Subsurface imaging understanding bridges observed geophysical data and quantitative geological models, supporting hydrocarbon exploration, CO2 storage site assessment, and geohazard monitoring. Over the past decade, deep learning has substantially reshaped interpretation workflows. To take stock of this progress, we systematically analyze 652 publications from 2015 to 2025 and organize the field into four major tasks: structural interpretation, geobody identification, seismic facies analysis, and property estimation. Yet subsurface imaging interpretation differs fundamentally from other AI-driven tasks, facing ambiguous signals, pronounced interpretive non-uniqueness, sparse semantics, unfixed target locations, and scarce reliable annotations. Building on the reviewed literature, we summarize three interrelated challenges that define its frontier: interpretation under complex geological conditions, cross-survey semantic generalization under low information density, and the absence of reliable benchmarks. Addressing them will hinge on integrating human expertise, physical constraints, and geological priors into model training or inference, and on treating uncertainty quantification as an intrinsic model output. Among these, the lack of unified benchmarks has been particularly consequential, making fair comparison difficult, hindering reproducibility, and fragmenting community efforts. We therefore propose a community benchmark spanning fault segmentation, relative geologic time estimation, geobody segmentation, and property modeling. It integrates unified evaluation protocols, pretrained models, and datasets that combine synthetic data for quantitative evaluation with real surveys for qualitative assessment. By coupling a decade-spanning review with an evolving benchmark, this work offers a timely reference and a reproducible foundation to accelerate future research and deployment.

We present a theoretical study of global and azimuthal-angle-dependent $Λ$ hyperon polarization in isobaric $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{NN}}=200$~GeV using the TRENTo3D initial condition model coupled to the (3+1)-D viscous hydrodynamic model CLVisc. A longitudinal flow velocity gradient, controlled by $f_v$, is introduced into TRENTo3D for the first time, providing an essential source of initial vorticity in this symmetric isobaric system. Within the isothermal polarization framework, the model provides a simultaneous description of STAR measurements of the global polarization $-P^{y}$ (centrality, $p_T$, and $η$ dependences) and the azimuthal modulation coefficients $P_{y,\mathrm{c0}}$ and $P_{y,\mathrm{c2}}$. The $p_T$ dependence reflects the competition between thermal vorticity and shear contributions: the thermal term decreases with $p_T$, while the shear term rises and increasingly shapes the curvature of the total polarization. In this decomposition, $P_{y,\mathrm{c2}}$ is dominantly shear-driven and serves as a clean probe of shear-induced polarization. Scans of $f_v$, $k_T$, and nuclear structure provide complementary constraints on the initial state, while the bulk-viscosity dependence is also examined; the five nuclear structure configurations from the STAR isobar blind analysis yield nearly indistinguishable polarization. For $P_z$, the isothermal scenario captures the azimuthal modulation but overpredicts the high-$p_T$ modulation amplitude, and comparison with the standard thermal treatment shows that neither scenario achieves a unified description of all observables.

Ultra-high-dimensional array-based CpG methylation studies require statistical frameworks that simultaneously provide supervised structure discovery, interpretability, scalable latent-dimension identification, and computational feasibility. We propose SOLAR (Supervised Orthogonal Low-rank Adaptive Regression), a supervised low-rank latent-factor framework for identifying CpG-level methylation structure associated with residualized DNAm age. SOLAR combines orthogonal low-rank regression with a penalized maximum a posteriori formulation, dimension-adaptive BIC-type penalization, and a trans-dimensional simulated-annealing strategy for automatic latent-rank selection, together with theoretical guarantees including identifiability, fixed-rank recovery, and rank-selection consistency under suitable regularity conditions. The framework additionally incorporates computationally and memory-efficient optimization strategies demonstrating scalability up to $p=10^7$, while analyses at $p=10^6$ remain feasible on standard desktop computing environments. Simulation studies demonstrate stable rank recovery, competitive supervised signal recovery, and strong scalability across moderate-, high-, and ultra-high-dimensional regimes. Using longitudinal EPIC-array CpG methylation data from the GUSTO birth cohort, comprising $n=1051$ methylation profiles collected across infancy and early childhood with approximately 860,000 assayed CpGs per sample, SOLAR identifies heterogeneous supervised methylation structure associated with residualized DNAm age beyond chronological age alone, together with biologically coherent CpG signatures and enrichment patterns.

