Papers

Ultra-long video temporal grounding requires balancing long-range evidence search with fine-grained event understanding under a limited visual budget, yet existing agentic methods still rely largely on predefined policies and tool capabilities. Motivated by this, we propose a novel policy-tool coevolution framework that jointly evolves high-level policies and executable media tools from the agentic reasoning trajectories of a VLM, forming a reusable skill without updating model parameters. During evolution, an external skill updater distills transferable task experience in long-video temporal grounding, accordingly refining the orchestration of long-range image-based and fine-grained video-based observations. Alongside these policy updates, the updater employs its coding capabilities to upgrade existing tools or create new ones, adapting the tools to long-video evidence acquisition. Equipped with the evolved skill, the VLM autonomously orchestrates tools under the guidance of the evolved policy, coordinating image and video observations for agentic inference without relying on a separate, stronger planning model. Extensive experiments spanning five benchmarks and three VLMs show that policy-tool coevolution consistently improves temporal grounding accuracy in ultra-long videos while reducing visual token cost at inference, and that the evolved skill yields substantial performance gains on general long-video QA without additional task-specific evolution, demonstrating the effectiveness and generalizability of our framework for long-video understanding.

Gromov-Wasserstein multidimensional scaling (GW-MDS) learns low-dimensional representations from relational data but remains transductive, providing no explicit mapping for unseen samples. We introduce an inductive framework based on barycentric distillation. A GW-MDS teacher learns a latent support and an optimal transport plan from the training data, and barycentric projection converts the resulting coupling into sample-aligned targets. A neural student then learns an explicit out-of-sample mapping, avoiding additional relational-matrix construction and GW optimization at inference. We formulate the approach for single-view data and extend it to Mean-GWMDS and Multi-GWMDS teachers through consensus and selected-projection targets learned by a multi-view student with view-specific encoders. We also investigate a direct neural baseline trained solely with a GW objective. Experiments on synthetic and real-world data using Euclidean, geodesic, and cosine relations show that the distilled models preserve the teacher geometry on unseen samples and consistently outperform direct neural GW training in sample-indexed relational preservation. These results establish barycentric projection as an effective bridge between transductive GW embeddings and inductive neural mappings.

This version contains the introduction and conclusion of my PhD thesis, "Freely Generated Categorical Structures and Automatic Differentiation", together with its English and Dutch summaries. The full thesis consists of an introductory chapter, six joint research papers, and a concluding chapter, developed during my PhD studies at Utrecht University under the supervision of Gabriele Keller and Matthijs Vákár. The research papers are available separately and are not reproduced here. The introduction presents the scope of the thesis, explains the contributions of the six papers and their connections, and introduces the categorical foundations of our approach. The guiding idea is that programming languages, viewed as freely generated categorical structures, provide a principled setting for constructing structure-preserving program transformations and proving their correctness. Automatic differentiation supplies the central application: we study forward- and reverse-mode differentiation for expressive typed languages, including higher-order functions, recursive types, iteration and partiality. The semantic requirements of these transformations also motivate independent mathematical results on free distributive and extensive categories, cartesian closedness, and Grothendieck constructions. The conclusion brings these contributions together, discusses their limitations, and outlines further directions. Throughout, the thesis develops a dialogue between theory and practice: categorical semantics guides the construction of reliable and practically useful program transformations, while the demands of computation lead to new categorical structures and results.

We construct a smooth complex projective rational surface whose automorphism group is discrete and not finitely generated. It is obtained by blowing up a point on a branch curve of a rational quotient of a product Kummer surface. Every point with transcendental coordinate gives such a surface. The proof uses leading jets along the branch curve, the complete family of blowups and the cubic intersection of the family, which are not being considered in relevant earlier works.

The evolution of wireless communication standards toward higher frequencies and wider bandwidths places increasing demands on acoustic filter technologies. Conventional resonators face scaling limitations above 5 GHz, where lithographic constraints, reduced electromechanical coupling coefficient (k2eff), and spurious mode excitation hinder practical filter implementation. Here, we introduce a bilayer X-cut lithium niobate (LiNbO3) thickness-shear bulk acoustic resonator architecture that leverages symmetry engineering as a new design degree of freedom. By vertically stacking two piezoelectric thin films with a tailored bonding angle, the second-order thickness-shear mode (SH2, slow) is selectively excited. Furthermore, the fast thickness-shear modes inherent to X-cut LiNbO3 are suppressed, yielding a spurious-free in-band response. Devices operating around 6 GHz demonstrate a k2eff of approximately 35%, in close agreement with finite-element simulations and confirming the symmetry-driven mode selection mechanism. Proof-of-concept ladder filters demonstrate a fractional bandwidth of 18.6%, highlighting the wideband capabilities of the proposed architecture. The proposed configuration enables thickness-defined frequency scaling while maintaining high coupling and spectral purity, offering a promising platform for wideband radiofrequency filters in next-generation wireless systems.

