Papers

The works of Rivoal, Zudilin, and Krattenthaler and Nesterenko give an explicit sequence $p_n/q_n$ ($p_n,q_n\in \mathbb{Z}, q_n>0$) of rational approximations to Catalan's constant $G=1-1/3^2+1/5^2-1/7^2+1/9^2-\cdots$ satisfying $\vert G-p_n/q_n\vert \leq 1/q_n^{0.52}$ for sufficiently large $n$. We build on their works to give an explicit sequence $p_n/q_n$ ($p_n,q_n\in \mathbb{Z}, q_n>0$) with $\vert G-p_n/q_n\vert \leq 1/{q}_n^{0.62}$ for sufficiently large $n$.

The EU Digital Services Act (DSA) requires Very Large Online Platforms and Search Engines (VLOPs/VLOSEs) to assess and mitigate systemic risks, including actual or foreseeable negative effects on fundamental rights, and subjects these assessments to independent audit. Yet how such rights-relevant risks should be identified, assessed, evidenced, and documented remains methodologically under-specified. We address this gap by introducing a decision-tree-based toolkit that operationalizes Article 34(1)(b) DSA and related audit requirements into a structured assessment process. The toolkit decomposes platforms as systems-of-systems and guides assessors through DSA applicability, context definition, subsystem and stakeholder identification, risk identification, risk assessment, reporting, and visualization. A central design contribution is its treatment of vulnerability as situational and relational: rather than assigning vulnerability to fixed groups, the toolkit asks how particular platform subsystems and dependencies may place stakeholders in vulnerable positions. It further makes fundamental rights-relevant judgments traceable by recording the affected right, interference and justification analysis within the structure of a proportionality test, while also covering a perception and impact dimension including severity, scope, duration, reversibility, as well as practical consequences. We developed the toolkit iteratively through a design-science process combining literature-derived design requirements, three interdisciplinary expert workshops (N=4; N=11; N=20) testing the framework design with two DSA user persona scenarios. We contribute an extensible methodological foundation for making fundamental-rights risk assessments under the DSA more streamlined, systematic, transparent, and auditable.

Concept drift, driven by the rapid evolution of Android malware, severely degrades the performance of machine learning detectors. Current adaptation strategies are often reactive, responding only after performance has dropped and imposing a significant manual annotation burden, or they are proactive but rely on unstable adversarial training and incomplete, single-level graph representations. To overcome these limitations, we propose HYDRA (Hybrid Drift Adaptation), a proactive adaptation framework that learns drift-invariant representations from hierarchically structured data. HYDRA first models applications using a hybrid graph structure, combining fine-grained Control Flow Graphs (CFGs) and coarse-grained Function Call Graphs (FCGs) to capture comprehensive behavioral patterns. It then introduces a novel cross-domain contrastive learning objective that aligns historical (source) and new (target) data distributions. By generating pseudo-labels for unlabeled target samples, our method pulls representations of semantically similar applications together, regardless of their domain, within a single, stable optimization process. This approach unifies feature learning and domain alignment, eliminating the need for complex adversarial objectives. Extensive experiments on large-scale, time-ordered malware datasets demonstrate that HYDRA achieves substantially lower False Negative and False Positive Rates than state-of-the-art baselines while requiring up to 87.5% fewer labeled samples. Our work thus offers a robust and efficient solution to combat concept drift in security applications.

We study the uniform stability of composite waves consisting of a degenerate Oleinik shock and a rarefaction wave for scalar viscous conservation laws. We consider cubic-type fluxes and arbitrarily large $L^2$ initial perturbations of the composite wave within the $H^1$ strong-solution class. We obtain a uniform $L^2$ estimate for such large perturbations. In particular, the estimate implies the contraction of a degenerate Oleinik shock, up to a dynamical shift. As a further consequence, the uniformity with respect to viscosity implies that the associated self-similar solution, composed of the degenerate shock and rarefaction, is stable in the class of inviscid limits. The main analytical difficulty is that the standard weighted Poincaré inequality underlying the $a$-contraction method fails to yield the required coercivity at the linear level. We overcome this obstruction by establishing a new degenerate Hardy–Poincaré inequality adapted to the degenerate structure of the shock profile. Combined with an exact nonlinear decomposition, this linear inequality yields a strict coercivity estimate that controls the quadratic energy together with the higher-order nonlinear terms, without any smallness assumption on the perturbation.

