Recent advancements in Korean large language models (LLMs) have driven numerous benchmarks and evaluation methods, yet inconsistent protocols cause up to 10 p.p performance gaps across institutions. Overcoming these reproducibility gaps does not mean enforcing a one-size-fits-all evaluation. Rather, effective benchmarking requires diverse experimental approaches and a framework robust enough to support them. To this end, we introduce HRET (Haerae Evaluation Toolkit), an open-source, registry-based framework that unifies Korean LLM assessment. HRET integrates major Korean benchmarks, multiple inference backends, and multi-method evaluation, with language consistency enforcement to ensure genuine Korean outputs. Its modular registry design also enables rapid incorporation of new datasets, methods, and backends, ensuring the toolkit adapts to evolving research needs. Beyond standard accuracy metrics, HRET incorporates Korean-focused output analyses-morphology-aware Type-Token Ratio (TTR) for evaluating lexical diversity and systematic keyword-omission detection for identifying missing concepts-to provide diagnostic insights into language-specific behaviors. These targeted analyses help researchers pinpoint morphological and semantic shortcomings in model outputs, guiding focused improvements in Korean LLM development.

Fully-supervised lesion recognition methods in medical imaging face challenges due to the reliance on large annotated datasets, which are expensive and difficult to collect. To address this, synthetic lesion generation has become a promising approach. However, existing models struggle with scalability, fine-grained control over lesion attributes, and the generation of complex structures. We propose LesionDiffusion, a text-controllable lesion synthesis framework for 3D CT imaging that generates both lesions and corresponding masks. By utilizing a structured lesion report template, our model provides greater control over lesion attributes and supports a wider variety of lesion types. We introduce a dataset of 1,505 annotated CT scans with paired lesion masks and structured reports, covering 14 lesion types across 8 organs. LesionDiffusion consists of two components: a lesion mask synthesis network (LMNet) and a lesion inpainting network (LINet), both guided by lesion attributes and image features. Extensive experiments demonstrate that LesionDiffusion significantly improves segmentation performance, with strong generalization to unseen lesion types and organs, outperforming current state-of-the-art models. Code is available at https://github.com/HengruiTianSJTU/LesionDiffusion.

Bayesian phylogenetics is vital for understanding evolutionary dynamics, and requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric phylogenetic trees. We present a novel variational family based on coalescent times of a single-linkage clustering and derive a closed-form density for the resulting distribution over trees. Unlike existing methods for ultrametric trees, our method performs inference over all of tree space, it does not require any Markov chain Monte Carlo subroutines, and our variational family is differentiable. Through experiments on benchmark genomic datasets and an application to the viral RNA of SARS-CoV-2, we demonstrate that our method achieves competitive accuracy while requiring significantly fewer gradient evaluations than existing state-of-the-art techniques.

AI-assisted imaging made substantial advances in tumor diagnosis and management. However, a major barrier to developing robust oncology foundation models is the scarcity of large-scale, high-quality annotated datasets, which are limited by privacy restrictions and the high cost of manual labeling. To address this gap, we present PASTA, a pan-tumor radiology foundation model built on PASTA-Gen, a synthetic data framework that generated 30,000 3D CT scans with pixel-level lesion masks and structured reports of tumors across ten organ systems. Leveraging this resource, PASTA achieves state-of-the-art performance on 45 of 46 oncology tasks, including non-contrast CT tumor screening, lesion segmentation, structured reporting, tumor staging, survival prediction, and MRI-modality transfer. To assess clinical applicability, we developed PASTA-AID, a clinical decision support system, and ran a retrospective simulated clinical trial across two scenarios. For pan-tumor screening on plain CT with fixed reading time, PASTA-AID increased radiologists' throughput by 11.1-25.1% and improved sensitivity by 17.0-31.4% and precision by 10.5-24.9%; additionally, in a diagnosis-aid workflow, it reduced segmentation time by up to 78.2% and reporting time by up to 36.5%. Beyond gains in accuracy and efficiency, PASTA-AID narrowed the expertise gap, enabling less-experienced radiologists to approach expert-level performance. Together, this work establishes an end-to-end, synthetic data-driven pipeline spanning data generation, model development, and clinical validation, thereby demonstrating substantial potential for pan-tumor research and clinical translation.

