before emission, while the late edge reflects slow resonances and interference and can also exhibit logarithmic enhancements. Thus, one- and two-site sectors can share the same leading resonance in their continued-fraction descriptions yet produce distinct cumulative occupation patterns. We illustrate this framework in thermal AdS$_2$, where a dressed oscillator yields, in the weak-coupling limit, a two-site shallow sector coupled to the conformal tail.

Natural language descriptions can provide rich semantic representations of audio-visual urban scenes, yet datasets that jointly describe both auditory and visual information remain limited. In this paper, we introduce AVSD-Scenes, a paired audio-visual scene description dataset for urban environments. The dataset contains 12,291 audio-visual scene descriptions generated from the TAU Urban Audio-Visual Scenes dataset. To construct the dataset, we first generate audio- and visual-based descriptions using Qwen2-Audio-7B and Qwen2.5-VL-7B, respectively. These modality-specific descriptions are then combined using large language models, namely Qwen3-14B, Mistral-Small-3.2-24B-Instruct-2506, and Gemma-3-27B-it, to produce multimodal descriptions that capture complementary information from both modalities. We benchmark AVSD-Scenes using semantic alignment, cross-modal retrieval, scene classification, LLM-as-a-judge evaluation, and human subjective assessment. Results show that multimodal descriptions improve semantic alignment and cross-modal retrieval performance compared with modality-specific descriptions while preserving strong scene-discriminative information. The generated descriptions achieve up to 94.5% accuracy in urban scene classification, while combining audio, visual, and description embeddings further improves accuracy to 95.4%. Furthermore, the descriptions remain highly scene-discriminative even when scene labels are removed from the prompting instructions, indicating that they capture semantic information derived from the audio-visual content rather than merely reflecting label information.

A recurring principle in many-body physics is that sufficiently distributed interactions or correlations lead to an effectively mean-field description. For fermionic Gaussian states, we establish a quantitative version of this principle directly at the level of Majorana covariance matrices. The main observation is that the admissibility condition for fermionic covariance matrices imposes a quantitative monogamy constraint on two-point correlations: a fixed region has only a bounded covariance budget to distribute among many disjoint regions. We use this principle in three directions. First, for quadratic fermionic Hamiltonians on finite simple graphs of high degree, we obtain product-state approximations to both the ground-state energy and the finite-temperature free energy, with error of order \(D^{-1/2}\) for \(D\)-regular graphs. Second, we prove a finite fermionic Gaussian de Finetti theorem: a \(k\)-copy Gaussian state that is \(n\)-exchangeable under graded fermionic copy permutations is \(O(k/n)\)-close in trace norm to the product of its one-copy marginal. In particular, infinite exchangeability within the Gaussian class implies exact product structure. Third, for spatial fermionic Gaussian states with exponentially clustering mutual information, we prove that the conditional mutual information across a separating buffer decays as \(O(r^{-1})\), and hence, by recoverability, the state admits an \(O(r^{-1/2})\) trace-norm approximation by a recovered state. These results show that product and de Finetti approximations and recoverability estimates for fermionic Gaussian systems can all be derived directly from covariance-level structure.

This paper proposes a local recursive least squares (RLS) estimation strategy for discrete-time adaptive fuzzy control of nonlinear systems represented in quasi-Linear Parameter Varying (qLPV)/Takagi–Sugeno (TS) form. Unknown nonlinear terms are approximated by a constant-consequent TS fuzzy model, and the consequent parameters are updated by a membership-function-weighted RLS law with a forgetting factor. The proposed estimator keeps a different covariance for each rule, considerably reducing the memory footprint of the least-squares updates. The adaptation is also simplified since each rule is only adapted when it is active. From these properties, we are capable of showing that the adaptation law ensures bounded local adaptation errors. Building upon this adaptation law, Linear Matrix Inequality (LMI) synthesis conditions are presented for matched, sector-bounded and norm-bounded unknown nonlinearities, guaranteeing ultimate uniform boundedness of the adaptive control system in closed loop. Three numerical examples are presented to illustrate the adaptive control conditions in the three cases: a planar manipulator with unknown gravity direction, a two-tank system with unknown coupling, and a Brushless DC (BLDC) motor acting as thrust for an efficiency vehicle.

We study a one-dimensional $2x2$ system of conservation laws with discontinuous flux. We prove the global existence of weak solutions for initial data with sufficiently small total variation. We construct explicitly the associated Riemann solver and analyze its main properties. Finally, we introduce a Glimm-type numerical scheme tailored to the exact Riemann solver and use it to reproduce the wave patterns obtained analytically.