We prove the existence of numerically good minimal models for generalized klt pairs of relative log numerical dimension zero, assuming Generalized Nonvanishing. To this end, we establish a numerical version of the generalized canonical bundle formula, which may be of independent interest.

Automatic Modulation Recognition (AMR) is a key enabling technology for cognitive radio and intelligent spectrum management in next-generation wireless systems. However, current deep learning-based AMR methods predominantly rely on static multi-scale fusion strategies, which lack the flexibility to adapt to the highly dynamic temporal variations of modulation signals. To address this limitation, we propose MoEformer, an adaptive Multi-Scale Mixture-of-Experts Transformer network that directly processes I/Q signals to preserve their temporal and phase structures. Specifically, MoEformer constructs multi scale expert views through temporal resampling, employs an input-dependent gating mechanism for dynamic expert fusion, and integrates Rotary Position Embeddings (RoPE) within Transformer encoders to capture both local and global tem poral dependencies. Comprehensive evaluations on three widely adopted benchmarks (RadioML2016.10a, RadioML2016.10b, and RadioML2018.01A) demonstrate that MoEformer outperforms the competitive baselines, achieving superior average recognition accuracies of 63.74%, 66.24%, and 64.22%, respectively. In addition, the proposed method strikes an optimal trade-off between recognition performance and model complexity.

Understanding vehicle movement on road networks is closely related to various practical and theoretical issues. While recent works have focused on which cost vehicles minimize while moving, how they move to minimize that cost remains less explored. In this work, we analyze large-scale data of individual vehicle trajectories in real-world road networks to identify cost-minimizing movement patterns of vehicles and the influence of road network structure on such movement. We observed that vehicle movements exhibit three phases: the beginning, middle, and end of trips. At the beginning and end, vehicles detour more, lose directional memory quickly, and travel at lower speeds than during the middle. In contrast, during the middle, they tend to detour less, maintain directional memory, and travel faster than at the beginning and end. Finally, at the beginning and end, vehicles exhibit similar detour and velocity patterns, except the direction of movement. To understand these patterns, we propose a double-layered network model mimicking the hierarchical structure of real-world road networks. We found that when vehicles move across our model network while minimizing travel time, they tend to concentrate on high-level roads, and the three observed movement phases are reproduced. Consequently, when a vehicle moves between a given origin-destination pair, it must enter and exit these high-level roads. This causes it to deviate from the trajectory that minimizes travel distance between the same origin-destination pair -- particularly at the beginning and end of the trip. Our results reveal common patterns underlying individual vehicle movements that appear highly diverse at first glance, demonstrating that these patterns emerge because vehicles leverage the characteristics of hierarchical road networks to minimize travel time.

Multimodal sequential recommendation (MSR) incorporates textual and visual information to improve recommendation quality. However, recent studies and our empirical analysis show that visual features are often underutilized, thereby contributing far less than textual signals. We attribute this issue to two factors: insufficient visual representation learning (pretrained encoders fail to capture preference-relevant cues) and unbalanced visual-text optimization (textual features dominate the learning process). To address these issues, we propose Teach Multimodal Recommendation Model to See via Personalized Visual Extraction and Adaptive Learning (REVEAL), a plug-and-play framework that enhances visual representation learning and cross-modal optimization without modifying the original recommendation backbone. REVEAL consists of Feedback-Guided Visual Extraction (FVE), which refines prompt-guided visual extraction through task-level feedback, and Adaptive Visual Learning (AVL), which dynamically reweights visual learning to alleviate modality imbalance. Experiments on multiple real-world datasets and MSR backbones demonstrate that REVEAL consistently improves recommendation performance. Further analysis shows that these gains arise from more effective attention to preference-relevant visual regions and better visual utilization during training. The code is available at https://github.com/YutongLi2024/REVEAL.

We prove local centralizer rigidity results for elements of Weyl chamber flows and twisted Weyl chamber flows on compact homogeneous spaces. For generic elements in the twisted setting, sufficiently large dimension of the centralizer forces smooth conjugacy to an algebraic model. For many non-generic elements, we prove analogous rigidity under a virtual centralizer-isomorphism hypothesis.