Total Variation Denoising (TVD) is a fundamental denoising and smoothing method. In this article, we identify a new local minmax/maxmin formula producing two estimators which sandwich the univariate TVD estimator at every point. Operationally, this formula gives a local definition of TVD as a minmax/maxmin of a simple function of local averages. Moreover we find that this minmax/maxmin formula is generalizeable and can be used to define other TVD like estimators. In this article we propose and study higher order polynomial versions of TVD which are defined pointwise lying between minmax and maxmin optimizations of penalized local polynomial regressions over intervals of different scales. These appear to be new nonparametric regression methods, different from usual Trend Filtering and any other existing method in the nonparametric regression toolbox. We call these estimators Minmax Trend Filtering (MTF). We show how the proposed local definition of TVD/MTF estimator makes it tractable to bound pointwise estimation errors in terms of a local bias variance like trade-off. This type of local analysis of TVD/MTF is new and arguably simpler than existing analyses of TVD/Trend Filtering. In particular, apart from minimax rate optimality over bounded variation and piecewise polynomial classes, our pointwise estimation error bounds also enable us to derive local rates of convergence for (locally) Holder Smooth signals. These local rates offer a new pointwise explanation of local adaptivity of TVD/MTF instead of global (MSE) based justifications.

As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and available item features to continuously optimize assortments over time. In this paper, we consider the dynamic assortment problem with dual contexts -- user and item features. In high-dimensional scenarios, the quadratic growth of dimensions complicates computation and estimation. To tackle this challenge, we introduce a new low-rank dynamic assortment model to transform this problem into a manageable scale. Then we propose an efficient algorithm that estimates the intrinsic subspaces and utilizes the upper confidence bound approach to address the exploration-exploitation trade-off in online decision making. Theoretically, we establish a regret bound of $\tilde{O}((d_1+d_2)r\sqrt{T})$, where $d_1, d_2$ represent the dimensions of the user and item features respectively, $r$ is the rank of the parameter matrix, and $T$ denotes the time horizon. This bound represents a substantial improvement over prior literature, achieved by leveraging the low-rank structure. Extensive simulations and an application to the Expedia hotel recommendation dataset further demonstrate the advantages of our proposed method.

Contemporary applications, such as recommendation systems and mobile health monitoring, require real-time processing and analysis of sequentially arriving high-dimensional tensor data. Traditional offline learning, involving the storage and utilization of all data in each computational iteration, becomes impractical for these tasks. Furthermore, existing low-rank tensor methods lack the capability for online statistical inference, which is essential for real-time predictions and informed decision-making. This paper addresses these challenges by introducing a novel online inference framework for low-rank tensors. Our approach employs Stochastic Gradient Descent (SGD) to enable efficient real-time data processing without extensive memory requirements. We establish a non-asymptotic convergence result for the online low-rank SGD estimator, nearly matches the minimax optimal estimation error rate of offline models. Furthermore, we propose a simple yet powerful online debiasing approach for sequential statistical inference. The entire online procedure, covering both estimation and inference, eliminates the need for data splitting or storing historical data, making it suitable for on-the-fly hypothesis testing. In our analysis, we control the sum of constructed super-martingales to ensure estimates along the entire solution path remain within the benign region. Additionally, a novel spectral representation tool is employed to address statistical dependencies among iterative estimates, establishing the desired asymptotic normality.

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations (PDEs) with interfaces and some control constraints. The resulting algorithm is mesh-free and scalable to different PDEs, and it ensures the control constraints rigorously. Since the boundary and interface conditions, as well as the PDEs, are all treated as soft constraints by lumping them into a weighted loss function, it is necessary to learn them simultaneously and there is no guarantee that the boundary and interface conditions can be satisfied exactly. This immediately causes difficulties in tuning the weights in the corresponding loss function and training the neural networks. To tackle these difficulties and guarantee the numerical accuracy, we propose to impose the boundary and interface conditions as hard constraints in PINNs by developing a novel neural network architecture. The resulting hard-constraint PINNs approach guarantees that both the boundary and interface conditions can be satisfied exactly or with a high degree of accuracy, and they are decoupled from the learning of the PDEs. Its efficiency is promisingly validated by some elliptic and parabolic interface optimal control problems.