Photospheric vector magnetic fields are foundational to modeling, understanding, and forecasting solar activity. These data are usually produced by inverting and disambiguating the full Stokes vector at multiple passbands, which is demanding. Here, we investigate how well we can estimate photospheric vector magnetograms from UV/EUV filtergrams. This problem is challenging and intrinsically ambiguous without polarization information, as the mapping from UV/EUV intensity to the magnetic field is indirect and ill-posed. We introduce MAGiDiff, a machine-learning-based method that uses denoising diffusion models to estimate vector magnetograms from UV/EUV filtergrams. As input, MAGiDiff takes a stack of filtergrams from the Solar Dynamics Observatory (SDO) / Atmospheric Imaging Assembly (AIA); as output, it is trained to estimate the disambiguated vector magnetogram as seen by Hinode / Solar Optical Telescope-Spectro-Polarimeter (SOT-SP). We show that MAGiDiff can accurately mimic the Hinode ground-truth. Additionally, we probe MAGiDiff's understanding of the physical structure and magnetic connectivity. On full-disk, we show that it produces plausible structures for active regions. MAGiDiff generalizes across solar cycles despite hemispheric polarity reversal, and can be fine-tuned to other EUV instruments including STEREO/EUVI and GOES-R/SUVI. While clearly not a substitute for a dedicated instrument, MAGiDiff opens the door to new capabilities.

For any pseudo-Euclidean space $V \simeq \mathbb{R}^{p, q}, p \geq 3$ and module $W$ over the even Clifford algebra $\text{Cl}^{0}(V)$, V. Córtes constructed noncompact homogeneous quaternion pseudo-Kahler space. In particular, such homogeneous space is always Einstein and for $p=3$ it is Riemannian. Based on this approach we construct the series of Riemannian Einstein homogoneous spaces with negative scalar curvature associated with $V\simeq \mathbb{R}^{p, q}, p\equiv 3 \pmod{4}$ and an irreducible $\text{Cl}^{0}(V)$-module $W$.

We present MGhana-ST, a speech translation dataset for four low-resource Ghanaian language varieties: Ga, Twi (Akuapem and Asante), Ewe, and Fante. MGhana-ST is an ongoing annotation effort; the experiments here use a fixed subset of about 16.1 hours of paired speech and English translations. The audio is curated from two existing Ghanaian speech resources. Unlike in those resources, the English translations are produced directly from audio by 37 native-speaker annotators and include verbal and non-verbal event annotations. Using Whisper-small, we compare monolingual and multilingual training under severe data scarcity, reporting means over three seeds. Flat multilingual training benefits no variety in this regime. Ga and Twi are unchanged within seed variance (+0.51 and +0.06 BLEU against monolingual standard deviations of 1.63 and 2.20), while Ewe declines by 6.99 BLEU and Fante by 5.11. The degrading varieties are Ewe, which is linguistically distinct and drawn from a different source corpus, and Fante, the least-resourced. Comparing empirical cross-lingual transfer with typology-based similarity, we find that transfer BLEU identifies closely interacting language pairs better than URIEL similarity, though neither predicts which varieties benefit from joint training. We also report a methodological finding. An earlier single-run analysis found positive transfer for three of four varieties; this did not survive replication across seeds. For Ga and Twi, monolingual baselines trained on 1.6 to 6.2 hours of audio have seed standard deviations roughly five and thirty times those of the multilingual models (0.35 and 0.07 BLEU). When the monolingual condition is noisier, a single-run comparison can show apparent transfer of this size from seed variation alone. We release MGhana-ST to support research on African language speech technology and low-resource speech translation.