In the development of next-generation tracking detectors for gamma-ray space observations, the integration of advanced deep learning techniques into event reconstruction algorithms is a promising approach for improving the performance of the mission, reducing systematic uncertainties and maximizing the scientific output. In this study, we investigate the application of deep learning techniques such as Graph Neural Networks (GNNs) for the identification and reconstruction of particle tracks resulting from pair production events within the tracker of the AMEGO-X proposed concept. The goal is improving the angular resolution and the detection efficiency of the telescope, especially in the soft energy range (below 100 MeV) where multiple Coulomb scattering significantly degrades track reconstruction and consequently limits the sensitivity in the so-called MeV gap. We use the Geant4-based MEGAlib framework and a Python-based dedicated read-out and data handler processor to format the input datasets as close as possible to the real data. The simulated datasets are then used to train and evaluate two graph neural network architectures, GraphSAGE and Interaction Networks, and to compare their performance in pair-production event reconstruction in terms of Point Spread Function 68% containment radius and effective area, also with that obtained using standard reconstruction techniques. The results of this study indicate that graph neural network-based reconstruction is a promising approach for pair-production event reconstruction below 100 MeV when compared with standard reconstruction methods, with significant potential for further optimization.

We study the infinite-horizon optimal investment and consumption problem in a general class of continuous financial markets, where uncertainty is driven by a continuous non-decreasing stochastic clock representing accumulated variance. This framework encompasses classical Markovian and non-Markovian stochastic volatility models as well as singular realized-variance models in which no spot volatility process exists. We characterize the value process and optimal investment and consumption strategies in terms of a non-linear infinite-horizon backward stochastic differential equation driven jointly by calendar time and the stochastic clock. We develop a general well-posedness theory for this new class of IVC-BSDEs based on the method of sub- and supersolutions, establishing existence, uniqueness, and stability under natural conditions that might be of independent interest beyond the financial application at hand. We are moreover able to identify the sign of the $Z$-component of the solution using Malliavin calculus. We then apply our results to Volterra Heston models with locally integrable kernels, covering both rough and hyper-rough regimes. Exploiting the affine structure of the model, we verify the optimality of the candidate strategies in incomplete markets and obtain an explicit representation of the solution in the complete market case. Owing to the generality of the framework and the weak assumptions imposed on the stochastic clock, our results unify and extend several existing results for optimal investment and consumption, including classical Markovian stochastic volatility models.

A lowering of the post-inflation reheating temperature $T_{\rm RH}$ has attracted much attention as a means to facilitate obtaining the correct Dark Matter (DM) relic abundance. We take a relook at the paradigm under the assumption that the inflaton decay is essentially instantaneous, with the thermal bath coming into existence only at a relatively low temperature. We demonstrate that, contrary to the popular misconception, the relevant scale is not necessarily the DM mass itself, but the characteristic temperature at which the dominant DM production processes are thermally efficient. With $T_{\rm RH}$ setting the maximum temperature available for thermal production, and thereby determining the accessible stages of the production history, lowering $T_{\rm RH}$ tends to reduce the relic abundance. While this effect could, in principle, be offset by altering the couplings defining the theory, there exists a minimum $T_{\rm RH}$—determined by the mass spectrum—below which the relic abundance falls to minuscule levels, whether the mechanism be freeze-in or freeze-out.

The scarcity of non-English language data in specialized domains significantly limits the development of effective Natural Language Processing (NLP) tools. We present TransBERT, a novel framework for pre-training language models using exclusively synthetically translated text, and introduce TransCorpus, a scalable translation toolkit. Focusing on the life sciences domain in French, our approach demonstrates that state-of-the-art performance on various downstream tasks can be achieved solely by leveraging synthetically translated data. We release the TransCorpus toolkit, the TransCorpus-bio-fr corpus (36.4GB of French life sciences text), TransBERT-bio-fr, its associated pre-trained language model and reproducible code for both pre-training and fine-tuning. Our results highlight the viability of synthetic translation in a high-resource translation direction for building high-quality NLP resources in low-resource language/domain pairs.