Linear layouts are a graph visualization method that can be used to capture an entry pattern in an adjacency matrix of a given graph. By reordering the node indices of the original adjacency matrix, linear layouts provide knowledge of latent graph structures. Conventional linear layout methods commonly aim to find an optimal reordering solution based on predefined features of a given matrix and loss function. However, prior knowledge of the appropriate features to use or structural patterns in a given adjacency matrix is not always available. In such a case, performing the reordering based on data-driven feature extraction without assuming a specific structure in an adjacency matrix is preferable. Recently, a neural-network-based matrix reordering method called DeepTMR has been proposed to perform this function. However, it is limited to a two-mode reordering (i.e., the rows and columns are reordered separately) and it cannot be applied in the one-mode setting (i.e., the same node order is used for reordering both rows and columns), owing to the characteristics of its model architecture. In this study, we extend DeepTMR and propose a new one-mode linear layout method referred to as AutoLL. We developed two types of neural network models, AutoLL-D and AutoLL-U, for reordering directed and undirected networks, respectively. To perform one-mode reordering, these AutoLL models have specific encoder architectures, which extract node features from an observed adjacency matrix. We conducted both qualitative and quantitative evaluations of the proposed approach, and the experimental results demonstrate its effectiveness.

Codimension-two vortex solutions are important solitonic objects in both quantum field theory and gravity. In this paper, we construct a class of codimension-two Alice-vortex solutions in axio-dilaton gravity, in which monodromy around the vortex enacts the axion transformation $C_0 \mapsto -C_0$. In IIB supergravity, this furnishes a class of R7-brane backgrounds of the sort predicted by the Swampland Cobordism Conjecture. Such configurations generically carry an intrinsic dipole moment. We extract additional properties of such branes from scattering probes. These results provide further evidence that the worldvolume theory of an R7-brane is an 8D non-supersymmetric interacting quantum field theory.

Lattice gauge theories (LGTs) provide a powerful framework for studying confinement, topological order, and exotic quantum matter. In particular, the paradigmatic phenomenon of confinement, where dynamical matter is coupled to gauge fields and forms bound states, remains an open problem. In addition, LGTs can provide low-energy descriptions of quantum spin liquids, which is the focus of ongoing experimental research. However, the study of LGTs is often limited theoretically by their numerical complexity and experimentally in implementing challenging multi-body interactions, such as the plaquette terms crucial for the realization of many exotic phases of matter. Here we investigate a $(2+1)$D $\mathbb{Z}_2$ LGT coupled to hard-core bosonic matter featuring a global U(1) symmetry, and show that dynamical matter naturally induces sizable plaquette interactions even in the absence of explicit plaquette terms in the Hamiltonian. Using a combination of density matrix renormalization group simulations and neural quantum state calculations up to a system size of $20 \times 20$, we analyze the model across different fillings and electric field strengths. At small coupling strength, we find a large plaquette expectation value, independent of system size, for a wide range of fillings, which decreases in the presence of stronger electric fields. Furthermore, we observe signatures of a confinement-deconfinement transition at weak coupling strengths. Our results demonstrate that dynamical U(1) matter can induce complex multi-body interactions, suggesting a natural route to the realization of strong plaquette terms and paving the way for realizing a topological quantum spin liquid protected by a large gap.

Spinodal decomposition, a key mechanism to microstructure formation in materials, has long posed challenges for predictive modeling, due to the need for parameter-free approaches that accurately capture local energy landscapes. In this work, we propose an approach to predict spinodal behavior by introducing a disorder viscosity correction to bulk free energies computed from finite, small, representative cells. We approximate the energy penalty required to transition into a disordered state to enable the stabilization of locally concave bulk free energy regions - essential for interface formation - while suppressing long-range concentration fluctuations. This approximation circumvents the complexity of full ab initio parameterization of interfacial properties and is well-suited for high-throughput and machine-learning frameworks. Our approach captures the necessary physics underpinning spinodal kinetics, offering a scalable route to predict spinodal regions in compositionally complex and high-entropy materials.