Many microgravity experiments require centimeter-sized spherical liquid drops. In drop-tower experiments, only a few seconds of microgravity are available, so the drops must be generated and reach a nearly relaxed state within a very short time. We investigate capillary auto-ejection (puddle jumping) as a passive mechanism for producing free-floating drops and investigate how the supporting cavity can be shaped to minimize the relaxation time after ejection. For cavities with a parabolic cross-section filled with a fixed liquid volume, minimization of the initial liquid surface area yields a unique shape, and smoothed particle hydrodynamics simulations show that this shape also gives the shortest relaxation time within the parabolic family. Introducing a shallow central depression into the cavity reduces the relaxation time further, despite producing a larger initial liquid surface area. These results provide design principles for capillary-driven drop generators that enable the rapid production of relaxed centimeter-sized drops during the short microgravity intervals available in drop towers.

Vision-language-action (VLA) models unify visual perception, language understanding, and action generation, offering new opportunities for automation in additive manufacturing (AM). However, deployment in AM remains challenging because adapting these models to unseen robot embodiments is costly, and performance can degrade under environment changes. In this work, we present a framework for deploying OpenVLA-OFT on a FAIRINO FR3 robot in a fixed AM workcell. A data pipeline converts monocular real-world demonstrations into OpenVLA-compatible TFDS/RLDS datasets to support adaptation to the FR3 embodiment. At runtime, each inference request predicts an eight-step chunk of 7-D actions. The FR3 executes each chunk open loop before capturing a new observation, providing closed-loop feedback between chunks. The system uses a cloud-edge architecture in which the FR3 client streams observations to a remote inference server through a FastAPI interface. In 42 physical A-to-B object-transfer trials, evenly split between red and blue targets, the system succeeded in 39 (92.9%). All three failures occurred during final placement, when insufficient release-height control caused the object to topple. An illumination sweep identified a low-error luminance range of 85-125 on a 0-255 scale, with the lowest mean spatial error at 95.

We develop a Quantum Optimal Transport (QOT) barycenter framework for quantum states, as an analog of Wasserstein barycenters~\cite{AguCar}, and establish existence and duality results for a broad class of possibly unbounded transport costs on separable Hilbert spaces. Our framework provides, in particular, a unified treatment of $2$-quantum Wasserstein (QW) barycenters in both the quantum-state and quantum-channel formulations by specializing to the canonical quadratic cost operators associated with the $2$-quantum Wasserstein distances of Caglioti–Golse–Mouhot–Paul~\cite{caglioti2021towards,Golse-Mouhot-Paul:2016} and De Palma–Trevisan~\cite{DPaTre19}. The central results concern Gaussian input states and, in particular, Gaussian rigidity: whether Gaussian input states force the 2-QW barycenter itself to be Gaussian and uniquely determined when the minimization is taken over all quantum states. We first show that the barycenter problem admits a Gaussian minimizer and reduces to a finite-dimensional convex optimization problem over covariance matrices. The main difficulty is that uniqueness of the optimal covariance does not, in general, imply uniqueness of the underlying quantum state. We bridge this gap through a state-reconstruction principle under covariance complementary slackness that upgrades uniqueness of the optimal covariance to uniqueness of the full quantum state, and thereby prove a global rigidity theorem: if at least one Gaussian input is faithful, then the barycenter is unique among all quantum states and is necessarily Gaussian. Faithfulness is sufficient but not necessary: families of pure inputs still determine a unique barycenter, whereas partially pure nonfaithful Gaussian inputs may admit multiple barycenters.

Liftability was first introduced for paving matroids, where it was used to systematically construct polynomials in the ideals of the associated matroid varieties. In this paper, we generalise the notion of liftability to matroids with realisable truncations. We additionally introduce the notion of generic realisability of a matroid; a strong notion of realisability that implies both realisability and liftability of the matroid. We study the behaviour of liftability and generic realisability under the weak order of matroids within the lattice of matroids with fixed truncation. We develop a unified framework for studying liftability of matroids through Oxley–Wang derived matroid of generic matroid realisations. We characterise liftability and generic realisability in terms of Oxley–Wang derived matroids. Moreover, we give an algebraic description of the bases of the generic Oxley–Wang derived matroids in terms of coordinate sections of matroid realisation spaces and relate our constructions to slack realisation spaces of matroids. As an application of our framework, we obtain a combinatorial characterisation of liftable and generically realisable paving matroids and connect it with Whiteley's theory of scene analysis. In particular, our approach gives a new proof, via Oxley–Wang derived matroids, of Whiteley's characterisation of hypergraphs admitting non-trivial (sharp) scenes. Finally, we compute the generic Oxley–Wang derived matroid for a special class of sparse paving matroids.