In this paper, we study a problem posed by Matsumura on the extension of pluricanonical forms in Kähler families with a relatively nef canonical bundle. We give an affirmative answer in the smooth case, and for one-parameter degenerations under the additional assumption that the relative canonical bundle restricts to a big line bundle on an irreducible component of the central fiber. In particular, we confirm Siu's conjecture on the invariance of plurigenera for a smooth Kähler family with one fiber admitting the nef canonical bundle. The key step in the smooth case is to construct a semipositively curved singular metric on the relative canonical bundle with the integrability required for Cao's $L^2$ extension theorem, using Păun's twisted form of Schumacher's curvature formula and a uniform Monge–Ampère estimate obtained by adapting the capacity method of Boucksom–Eyssidieux–Guedj–Zeriahi. For one-parameter degenerations, we propagate bigness from an irreducible component of the central fiber to nearby smooth fibers and then apply Matsumura's relative Kawamata–Viehweg vanishing theorem on a projective modification to obtain the desired extension.

We provide generalized linearization theorems for skew-product flows on abstract Banach bundles over locally compact metric spaces, allowing for a unified treatment of uniform and nonuniform, exponential and strong exponential dichotomies. This is accomplished by constructing an operator whose fixed points are exactly the conjugacies that are bounded perturbations of the identity, and by giving criteria under which this operator is a contraction. Under stronger assumptions we refine the argument to obtain Hölder regularity of the conjugacy. Finally, we apply our results to recover known results for non-autonomous differential equations and to obtain new linearization results for control-affine systems on manifolds.

Finite-bandwidth reservoir engineering can suppress unwanted transitions in a quantum thermal machine, but a physical filter also introduces a finite response time. We study this competition in a continuous three-level heat engine whose hot environment couples parasitically to the cold transition. The corresponding three-state rate network is solved exactly, showing that the parasitic transition produces a hot-to-cold thermodynamic short circuit and yielding a closed threshold for the loss of positive-power operation. We then retain a damped auxiliary mode explicitly as a physical spectral filter. Its Lorentzian response suppresses the detuned parasitic transition, whereas excessive narrowing limits the useful energy throughput. Independent local-GKSL and nonsecular Bloch–Redfield calculations both recover the no-leak Markovian engine in the weak-coupling limit and predict a finite maximum-power bandwidth, although its precise location is model dependent. A frequency-resolved Lorentzian-rate reduction, by contrast, has no interior optimum. The resulting design principle is that spectral selectivity can protect the useful thermodynamic cycle, but a real filter cannot be narrowed without a dynamical throughput cost.

Few-step autoregressive video generation enables efficient streaming synthesis, but errors introduced in early temporal blocks are reused as context and can propagate through subsequent rollouts, leading to detail degradation, structural drift, and unstable motion. Existing distribution matching distillation (DMD) primarily aligns student and teacher distributions in diffusion latent space, but provides no direct supervision over the perceptual quality of decoded videos. We introduce Radian, a representation-space adversarial distillation framework that complements on-policy DMD with real-data adversarial supervision in the feature space defined by a frozen visual foundation model (VFM). During training, Radian sparsely decodes frames from autoregressive student rollouts, extracts multi-level visual representations, and applies lightweight discriminator heads to distinguish generated outputs from real video frames. The DMD objective anchors the student to the pretrained teacher, while the representation-space adversarial objective supplies complementary perceptual and semantic gradients that promote high-quality modes. These additional components are discarded after training, leaving the generator architecture and inference-time denoising budget unchanged. Experiments on Wan2.1-1.3B cover four-step chunk-wise, one-step frame-wise, and minute-long autoregressive generation. Our method achieves a VBench Total of 0.8444 and a VideoAlign Total of 0.8033 under four-step generation, and improves VBench-Long from 0.7805 to 0.8041 over Rolling Forcing while using fewer denoising steps. Controlled comparisons across image, video, and diffusion representations further indicate that the choice of representation spaces induces distinct adversarial signals, and external VFM gradients complement DMD more effectively than adversarial supervision derived from diffusion-internal features.