One of the promising dark matter (DM) candidates is a keV scale sterile neutrino. In the early universe the observed relic of the sterile neutrino DM is generated via the \textit{Dodelson-Widrow} mechanism. However, this production scenario is severely constraint by various astrophysical observations. Many non-standard interactions between active ($ν_a$) and sterile ($ν_s$) neutrino have been proposed to evade these astrophysical bounds. Here, we study sterile neutrino in the context of a mass-varying scenario by coupling both active and sterile neutrino to a scalar field. This novel mechanism opens up a new parameter space that generates the observed DM relic and alleviates the \textit{Hubble tension}. We find that the resulting parameter space can be fully probed by future X-ray missions.

Diamond to graphite transformation is a complex kinetically driven process which has been studied under various conditions for its fundamental importance. We report the transformation of diamond embedded ceramic matrix composites during hypersonic impact. Diamond particles embedded in cubic boron nitride matrix provide a superhard composite that was subjected to high impact collisions of metal projectiles travelling at speeds reaching Mach 8.45. Our observations suggest that the energy absorption and fracture of the composite is primarily enabled via the phase change of diamond into graphite. Characterization of the impact-fractured composite shows transformed diamond particles and provides details of the shock-induced phase transformation and the nature of diamond-graphite interfaces formed during rapid phase change. The study provides new understanding of phase transformation of diamond under extreme conditions.

In this article, we present a method for computing accurate and scalable nuclear forces within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) framework. Our approach leverages automatic differentiation of the energy functional to obtain nuclear gradients at a computational cost comparable to that of energy evaluation. The accuracy of the method is validated against finite difference calculations, showing excellent agreement. We then explore several machine learning (ML) strategies for learning noisy AFQMC data. These ML potentials are subsequently used to perform geometry optimizations and nudged elastic band (NEB) calculations, successfully identifying the transition state of the formamide-formimidic acid tautomerization. The resulting transition state geometry and barrier heights are in close agreement with coupled-cluster reference values. This work paves the way for highly accurate geometry optimization, molecular dynamics, or reaction path calculations.

Unbinned likelihood fits aim at maximizing the information one can extract from experimental data, yet their application in realistic statistical analyses is often hindered by the computational cost of profiling systematic uncertainties. Additionally, current machine learning-based inference methods are typically limited to estimating scalar parameters in a multidimensional space rather than full differential distributions. We propose a general framework for Simulation-Based Inference (SBI) that efficiently profiles nuisance parameters while measuring multivariate Distributions of Interest (DoI), defined as learnable invertible transformations of the feature space. We introduce Factorizable Normalizing Flows to model systematic variations as parametric deformations of a nominal density, preserving tractability without combinatorial explosion. Crucially, we develop an amortized training strategy that learns the conditional dependence of the DoI on nuisance parameters in a single optimization process, bypassing the need for repetitive training during the likelihood scan. This allows for the simultaneous extraction of the underlying distribution and the robust profiling of nuisances. The method is validated on a synthetic dataset emulating a high-energy physics measurement with multiple systematic sources, demonstrating its potential for unbinned, functional measurements in complex analyses.

Co-design is an increasingly popular approach in HCI and visualization, yet there is little guidance on how to effectively apply this method in visualization contexts. In this paper, we visually present our experience of a two-and-a-half-year co-design project with the local arts community. Focusing on facilitating community exploration and sense-making around arts funding distribution, the project involved a series of co-design sessions between visualization researchers and members of the arts community. Through these iterative sessions, we built shared understanding and developed visualization prototypes tailored to community needs. However, the practice is far from complete, and we found ourselves continually returning to the "fuzzy front end" of the co-design process. We share this ongoing story through comic-style visuals and reflect on three fuzzy front ends that we encountered during the project. By sharing these experiences with the visualization community, we hope to offer insights that others can draw on in their own community-engaged co-design work.