Political discourse is widely perceived to be growing more hostile, yet robust evidence remains scarce. This study examines blame attribution in the Danish Parliament from 1997 to 2026, combining a purpose-built classifier, BlameBERT (F1: 0.80), with multilevel statistical modeling. The classifier is constructed using an annotation-efficient pipeline for blame attribution in low-to-mid resource languages. The results reveal a banana-shaped trajectory, with blame declining until around 2016 before entering a significant and sustained increase in recent years (2019-2026). Government status consistently influenced blame attribution - an effect we term political contrasting - with opposition parties blaming substantially more than governing parties. This effect was moderated by ideology: The blame-dampening effect of governing was less pronounced among right-wing parties, and ideological extremity amplified blame more strongly on the right. In recent years, the interaction between political wing and ideological extremity intensified, suggesting an ideological hardening of the blame rhetoric concentrated on the right of the political spectrum. Taken together, these patterns suggest that the perceived rise in harsh political language reflects not merely a general rhetorical drift, but an ideologically asymmetric hardening of political discourse. A sensitivity analysis showed that the conclusions were robust to varying classification thresholds.

SMT solvers make automated verification convenient. At the same time, solvers suffer from instability, whereby seemingly inconsequential changes to the input may cause a previously quickly produced proof to fail or time out. This paper addresses a common cause of outcome instability (i.e., unsat/unknown fluctuations) in the context of program verification. We demonstrate that the generation (i.e., depth) accounting used to make quantifier instantiation practical and implemented in multiple state-of-the-art SMT solvers is non-confluent (i.e., prone to divergence), and that this leads to instability. We then address this deficiency and develop a new accounting method that is stable. The new method is justified using a sequence of refinements from an abstract, confluent solver model all the way to our implementation in Z3. Our empirical evaluation demonstrates that our implementation reduces outcome instability by 94% in the unstable core of the Mariposa benchmark without leading to performance regressions.

The phenomenon of bias-driven circular charge and spin currents in a ring nanojunction is investigated in the presence of electron-electron (e-e) and electron-phonon (e-ph) interactions within a tight-binding framework based on the non-equilibrium Green's function formalism. The Lang-Firsov transformation is employed to map the interacting system onto an effective electronic model, which is subsequently treated within the Hartree-Fock mean-field scheme. By exploring the interplay among e-e interaction, e-ph coupling, and electrode-ring interface sensitivity, several intriguing features emerge in both circular charge and spin currents that, to the best of our knowledge, have not been reported previously. In addition to bias-driven circular currents, charge and spin-dependent junction currents through the nanojunction are also analyzed. Selective spin transport is achieved, leading to a high degree of spin polarization. All four current components, two associated with circular currents and two with transport currents, are systematically inspected over a wide range of parameter regimes to assess the sensitivity of the results to the relevant system parameters. Our findings provide useful insights into charge and spin transport phenomena in interacting nanojunctions with single- and multi-loop geometries.

In-depth characterization of heterogeneous materials has long been a challenge in non-destructive testing. Here, a method is proposed to determine the elastic constants of metallic polycrystalline materials using back-scattered ultrasound. The waves scattered by the microstructure are analyzed to image the effective bulk velocities. To this end, a reflection matrix is acquired with an array of transducers. The projection of this matrix onto a focused basis is used to estimate an average point spread function. Optimizing this function with respect to the propagation model leads to an estimation of the longitudinal velocity. Additional treatments are developed to adapt the method to map the shear wave velocity. The local Poisson's ratio is then deduced from the ratio between those two velocities. Young's modulus and shear modulus can also be obtained assuming known densities. This matrix approach is experimentally validated on different polycrystalline materials. A sample displaying heterogeneous mechanical properties is then simulated to assess the accuracy and the resolution of the method. Its strengths and limitations are discussed, demonstrating its potential for quantitative non-destructive material characterization.