Decoded Quantum Interferometry (DQI) reduces optimization problems with two-variable constraints to decoding cycle codes. For one such problem, namely MaxCut, prior work showed that DQI achieves a nontrivial satisfaction fraction guarantee only on linear-girth graphs, for which MaxCut is classically easy. However, these no-go results rely on minimum distance assumptions that do not represent true decodability thresholds for common noise channels, thus underestimating actual DQI performance. To estimate the true performance, we derive DQI satisfaction guarantees in the presence of imperfect decoding for fixed instances and generalize prior results for random instances. We then study homological cycle codes over arbitrary finite fields, and show that minimum-weight decoding is NP-hard for every field of size $q>2$, in contrast with known results for binary cycle codes. On the Linial–Simkin ensemble of regular graphs with logarithmic girth, we prove maximum-likelihood recovery bounds and a strong converse for a family of non-uniform additive noise channels. Moreover, LP decoders provide polynomial-time recovery of a positive fraction of randomly located errors with arbitrary values. These results allow us to prove upper and lower bounds on the approximate optima achievable by DQI when restricted to classical decoders. These bounds rule out quantum advantage in the regimes we analyze but also identify a family of regular Max-$k$-Cut instances on which DQI efficiently achieves a nontrivial satisfaction fraction guarantee.

The policy-gradient theorem gives the exact gradient under the current policy, but finite on-policy samples may miss rare high-return trajectories. We study whether tree search improves their coverage within a fixed budget while controlling gradient bias. We introduce On-Policy Parallel Tree Search (OPTS) and Tree Trajectory Policy Optimization (TTPO) using on-policy tree trajectories, which sample new suffixes from the current policy at visited states. This needs no action-distribution correction, although branching changes state visitation. Our Branch Aggregation Lemma shows that branch-weighted tree statistics recover chain expectations when branch choices and weights are fixed before outgoing transitions are sampled. OPTS selects expansion states using estimated performance differences. Under deterministic dynamics, exact values, and max-backup advantages, the induced search policy's expected return improves monotonically with the budget. We bound the gradient bias from adaptive expansion and show that max backup assigns prefix credit to actions leading to better discovered suffixes. Against a finite chain reference, TTPG's measured bias stays near its no-branching level, while NaivePG's bias grows from 0.1251 to 0.4884. At matched budgets, reward- and value-guided OPTS improve correct-answer coverage and majority-vote accuracy over independent sampling. At matched branch counts, OPTS + TTPG gains coverage with a modest bias increase relative to Fixed-branch + TTPG. Under matched interaction or rollout budgets, OPTS-TTPO improves MuJoCo tail returns over PPO by up to 28.6%, achieves a 34-22-1 win-loss-tie record against PPO on Atari-57 under the last-100-log mean-return metric, and improves micro-averaged avg@32 and pass@32 over PPO across all four Qwen3 models.

Over the past decade, Machine Learning (ML) has been trained under dual objectives: minimizing prediction error via Empirical Risk Minimization (ERM) while controlling unfairness bias. In practice, however, fairness-aware training often yields limited improvements over standard ERM, making reliable post hoc auditing essential. Existing auditing approaches for black-box models either rely on model reconstruction –exposing systems to extraction attacks– or directly estimate fairness metrics, offering limited insight into which regions of the data distribution drive bias. More fundamentally, property-specific auditing –aimed at extracting only targeted fairness information without reconstructing the model– remains poorly understood. In this work, we introduce the bias probe framework, which enables targeted and adaptive querying to reveal bias structure while preserving model confidentiality. Building on this framework, we propose ALeBi, an active auditor that learns such probes to efficiently estimate multi-group fairness metrics. We establish novel sample complexity guarantees governed by a property-specific complexity measure, resolving a previously posed open question, and extend our analysis to adversarial settings where the model owner may strategically obscure bias. Our results uncover a fundamental trade-off between model confidentiality and reliable auditing, and show that property-specific probing enables both accurate estimation and interpretable identification of high and low-bias regions. Extensive experiments support our theoretical findings and demonstrate the practical effectiveness of our approach.

The interconversion among different quantum resources has attracted considerable attention, exemplified by the tradeoff between coherence and entanglement. However, the relationship between local and global quantum resources remains largely unexplored. Here, we propose and experimentally demonstrate a local global tradeoff in quantum resources, quantified respectively by the local maximum coherence and the quantum mutual information. Our experiments show that the sum of the local maximum coherence and the quantum mutual information is bounded by a definitive upper limit. These results not only establish a fundamental tradeoff inequality, but also provide direct experimental evidence of the complementarity between local and global quantum resources. Moreover, our findings reveal an important constraint in quantum networks: the local quantum resources available at individual nodes and the global quantum resources of the network are mutually exclusive, implying that enhancing one necessarily limits the other.