Moment equations offer a compelling alternative to the kinetic description of plasmas, gases, and liquids. Their simulation requires fewer degrees of freedom than phase space models, yet it can still incorporate kinetic effects to a certain extent. To derive moment equations, we use a parameterization of the distribution function using centered moments, as proposed by Burby. This yields moment equations for which the parameterized distribution function exactly solves the hyperbolic conservation law. Similarly, a particle model is derived based on a parametrization of the distribution function using phase space moments. Finally, we present the application of the method to the non-relativistic and relativistic Vlasov--Maxwell equations.

Multimodal Retrieval-Augmented Generation (MRAG) has emerged as a key paradigm for grounding MLLMs with external knowledge. While query pre-processing (e.g., rewriting) is standard in text-based RAG, existing MRAG pipelines predominantly treat visual inputs as static and immutable, implicitly assuming they are noise-free. However, real-world visual queries are often ``imperfect'' -- suffering from geometric distortions, quality degradation, or semantic ambiguity -- leading to catastrophic retrieval failures. To address this gap, we propose V-QPP-Bench, the first comprehensive benchmark dedicated to Visual Query Pre-processing (V-QPP). We formulate V-QPP as an agentic decision-making task where MLLMs must autonomously diagnose imperfections and deploy perceptual tools to refine queries. Our extensive evaluation across 46,700 imperfect queries and diverse MRAG paradigms reveals three critical insights: (1) Vulnerability -- visual imperfections severely degrade both retrieval recall and end-to-end MRAG performance; (2) Restoration Potential \& Bottleneck -- while oracle preprocessing recovers near-perfect performance, off-the-shelf MLLMs struggle with tool selection and parameter prediction without specialized training; and (3) Training Enhancement -- supervised fine-tuning enables compact models to achieve comparable or superior performance to larger proprietary models, demonstrating the benchmark's value for developing robust MRAG systems The code is available at https://github.com/phycholosogy/VQQP_Bench

We compute the superpotentials for known families of Koszul Artin-Schelter regular algebras of dimension four using Magma, and apply Schur-Weyl duality from representation theory to determine the relevant invariants. Through the Borel-Weil theorem, we interpret these invariants as sections of line bundles over partial flag varieties, resulting in geometric invariants that, in some cases, correspond to K3 surfaces. We compute discrete invariants of these geometric invariants and use them to distinguish algebras.

We introduce an absorption imaging technique for ultracold gases that suppresses interference fringes and coherence-induced artifacts by reducing the transverse spatial coherence of the imaging light. The method preserves the narrow spectral bandwidth required for resonant absorption imaging and is implemented as a modular extension to standard imaging setups using a rotating diffuser. We demonstrate tunability of the illumination light's coherence without modifying the imaging optics. Using this approach, we achieve reliable imaging of ultracold atomic clouds in micron-scale proximity to complex surfaces, where standing waves, edge diffraction, and speckle severely limit conventional absorption imaging.

How much work does it cost for a propelled particle to stay localised near a stationary target, defying both thermal noise and a constant flow that would carry it away? We study the control of such a particle in finite time and find optimal protocols for time-dependent swim velocity and diffusivity, without feedback. Accuracy, quantified via the mean squared deviation from the target, and energetic cost turn out to be related by a trade-off, which complements the one between precision and cost known in stochastic thermodynamics. We show that accuracy better than a certain threshold requires active driving, which comes at a cost that increases with accuracy. The optimal protocols have discontinuous swim velocity and diffusivity, switching between a passive drift state with vanishing diffusivity and an active propulsion state. This study highlights how a time-dependent diffusivity enhances optimal control and sets benchmarks for cost and accuracy of artificial self-propelled particles navigating noisy environments.