Residual Vector Quantization turns continuous representations into discrete, multi-level token sequences. Yet most methods operate in Euclidean space, despite the coarse-to-fine structure of the resulting codes and the latent hierarchies present in many data domains. Hyperbolic geometry offers a natural alternative for hierarchical representations, but naive hyperbolic extensions introduce geometric inconsistencies: non-associative hyperbolic addition prevents consistent residual aggregation, while standard straight-through gradient estimation ignores the geometry of the latent space. We propose a geometry-aware hyperbolic residual quantization that addresses these issues in both the forward and backward passes. In the forward pass, Hyperbolic Residual Aggregation restores the telescoping behavior of residual quantization on the Poincare ball. In the backward pass, a discounted Hyperbolic Straight-Through Estimator routes the reconstruction gradient through the quantizer as a single geometric block, avoiding unstable recursive gradient transport across residual stages. Evaluations on hierarchical prediction, recommendation, image tokenization, and neural audio coding tasks show that our method improves the stability and structural organization of hyperbolic residual codes over naive hyperbolic baselines. At the same time, we observe a clear structure-compression trade-off: Euclidean residual quantization remains preferable for pure compression, while geometry-aware hyperbolic quantization is most useful for hierarchically organized discrete latent spaces.

We theoretically investigate the role played by non-Markovianity in the charging of a quantum battery. We focus on the case of a Micromaser, where the energy is stored in a resonant cavity mode and memory effects are introduced and controlled by coupling this mode to a memory ancilla, described as a two-level system, that in turn sequentially interacts with a stream of two-level chargers through pairwise exchange interactions leading to a partial swap. Through numerical analysis, we show that non-Markovian memory effects act as a resource that enhances both the charging capacity and the stability of this device with respect to the Markovian counterpart. We conclude our study showing that the proposed scheme can be implemented in state-of-the-art solid-state platforms for circuit quantum electrodynamics.

For the semistable $J$-equation, we prove that the numerical $J$-null locus coincides with the ambient $C^2$-singular locus of Murakami's weak solution. Consequently, this singular locus is a proper analytic subset with finitely many irreducible components, and the weak solution is locally smooth outside the $J$-null locus. The proof relies on two analytic ingredients. First, we establish a regularization theorem for singular $J$-subsolutions, showing that Demailly's global regularization preserves quantitative strict cone conditions. Thus, singular strict subsolutions with prescribed analytic poles can be replaced by smooth strict subsolutions away from their pole sets. Second, we derive relative a priori estimates adapted to these subsolutions: a relative $L^\infty$-estimate from determinant control and a weighted second order estimate yielding uniform $C^2$-bounds on compact subsets of the regular locus.

Data-calibrated stochastic MPC typically builds separate risk margins for many events along the horizon, such as times, facets, state/input components, or obstacles, and then combines them with a union bound. This approach is valid, but it does not match the key object used in the tube-MPC recursive-feasibility proof, which shifts a complete error tube. This paper develops collective tube MPC (CT-MPC), where the calibrated uncertainty object is the finite-horizon prediction-error trajectory. A reusable trajectory tube is calibrated offline, its cross-sections define deterministic Pontryagin tightenings online, and the certified violation event is that a fresh prediction-error trajectory leaves the tube. For linear systems with additive uncertainty and fixed ancillary feedback, we prove joint state-input safety over the prediction horizon, one-step recursive feasibility from an explicit shifted candidate, a finite-deployment risk bound, and a practical value-decrease inequality. The finite-sample certificate is distribution-free under split calibration and has beta-binomial form; its complexity is the certified number of residual trajectories that can define the tube, rather than the number of horizon-constraint blocks. We also give implementable shift-compatibility tests for polytopic tubes and a stable-compression fallback for irregular tube designers. Numerical experiments compare CT-MPC with Bonferroni tightening, a sample-envelope tube, and a joint-in-time conformal MPC baseline. The collective tube reduces deterministic tightening while preserving empirical safety and recursive feasibility.