Measures of non-stabilizerness (“magic”) of a quantum evolution quantify how hard it is to simulate on a classical computer. A natural question is how to extract information about magic from physical correlators, for example at finite temperature or in the ground state. In this paper we show how to measure magic using out-of-time-order correlators evaluated in an arbitrary state. For every full-rank state, and in particular for every Gibbs state, the resulting quantity vanishes if and only if the evolution is Clifford. We establish its basic properties, relate it to the stabilizer entropy of the Choi state, and prove that, even with a single fixed probe operator, it gives a lower bound on the number of $T$ gates needed to implement the dynamics in any circuit architecture.

Digital image watermarking is increasingly critical in media contexts, as emerging regulations and industry practices require marking AI-generated content and ensuring traceable sources to prevent manipulation or misuse. Recent advances in invisible watermarking methods highlight the need to update existing benchmarking practices to reflect current techniques and evaluation criteria. We address this by introducing WARP – a unified framework and benchmark for evaluating the robustness of invisible watermarks. WARP incorporates 32 recent classical, deep, and generative watermarking methods, as well as 34 different erasing techniques, ranging from traditional distortions to more sophisticated adversarial, purification, and re-embedding attacks. It provides standardized, reproducible, and easily scalable protocols for evaluating perceptual quality, watermark readability, and attack resilience. Using WARP, we extensively evaluate current invisible watermarking techniques, collecting the largest robustness benchmark in the field. Results identify the most robust approaches under both distortion and adversarial conditions, and reveal consistent relationships between watermarking methods and the attack strategies most effective against them. Our experiments also highlight that some of the watermarking methods considered are highly vulnerable to reembedding, even if they are robust to standard distortions. The code is made available at https://github.com/ispras/wibe.

Adapting a pretrained generative model to an arbitrary preference expressed as a utility function underlies reward alignment, guided design, and constraint satisfaction, enabling diverse applications. Existing fine-tuning methods trade off generality against computational cost: they either restrict the family class of supported preferences to keep optimization simple or preserve generality at the expense of efficiency. We introduce Fenchel Tilt Flow Control (FTFC), which decouples utility optimization from generative-model fitting. FTFC first optimizes for a target distribution by jointly fitting an effective reward and density-ratio weights on pretrained samples. Method combines the utility's variational structure with Fenchel duality, supporting general $f$-divergence penalties that determine how rewards are transformed into an distribution-correction weights. These weights are then frozen and used to modify a diffusion or flow model in a single stage of importance-weighted denoising or flow matching, without differentiating through sampling trajectories. We establish exact duality for concave utilities under suitable conditions and show that weighted fitting reproduces the optimal target distribution for a given utility. Across image and molecule generation benchmarks, FTFC improves over baselines on diverse preference functions, while also being up to $20\times$ more efficient. roposed method enables adaptation beyond expected-reward maximization without complex optimization, while preserving robustness for more general class of the utility functions compared to baselines.

We compute $K$-theoretic invariants for four three-dimensional operator systems to illustrate the general theory. We find that in some cases the invariants distinguish the operator system from its $C^*$-envelope, while in others they do not. We also explore extensions of the theory.

We compute $K$-theoretic invariants for several finite-dimensional operator systems. These include the Toeplitz operator system and its dual (the Fejér-Riesz operator system), as well as operator systems associated to tolerance relations, aka graph operator systems. A variety of techniques is applied, adapted to each of these cases, ranging from a generalization of Carathéodory's factorization result for block Toeplitz matrices, to Wiener-Hopf factorization and Schur complements. In most instances we find that the invariants coincide with their analogues for the $C^*$-envelope, except for the $K_1$-invariants of the Fejér-Riesz operator system.

Causal action verifiers gate an agent's state-changing tool calls by checking whether each proposed intervention is identifiable against a committed action-state graph, and they issue a certificate that carries the identification argument and a one-sided lower confidence bound. One such verifier, CIVeX, reports zero false executions on a confounded tool-use benchmark. We red-team it by corrupting only the committed graph. Omitting a single bidirected edge takes it from zero false executions to 15.3% at the benchmark's published confounding strength, with 91% of its executions harmful and utility falling from +2.27 to +0.35. Reversing one arrowhead, so that a mediator is committed as a confounder, gives 48.9% false executions and no correct ones. Every one of these actions carries an internally valid certificate. An attestation step that tests each observationally certified execution against a bounded randomised sample detected both attacks, with 2 false alarms in 555 executions on a truthful graph; refusing what fails the test, or cannot be tested, gave zero false executions in every setting we measured. It does not restore beneficial execution: at the published strength 97.1% of beneficial actions are still never executed, because the same misspecification rejects them before attestation runs. Those rejections carry certificates too, and auditing them works, but its cost scales with the number of rejections rather than the number of executions. Recovering safety costs 127 experiments per 1,050 actions; recovering the lost value costs 614 more, at which point the audited verifier makes the honest graph's decisions on every instance and spends exactly its experiment budget. An audit that inspects only executions protects against wrongful action. Wrongful inaction has to be paid for separately.