Fast matrix multiplication algorithms are asymptotically faster than the classical cubic-time algorithm, but they are often slower in practice. One important obstacle is the use of complex coefficients, which increases arithmetic overhead and limits practical efficiency. This paper focuses on transforming complex-coefficient matrix multiplication schemes into equivalent real- or rational-coefficient ones. We present a systematic method that, given a complex-coefficient scheme, either constructs a family of equivalent rational algorithms or proves that no equivalent rational scheme exists. Our approach relies only on basic linear-algebraic properties of similarity transformations of complex matrices. This method recovers the previously known ad hoc results of Dumas, Pernet, and Sedoglavic (2025) and extends them to more general settings, including algorithms involving rational coefficients and square roots, with $i=\sqrt{-1}$ as a special case. Using this framework, we show that no rational scheme is equivalent to Smirnov's $\langle4,4,9,104\rangle$ $\mathbb{Q}[\sqrt{161}]$ algorithm (2022) and that no real scheme is equivalent to the $\langle4,4,4,48\rangle$ complex algorithm of Kaporin (2024). More generally, our approach can also be used to prove the non-existence of integer-coefficient schemes.

Software source code often harbours "hotspots": small portions of the code that change far more often than the rest of the project and thus concentrate maintenance activity. We mine the complete version histories of 91 evolving, actively developed GitHub repositories and identify 15 recurring line-level hotspot patterns that explain why these hotspots emerge. The three most prevalent patterns are Pinned Version Bump (26%), revealing brittle release practices; Long Line Change (17%), signalling deficient layout; and Formatting Ping-Pong (9%), indicating missing or inconsistent style automation. Surprisingly, automated accounts generate 74% of all hotspot edits, suggesting that bot activity is a dominant but largely avoidable source of noise in change histories. By mapping each pattern to concrete refactoring guidelines and continuous integration checks, our taxonomy equips practitioners with actionable steps to curb hotspots and systematically improve software quality in terms of configurability, stability, and changeability.

Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation describing the population distribution and a backward Hamilton-Jacobi-Bellman (HJB) equation defining the value function. Solving MFG systems efficiently is challenging, with the structure of each system depending on an initial distribution of players and the terminal cost of the game. We propose an operator learning framework that solves parametric families of MFGs, enabling generalization without retraining for new initial distributions and terminal costs. We provide theoretical guarantees on the approximation error, parametric complexity, and generalization performance of our method, based on a novel regularity result for an appropriately defined flow map corresponding to an MFG system. We demonstrate empirically that our framework achieves accurate approximation for two representative instances of MFGs: a cybersecurity example and a high-dimensional quadratic model commonly used as a benchmark for numerical methods for MFGs.

The rapid growth of decentralized systems in theWeb3 ecosystem has introduced numerous challenges, particularly in ensuring data security, privacy, and scalability [3, 8]. These systems rely heavily on distributed architectures, requiring robust mechanisms to manage data and interactions among participants securely. One critical aspect of decentralized systems is key management, which is essential for encrypting files, securing database segments, and enabling private transactions. However, securely managing cryptographic keys in a distributed environment poses significant risks, especially when nodes in the network can be compromised [9]. This research proposes a decentralized database scheme specifically designed for secure and private key management. Our approach ensures that cryptographic keys are not stored explicitly at any location, preventing their discovery even if an attacker gains control of multiple nodes. Instead of traditional storage, keys are encoded and distributed using the BFLUT (Bloom Filter for Private Look-Up Tables) algorithm [7], which enables secure retrieval without direct exposure. The system leverages OrbitDB [4], IPFS [1], and IPNS [10] for decentralized data management, providing robust support for consistency, scalability, and simultaneous updates. By combining these technologies, our scheme enhances both security and privacy while maintaining high performance and reliability. Our findings demonstrate the system's capability to securely manage keys, prevent unauthorized access, and ensure privacy, making it a foundational solution for Web3 applications requiring decentralized security.