Argument Mining (AM) transforms natural language into its underlying argument structures. This transformation is typically realized through a sequence of AM tasks that form an end-to-end AM pipeline. However, AM approaches often differ in how they conceptualize these tasks, making direct comparisons between them difficult and opaque. This calls for a more nuanced, task-level analysis of AM approaches to enable clearer comparison and assessment. This work presents a preliminary meta-study that systematically reviews several state-of-the-art end-to-end AM works and analyzes their pipelines through a triple-perspective framework—a linguistic, computational and domain perspective—to understand how the pipelines model arguments as structures, computes them, and integrates domain knowledge. We further propose a general design to the linguistic and computational perspectives, illustrating how key AM tasks are designed for modeling and computation of argument structures. Our proposed framework lays the groundwork for methodology-centered descriptions across AM approaches, facilitating deeper understanding and more systematic comparisons in future research.

Inductive definitions are an important form of knowledge in mathematics and computer science. Two common techniques to prove theorems about inductive definitions are the principle of mathematical induction and the principle of infinite descent. To formalize these principles, Brotherston and Simpson introduced the sequent calculus proof systems LKID, for mathematical induction, and LKID{\omega} and CLKID{\omega} , for infinite descent. LKID{\omega} is an infinitary system, in which proofs are infinite trees, and CLKID{\omega} a cyclic system, in which proofs are finite graphs. However, these calculi restrict to monotone definitions, while inductive definitions are generally non-monotone. The logic FO(ID) extends classical first-order logic with non-monotone inductive definitions. In earlier work, we provided a formalization of the principle of mathematical induction for non-monotone definitions by extending LKID to a sequent calculus SCFO(ID) for FO(ID). In this paper, we provide a formalization of the principle of infinite descent for non-monotone definitions by extending LKID{\omega} and CLKID{\omega} to sequent calculi SCFO(ID)-inf resp. SCFO(ID)-cyc for FO(ID). Furthermore, we extend several proof-theoretic results for LKID{\omega} and CLKID{\omega} to SCFO(ID)-inf and SCFO(ID)-cyc regarding soundness, completeness, cut-elimination and the relation with SCFO(ID).

Let $f=(f_1,\dots,f_r)$ be a complete factorization of a central hyperplane arrangement $D$ in $X=\mathbb{C}^n$. For a monoid ideal $K\subseteq \mathbb{N}^r$ we study the Bernstein-Sato ideal $B^K_f$ of $f$ along $K$, that is, the $\mathbb{C}[s]$-annihilator of $\mathcal{D}_X[s]f^s/\sum_{m\in K}\mathcal{D}_X[s]f^{s+m}$. When $D$ is free we compute two families of these ideals with the help of AI. For the unit shift $K=\langle e_i\rangle$ we prove that $B^{-e_i}_f$ is generated by an explicit product of linear forms indexed by the dense edges of $D$ contained in $D_i$. This determines all the Bernstein-Sato ideals $B^{a,b}_f=\operatorname{Ann}_{\mathbb{C}[s]}\mathcal{D}_X[s]f^{s-a}/\mathcal{D}_X[s]f^{s-b}$, $a\geq b$, of a free arrangement, generalizing formulas of Maisonobe (2016) and Bath (2020). The main new ingredient identifies the multiplicities of the relative characteristic cycle of $\mathcal{D}_X[s]f^s/\mathcal{D}_X[s]f^{s+e_i}$ along the conormal bundle of the origin with the coefficients of the Hilbert series of an Artinian complete intersection attached to a generic Ziegler restriction of $D$; the total multiplicity computed in Wu (2022) then forces all the resulting coefficientwise upper bounds to be equalities. For the coordinate monoid ideal $K=\langle e_1,\dots,e_r\rangle$ we show that $B^K_f$ is generated by one Euler relation for each irreducible factor of the essential quotient of $D$. Finally, we show that the zero locus of a Bernstein-Sato ideal along a monoid ideal need not be a finite union of translated linear subvarieties, even for a reduced free arrangement in $\mathbb{C}^2$: for $f=(x,y,x+y,x+2y)$ and $K=\langle 3e_1,3e_2\rangle$ we compute $B^K_f$ exactly and find an irreducible quadric component. This disproves a conjecture due to Budur.