In this paper, we study the number of bits required to construct a dynamic dictionary with optimal time for $\texttt{rank}/\texttt{select}$ operations. Using the standard (multiplication) Word-RAM model with $w$-bit words, we construct a data-structure for a dynamic $\texttt{rank}/\texttt{select}$ dictionary for a set $S\subseteq\{0,1,\cdots,u-1\}$ of $n$ elements that, given a parameter $1\leq k\leq \log^*w$, uses $$\operatorname{lg}\binom{u}{n}+\mathcal{O}(n\log^{(k)}w)\text{ bits}$$ taking optimal $\mathcal{O}(k+\log_w n)$ time (worst-case) for all operations. We show optimality for $n=w^{\mathcal{O}(1)}$ and $\log u=\Theta(w)$ by extending the lower bound of Li, Liang, Yu, and Zhou [FOCS 2023] to super-polynomial universes: any dynamic dictionary for $n\leq \sqrt{u}$ elements that uses $\operatorname{lg}\binom{u}{n}+\mathcal{O}(n\log^{(k)}n)$ bits requires $\Omega(k)$ time for operations. Lastly, we extend the data-structure to a dynamic fully indexable dictionary (that also supports $\texttt{rank}/\texttt{select}$ on the complement of $S$).

We determine the limiting distribution of the cover time of simple random walk on the two-dimensional discrete torus. For the continuous-time walk with total jump rate one on $(\mathbb Z/N\mathbb Z)^2$, let $T_N$ denote its cover time. We prove that $\frac{T_N}{(2/\pi)N^2\log N}-2\log N+\log\log N \Longrightarrow G+\log(\kappa Z)$, where $G$ is a standard Gumbel random variable, $Z$ is the total mass of the critical Gaussian multiplicative chaos associated with the zero-average Gaussian free field on the unit torus, $G$ and $Z$ are independent, and $\kappa>0$ is deterministic. This answers the limit-law question suggested by Aldous and recorded by Dembo, Peres, Rosen and Zeitouni. The proof identifies the random fluctuations in the number of small, well-separated unvisited components at a deterministic time before coverage, and then estimates the time needed to visit the remaining components.

In the primary drying step of pharmaceutical freeze drying, it is well known that amorphous excipients are prone to "microcollapse" as they approach their glass transition temperature. Existing modeling approaches for this phenomenon generally entail either avoidance of this regime or an experimentally burdensome empirical assessment of the resulting drop in resistance to mass transfer. In this work, we approach the phenomenon head-on by developing a population balance model for the pore size distribution of a freeze-dried cake during microcollapse and relating the pore size to mass transfer resistance. By treating the population balance with the method of moments and an interpolative closure, we keep the model's computational burden on par with the literature-standard model for primary drying. For a literature example when mass transfer resistance clearly varies as a function of product temperature during drying, we fit the population balance model to cases with high and low product temperature and show that it can then simulate intermediate cases with equal accuracy. The validity of the expression for mass transfer resistance is demonstrated with another literature data set, where pore size distributions were measured after the fact for a formulation without microcollapse; only a single parameter from this model needs to be fit to those cases to yield predictive accuracy in product temperature on par with post-hoc empirical assessment. Finally, a sophisticated multi-experiment fit for one formulation across a range of conditions yields quantitative agreement in product temperatures, suggesting that the rate constant for microcollapse behavior may be a material parameter and independent of the precise porous geometry.

A growing number of gamma-ray bursts (GRBs) have been observed at large projected offsets from the centres of their putative host galaxies, sometimes extending to several tens of kiloparsecs. When the GRB is associated with a kilonova, a compact binary with at least one neutron star is expected to be involved, and the cause of the offset can be attributed to the neutron star natal kick. In this work, we explore an alternative mechanism: the gravitational scattering of compact binaries populating the nuclear region of the host galaxy, by an intermediate-mass black hole or secondary supermassive black hole. We specifically consider populations of neutron star-neutron star (NS-NS), neutron star-black hole (NS-BH), and neutron star-white dwarf (NS-WD) binaries, and analyse the ejection of bound systems from the nuclear region through a gravitational-slingshot effect. We proceed analytically to derive the conditions for binary survival and to parametrise the post-encounter velocity. To quantify the associated merger offsets, we numerically integrate the post-slingshot trajectory of the binary centre-of-mass in host-galaxy potentials that include the primary SMBH, the stellar component, and the dark-matter halo, considering both elliptical-like and spiral-like galaxy profiles. Our parameter sampling shows that NS-NS and NS-WD binaries typically merge farther from the galactic centre than NS-BH systems, with approximately 30-45% of successful ejections merging at three-dimensional distances exceeding 100 kpc; these extreme-offset mergers occur within $\sim$0.1-10 Gyr after ejection. These results motivate the analysed mechanism as a candidate channel for observed extreme-offset transients.