Continuous measurements simultaneously reveal and modify the dynamics of a quantum system. In this work we consider the tunneling motion of particles between the sites of a one-dimensional lattice. We investigate how weak continuous probing of the occupation of a single lattice site induces entanglement and selects definite values for system properties such as wave function parity and permutation symmetry. Our simulations show how continuous measurement can steer systems of two and three particles, with no prior permutation symmetry, into stable bosonic, fermionic and parastatistical symmetry sectors.

We focus on the Becchi-Rouet-Stora-Tyutin (BRST) quantized version of the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory and (i) discuss its infinitesimal, continuous and off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations, and (ii) derive the corresponding Noether conserved (anti-)BRST and (anti-)co-BRST charges. We demonstrate that these charges are not invariant under the above nilpotent symmetry transformations. We systematically derive the modified versions of the above Noether charges which are found to be invariant under the above symmetry transformations. As a consequence, both types of the above charges anticommute with each-other which proves their linear independence. We also derive the (anti-)BRST and (anti-)co-BRST invariant Curci-Ferrari (CF) type restrictions from the algebraic structures of the Noether conserved charges. In all the above proofs and derivations, we take into account the deep mathematical relationship that exists between the infinitesimal and continuous symmetry transformations and their generators as the Noether conserved charges.

We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a directed acyclic graph, our method automatically derives valid factorizations of the joint posterior and matching neural network architectures. The key steps, graph expansion and graph inversion, yield an inverse graph that determines how inference networks are stacked and conditioned, producing factorizations that amortize over the number of groups and the number of observations within each group. Unlike approaches that simplify the dependency structure to speed up learning or inference, our method preserves all conditional independence and exchangeability assumptions of the generative model. Across three case studies, it closely matches gold-standard samplers on models with more than 6,500 parameters while reducing inference to a near-instant forward pass once trained.

We investigate a recently introduced generalisation of determined directions in affine planes. A direction $(d)$ in an affine plane is a point of the line at infinity in the projective completion, and hence corresponds to a parallel class. A (multi)set $S$ of points is equidistributed from direction $(d)$ if all lines from that parallel class intersect $S$ in the same number of points. In this paper, we give a construction of point (multi)sets that are inequidistributed from exactly 3 directions in any finite translation plane, and prove that all such (multi)sets arise from this construction, generalising a result of Kiss and Somlai in Desarguesian planes of prime order. We also use ideas from algebraic graph theory to prove results on directions associated with a pair of point sets $S$ and $T$. If for every direction $(d)$ either $S$ or $T$ is equidistributed from $(d)$, we prove that $|S \cap T| = |S||T|/q^2$, where $q$ is the order of the affine plane. In the appendix, we give a combinatorial alternative approach to proving this equality, which can be of independent interest. We also introduce the notion of directions cross-determined by a pair of sets $S$ and $T$, and prove that $|S| |T| \leq q^2$ if $(S,T)$ cross-determines at most half of the directions, where equality forces $S = T$.

The goal of quantum metrology is to estimate an unknown parameter with better-than-classical precision and, ideally, to attain Heisenberg scaling. In realistic settings, however, noise can substantially reduce this advantage and, in many cases, restore standard-quantum-limit-like performance. Preserving the quantum enhancement therefore requires noise-robust strategies, which can be implemented using quantum error correction. In this work, we develop and analyze a quantum-metrology protocol based on Calderbank-Shor-Steane (CSS) codes. The main result is that, for noise perpendicular to the sensing Hamiltonian, discrete-time error correction preserves Heisenberg-like temporal scaling over a finite interrogation-time window whose duration depends on the correction frequency. It is further shown that recovery applied only after the sensing evolution provides no metrological advantage over the corresponding uncorrected noisy protocol in the setup considered here. An analytical framework is developed for arbitrary CSS codes and applied to the Steane and Shor codes, for which the discrete-time corrected dynamics, the Heisenberg-like-to-SQL-like crossover, and the optimal interrogation time are determined and numerically analysed.