We introduce labelled packing measure by a covering construction in which each set has an independent positive label bounding its diameter and the radii in its local packing cost. Letting the labels tend to zero defines a metric outer measure $M^s$. For every $s>0$ and every metric space $(X,d)$, we prove \[ 2^{-s}{P}^s(F)\le{M}^s(F) \le C(s) P^s(F)\qquad(F\subset X), \] where $ P^s(F)$ is the classical packing measure and $C(s)$ depends only on $s$. Thus labelled packing measure and classical packing measure have the same null sets and critical exponent. Allowing arbitrary finite positive labels defines labelled packing content. At the common positive Hausdorff and packing dimension, this content and the labelled packing measure agree on cylinders associated with irreducible subshifts of finite type. In particular, equality holds for non-singleton self-similar attractors and components of finite strongly connected graph-directed systems, without separation assumptions.

The dimensional collapse of representations in self-supervised contrastive learning is an ever-present issue. One notable technique to prevent such a collapse of representations is using a multi-layered perceptron network called Projector. In several works, the projector has been found to heavily influence the quality of representations learned in a self-supervised contrastive pre-training task. However, the question still lingers. What role does the projector play? Assuming the projector mitigates dimensional collapse, what prevents the terminal layer of the base encoder from functioning as the projector in the absence of an explicit multi-layer perceptron (MLP) head? In this work, we intend to study what happens inside the projector by examining the rank dynamics of the same and the encoder through empirical study and analysis. Through mathematical analysis, we observe that the effect of rank reduction predominantly occurs in the last layer. Motivated by this insight, we propose a weight regularization strategy applied specifically to the last layer. We demonstrate that this targeted approach yields better performance than applying orthogonal weight regularization across the entire network (WeRank), both with and without a projector. Our method improves Top-1 accuracy by more than 1% on SimCLR on the ImageNet100 dataset and consistently outperforms baseline SimCLR variants on CIFAR datasets, supporting our interpretation of the projector's role.

Prefill and decode reward different approaches to quantization: low-precision arithmetic accelerates prompt processing, while compact weights reduce memory traffic during generation. We propose "disaggregated quantization" (DQ), which specializes computation formats, weights and storage placement to both of these phases. On Qwen 3 and Gemma 3, removing activation quantization specifically on decode improves accuracy on decode-heavy tasks without increasing inference cost. Training separate compute-native prefill weights accelerates prompt processing relative to weight-only inference while matching or exceeding its accuracy at 2-3-bit decode on both decode-heavy and prefill-heavy tasks. With released Qwen3.8-27B GGUF decoders, training an NVFP4 prefiller improves 1-bit accuracy by 32.5 points on MMLU-Pro and 35.3 on MMMU-Pro without modifying the decode checkpoint. To accommodate the additional checkpoint on a single device, offloaded disaggregated prefill (ODP) streams its weights from SSD, amortizing loading over prompt length. On the same 27B model, ODP delivers a 1.78x time-to-first-token speedup over the weight-only baseline at 8K prompt length in llama.cpp. We evaluate accuracy under disaggregated serving in vLLM and further validate shared-weight format disaggregation through post-training quantization on models up to 2.8T parameters.

Surfactant adsorption at solid-fluid interfaces strongly influences contact line dynamics, yet most surfactant-laden phase-field models neglect solid adsorption and rely on Cahn-Hilliard-type equations. We develop a thermodynamically consistent and conservative Allen-Cahn-Navier-Stokes model for surfactant-laden contact line dynamics with solid adsorption. A unified free-energy formulation accounts for surfactant transport, adsorption, and wetting dynamics, yielding consistent wetting and adsorption boundary conditions. Second-order Allen-Cahn-type equations govern both the phase field and surfactant concentration, avoiding the numerical complexity of fourth-order formulations. A classical linear constraint ensures exact conservation of total surfactant mass, whereas a generalized nonlinear conserved quantity is introduced for the phase field to improve geometric volume conservation. The resulting weighted Lagrange-multiplier correction vanishes in the bulk phases and is confined to the diffuse interface, suppressing the leading-order curvature-induced bulk shift associated with the linear constraint while preserving the energy-dissipation structure. Matched asymptotic analysis shows that the nonlinear formulation can achieve formal second-order geometric-volume accuracy. A lattice Boltzmann method is developed to solve the coupled system. Numerical results confirm the predicted second-order convergence, demonstrate enhanced volume preservation for high-curvature droplets, and reproduce wetting responses induced by preferential solid adsorption, including hydrophilization and autophobing. Under shear flow, the results also show that solid adsorption can significantly influence contact line recession and droplet detachment.