Transitions between distinct dynamical regimes are ubiquitous in nonequilibrium systems. As a prototypical example, deposition growth is often accompanied by irreversible morphological instabilities. Forecasting such transitions from pre-transition configurations remains fundamentally challenging, as early precursors are weak, spatially heterogeneous, and masked by inherent fluctuations. Here, we investigate compact-to-dendritic transitions (CDTs) in a two-dimensional particle-based electrodeposition model and formulate a horizon-based early-warning task using trajectory-resolved transition points. We demonstrate that anticipating the CDT is intrinsically a spatiotemporal problem: neither static morphological descriptors nor temporal learning applied to predefined features alone yields reliable predictive signals. In contrast, end-to-end learning of jointly optimized spatial and temporal representations from growth images enables robust anticipation across a wide range of prediction horizons. Analysis of the learned latent dynamics reveals the emergence of a low-dimensional surrogate variable that tracks progressive morphological destabilization and undergoes reorganization near the transition. We further show that the learned spatiotemporal representation exhibits limited but systematic transferability across reaction-rate conditions, with predictive performance degrading as the inference condition departs from the training condition, consistent with changes in the latent-state dynamics. Overall, our results establish a general formulation for forecasting incipient instabilities in nonequilibrium interfacial growth, with implications for the predictive monitoring and control of pattern-forming driven systems.

We provide a Macaulay2 code for computing the dimension of the tangent space to $\mathcal{B}(e,c_2)$ in certain cases. Using this code, we identify components of $\mathcal{B}(e,c_2)$ containing singular points and compute the dimension of the irreducible component $M_4$ of $\mathcal{B}(-1,6)$, whose existence was proved in \cite{MF2021}. Furthermore, we prove the existence of infinite families of irreducible components of $\mathcal{B}(0,c_2)$.

Determining the three-dimensional structure of a protein from its amino-acid sequence remains a fundamental problem in biophysics. The discrete Frenet geometry of the C$_α$ backbone can be mapped, via a Hasimoto-type transform, onto a complex scalar field $ψ=κ\,e^{i\sumτ}$ satisfying a discrete nonlinear Schrödinger equation (DNLS), whose soliton solutions reproduce observed secondary-structure motifs. Whether this mapping, which provides an elegant geometric description of folded states, can be extended to a predictive framework for protein folding remains an open question. We derive an exact closed-form decomposition of the DNLS effective potential $V_{\text{eff}}=V_{\text{re}}+iV_{\text{im}}$ in terms of curvature ratios and torsion angles, validating the result to machine precision across 856 non-redundant proteins. Our analysis identifies three structural barriers to forward prediction: (i)~$V_{\text{im}}$ encodes chirality via the odd symmetry of $\sinτ$, accounting for ${\sim}31\%$ of the total information and implying a $2^N$ degeneracy if neglected; (ii)~$V_{\text{re}}$ is determined primarily (${\sim}95\%$) by local geometry, rendering it effectively sequence-agnostic; and (iii)~self-consistent field iterations fail to recover native structures (mean RMSD $= 13.1$\,Å) even with hydrogen-bond terms, yielding torsion correlations indistinguishable from zero. Constructively, we demonstrate that the residual of the DNLS dispersion relation serves as a geometric order parameter for $α$-helices (ROC AUC $= 0.72$), defining them as regions of maximal integrability. These findings establish that the Hasimoto map functions as a kinematic identity rather than a dynamical governing equation, presenting fundamental obstacles to its use as a predictive framework for protein folding.

We develop methodology to detect structural breaks in the slope function of a concurrent functional linear regression model for functional time series in $C[0,1]$. Our test is based on a CUSUM process of regressor-weighted OLS residual functions. To accommodate both global and local changes, we propose $L^2$- and sup-norm versions, with the sup-norm particularly sensitive to spike-like changes. Under Hölder regularity and weak dependence conditions, we establish a functional strong invariance principle, derive the asymptotic null distribution, and show that the resulting tests are consistent against a broad class of alternatives with breaks in the slope function. Simulation studies illustrate finite-sample size and power. We apply the method to sports data obtained via body-worn sensors from running athletes, focusing on hip and knee joint-angle trajectories recorded during a fatiguing run. As fatigue accumulates, runners adapt their movement patterns, and sufficiently pronounced adjustments are expected to appear as a change point in the regression relationship. In this manner, we illustrate how the proposed tests support interpretable inference for biomechanical functional time series.