We present a deep large-scale infrared survey of young stellar objects in the Rosette Nebula. Our analysis is based on stacked archival Spitzer/IRAC images. The images have been treated with the software DeNeb to remove nebulous emission. Our catalogue contains ~20000 sources with photometry in all 4 IRAC bands from 3.6 to 8.0 microns, complemented with near-infrared and optical data. From this database, we identify YSOs using multi-filter colour-colour criteria. We select 1528 YSOs, from which 1303 are Class II and 225 are Class I. Using this sample, we compile a list of clusters and groups of YSOs in the Rosette region, including previously known ones, plus three newly identified groups. Using our census of YSOs, in combination with the literature, we derive the Class I ratios and disk fractions for clusters in the nebula. The main clusters in the central cavity, NGC 2244 and NGC 2237 are almost devoid of Class I sources, indicating that star formation has ceased in this area. On the other hand, in an annulus around the centre with radii of 11-16 pc, roughly coinciding with the expanding HII front, about 30% of the YSOs are Class I, a clear sign of ongoing star formation. Other groups further out in the cloud also exhibit a high Class I ratio. Similar patterns are seen in the disk fractions. Our results are consistent with possible triggering by the expanding HII region, combined with star formation beyond the ionisation front.

Quantum Random Access Memory (qRAM) is a critical component for achieving quantum advantage in algorithms ranging from database search to quantum machine learning. In a recently introduced model [arXiv:2508.02855], we proposed a resource-efficient qRAM architecture based on discrete-time quantum walkers. This article serves as a comprehensive technical follow-up, providing the full mathematical derivations, detailed protocol specifications, and in-depth resource analysis. Moreover, we extend the original proposal with novel techniques for the purpose of making the qRAM implementation more realistic. Our model resolves the primary drawbacks of leading qRAM proposals: it avoids the exponential number of active nodes $\mathcal{O}(2^n)$ required by the "Bucket Brigade" architecture by employing a number of quantum walkers that scales linearly with the address and message sizes, $n$ and $m$, respectively. Simultaneously, it overcomes the spatial bottlenecks of previous quantum-walker schemes by eliminating the need for multiple parallel trees. We propose two algorithmic paradigms: the long- and the short-range approaches, which differ by the length of interaction of the main routing gates employed in the qRAM. We formalize the routing, message-copy, and walker retrieval phases for both variants and we show how, while the long-range scheme employs controlled gates having a multitude of target systems, the short-range approach decomposes these interactions into sequences of 2- and 3-body local gates, which improves the architecture's feasibility for near-term experimental implementation. Finally, our comprehensive resource analysis confirms that the short-range approach achieves the optimal $\mathcal{O}(n+m)$ circuit depth. Within these two paradigms, we explore the potential of different types of quantum walkers, namely bosons, dual-rail qubits and four-level qudits.

Fits to binned, Poisson-distributed data are common in high-energy and heavy-ion physics, and they are particularly delicate in correlation function measurements, where the fitted observable is the ratio of two histograms. We compare several goodness-of-fit estimators on large toy data sets: the Neyman and Pearson $\chi^2$, their Yates continuity-corrected versions, a Neyman $\chi^2$ with the variance shifted by $1/2$, the Poisson log-likelihood, and the correlation function likelihood in which both the signal and the reference histogram are treated as Poisson distributed. For a single histogram with mean occupancy $\lambda$, the Neyman $\chi^2$ underestimates the bin content by approximately one count, while the Pearson $\chi^2$ overestimates it by approximately half a count; shifting the variance by $1/2$ changes the Neyman result only at order $1/\lambda$, and only the log-likelihood recovers the mean without bias. For the ratio of two histograms, Neyman-type estimators are biased by approximately $-3/\lambda$ in relative terms (3% at $\lambda=100$), whereas the Pearson and likelihood-based fits are unbiased in the symmetric configuration studied here. The Yates correction leaves the fitted values essentially unchanged but systematically deflates the $\chi^2$, resulting in unrealistically high confidence levels. Simple analytic expressions are derived that reproduce all observed biases. Since these biases do not decrease with the number of bins, whereas the statistical uncertainties do, they can dominate the uncertainty of high-statistics, finely binned measurements. We therefore recommend likelihood-based fits, in particular the correlation function likelihood, for femtoscopic and similar ratio analyses.