Synthetic multispectral and hyperspectral data are increasingly used to address limited measurements, labels, and acquisition resources in spectral-imaging research. Yet the scope of the evidence produced by these experiments depends not only on the synthesis method, but also on sensing conditions, sample variability, data provenance, evaluation design, and downstream use. We present a literature-informed taxonomy for experiments using synthetic MSI/HSI data through spectral reconstruction and/or data augmentation, with a deliberate focus on agri-food research. The taxonomy is paired with a traversal procedure that connects available evidence, sensing constraints, experimental choices, and evaluation design to the forms of generalization that were actually tested, producing a compact experiment characterization record. Although primarily intended for studies with an existing research question, the same structure can also support earlier-stage planning when only an object of study, dataset, or sensing setup is initially defined. The framework was developed through question-driven reading, practical research experience, and iterative refinement against additional recent studies, and is offered as a basis for further use and refinement.

Differential equations can be encoded as ground-state problems by constructing a positive-semidefinite effective Hamiltonian whose minimum-energy state represents the solution. We extend this framework in several directions. First, we show how multiple nonzero initial, boundary, and data conditions can be incorporated into the homogeneous formulation $A | f\rangle=0$ using a known nonzero reference condition. We then analyse an alternative formulation based on $A |f\rangle = | b\rangle$, with Hamiltonian $H_b=A^\dagger(I-|b\rangle\langle b|)A$, which incorporates source terms and nonzero constraints through an augmented system. For nonlinear differential equations, we examine the unphysical ground-state degeneracy introduced by tensor-product representations and consider both Hamiltonian constraints and ansatz-level restrictions for targeting physically valid product states. Finally, we develop grid-value amplitude-encoded versions of both Hamiltonian constructions and compare them with spectral coefficient encoding. Through linear and nonlinear examples, we assess how the choice of Hamiltonian formulation and function representation affects solution recovery, spectral gap, degeneracy, and readout. These results broaden the applicability of ground-state-based quantum differential-equation solvers while clarifying their principal practical trade-offs.

We prove a quantitative palette-transference principle for rainbow spanning configurations in uniformly edge-coloured pseudorandom graphs. The input to our transference principle is an embedding result of a spanning configuration in an appropriately bijumbled graph $H$ with sufficiently large minimum degree. The output of our transference principle is the asymptotically almost sure existence of a rainbow copy of the same configuration in a uniformly edge-coloured graph $G$ whose bijumbledness and minimum are comparable and sometimes coincide with those of $H$. We then apply our transference principle in order to asymptotically almost surely obtain $K_k$-factors, including perfect matchings, Hamilton cycles, and a prescribed bounded-degree spanning tree in bijumbled graphs with appropriate parameters. In all of our results, the palette size exceeds the size of the target configuration by $\varepsilon n$, where $\varepsilon > 0$ is arbitrarily small yet fixed, and $n$ is the order of the configuration.

Measuring disease burden is an important part of both public health research and health economics. Some measures of disease burden, such as hospitalisations, are made up of recurrent events. Assessing what events are related to a particular disease is however non-trivial. We extend the notion of relative survival to recurrent events by developing a novel non-parametric estimator. The estimator combines data from some cohort with aggregated population level data to estimate the number of excess recurrent events. Using empirical process theory, we show that the estimator converges weakly to a mean zero Gaussian process under mild regularity conditions, and provide a consistent estimator for the covariance function. We also evaluate the finite sample properties of the estimator through simulations and provide a practical example using data from Swedish patients with rectal cancer.

The five-compartment tumour-immune model introduced by Kuznetsov et al. captures critical clinical phenomena, including tumour dormancy, immune evasion (`sneaking through'), and immunostimulation. Recent studies by Osojnik et al. highlighted the model's excitable and oscillatory dynamics, providing a mechanism for tumour relapse. In this paper, we recast these findings through the lens of geometric singular perturbation theory (GSPT) and the blow-up method, establishing a formal mathematical foundation for these phenomena. Because the model features a multiple-time-scale structure with dynamics separated by up to three orders of magnitude, standard Tikhonov-Fenichel theory is insufficient. To resolve this, we employ the parametrisation method to systematically compute higher-order approximations of the slow vector fields. We introduce a methodological novelty by demonstrating that the parametrisation method is indispensable within the geometric blow-up analysis. Specifically, we show that higher-order correction terms to the local centre manifolds are required to match the vector field on the corresponding slow manifold. Using these combined tools, we rigorously prove the existence of stable relaxation oscillations and transient large excursions. We uncover a rich collection of singular bifurcations, including a saddle-node on invariant circle and two distinct singular Andronov-Hopf bifurcations that drive complete and incomplete canard explosions. At the highly degenerate origin, our blow-up analysis reveals the spatial collision of a singular transcritical bifurcation and a nilpotent pseudo-singularity. We conjecture that this collision forms a novel singular transcritical Bogdanov-Takens organising centre. Ultimately, these geometric findings yield a precise bifurcation diagram in the parameter space of effector cell supply and death rates.

We study preference elicitation under the Bradley-Terry-Luce (BTL) model where the true partworth vector is unknown and has to be estimated as a parameter with elicited preference information. The set of selected pairwise queries is non-uniform, deterministic, and arbitrary over a collection of alternatives, provided that it satisfies a joint identifiability condition. We focus on understanding when the canonical maximum likelihood estimator (MLE) is finite and admits sharp error bounds without explicit compactness constraints on the feasible set or external regularizers. To this end, we derive minimax lower bounds under the standard bounded dynamic range condition, and find that the same Fisher-information geometry in the classic Cramér-Rao lower bounds underpins the finite-sample difficulty of the estimation problem. By combining a non-asymptotic expansion of the likelihood score equation with a fixed-point localization argument, we identify a design-dependent sample size threshold above which the unconstrained canonical MLE exists and is unique with high probability. The same expansion yields a decomposition of the estimation error into a linear stochastic term, an explicit second-order bias, and a higher-order remainder. A refined analysis gives sufficient sample size conditions under which the canonical MLE attains the minimax rates up to logarithmic and constant factors. These results provide a unified non-asymptotic theory for parametric utility elicitation and reveal when the inference is determined by response data alone rather than by external regularization. Preliminary numerical results are consistent with the theoretical findings.

Camera-based 3D object detection and online vectorized HD mapping provide compact scene representations for autonomous driving, but both depend on accurate metric geometry and remain limited by depth ambiguity. Over long-term deployment, observations from repeated traversals can be accumulated into persistent point cloud priors that provide geometric context beyond the current observations. Existing explicit point cloud prior approaches, however, rely on LiDAR-based map construction and therefore require expensive 3D ranging sensors. We propose a framework that constructs a static point cloud prior map from previous camera traversals using Pi3X and augments each point with DINOv3 features. At runtime, a local prior patch is retrieved using global localization, encoded with a sparse voxel backbone, and fused in bird's-eye view (BEV) with lifted multi-view camera features. Task-specific sparse transformer heads then predict 3D objects and vectorized map elements from the fused representation. On Argoverse 2, the vision-based prior improves a strong baseline from 0.287 to 0.299 CDS and from 0.669 to 0.750 vectorized mapping mAP. Ablations show that semantic DINOv3 features are particularly important for vectorized mapping. These results demonstrate that vision-built geometric-semantic priors provide an effective form of long-term scene memory for camera-based perception, improving both tasks without LiDAR for prior-map construction or online inference.