Aims. We expand the planetary census around massive stellar hosts through a long-term campaign of high-precision radial velocity (RV) measurements on evolved stars. Methods. We analyse data acquired with the CORALIE spectrograph covering 15-18 years on HD125136, HD127195, and HD220218. Stellar parameters are derived through different methods for a comprehensive characterization of each star. We then evaluate the presence of planetary signals in the RV time series using the Bayesian inference tool kima. Finally, we design an observing strategy aimed at mitigating the impact of pulsations on evolved stars and test its effectiveness on the low-luminosity red giant HD127195. Results. We detect signals that are accurately modelled by Keplerian curves in the RV data of the three stars: one on HD 125136, two on HD 127195, and one on HD 220218. While the signals on the first two stars seem to be of planetary origin, the signal on the third one shows several signs of stellar activity. We therefore identify a planetary companion around HD125136 with a minimum mass of 2.26 MJup on an 850 d orbit, and on HD127195 we identify a system composed of planets with 0.66 MJup and 0.78 MJup with orbital periods of 535 d and 834 d, respectively. Conclusions. We detect three massive planets around two low-luminosity red giant stars in a region of the parameter space that is poorly populated in both stellar mass and planetary orbital periods. The dedicated observing campaign on HD127195 showcases how stellar pulsations can be efficiently averaged out to below 5 m/s in low-luminosity giant stars.

This paper proposes a novel Adaptive Decentralized Quasi-Newton (AdaDQN) method for solving smooth nonconvex optimization problems over undirected networks. While existing decentralized algorithms with multiple local updates suffer from a pessimistic theoretical bottleneck, where the convergence stepsize must be inversely proportional to the number of local updates, our work overcomes this limitation. We revisit local update methods through a Majorization-Minimization (MM) lens and establish a Robust Inexact Algorithm (RIA) framework. Inspired by this framework, AdaDQN integrates a safeguarded consensus-aware termination criterion to dynamically balance local computational gains against consensus error, complemented by a scalable memoryless BFGS update and an event-triggered communication protocol to significantly reduce communication overhead. We establish the global convergence of AdaDQN to a first-order stationary point. Crucially, we prove that the convergence stepsize bound is decoupled from the reciprocal of maximum number of local updates. Numerical experiments demonstrate that AdaDQN achieves a superior computation-communication tradeoff, outperforming state-of-the-art decentralized methods across various performance metrics.

Let $H$ be a finite-dimensional, non-semisimple Hopf algebra over an algebraically closed field $\mathbf{k}$. This paper investigates the asymptotic behavior of the core of left $H$-modules through the lens of the gamma invariant $γ_{\mathfrak{X}}$ relative to a representation ideal $I_{\mathfrak{X}}$. We establish an equivalent characterization for the quotient of the Green ring $R_{\mathfrak{X}}$ to be a transitive fusion ring, demonstrating that transitivity is synonymous with the non-degeneracy of a naturally induced bilinear form and the collapse of the ideals $P_{+}$, $P_{-}$ and $I_{\operatorname{max}}$ into a single ideal. Furthermore, we prove that the Green ring exhibits the structure of a representation ring in the sense of Benson, provided that the square of the antipode is an inner automorphism and the equality $I_{\operatorname{max}}=I_{\operatorname{proj}}$ holds. As an explicit application of these frameworks, we analyze the Drinfeld double $D(H_4)$ of the Sweedler algebra, identifying an infinite family of distinct representation ideals and proving that the maximal gamma invariant $γ_{\operatorname{max}}$ induces a genuine ring homomorphism. Finally, for Hopf algebras of finite representation type under the assumption $P_{+} = P_{-} = I_{\operatorname{max}}$, we show that $γ_{\operatorname{max}}$ coincides precisely with the Frobenius--Perron dimension, and we explicitly compute the gamma invariants for the standard basis elements of the Green ring of the Taft algebra $H_n(q)$.

We study the behaviour of the smallest possible constant $d(a,b, p,ε)$ in Hardy inequality $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^px^ε\,dx\leq d(a,b,p,ε)\,\int_a^b [f(x)]^px^ε\, dx, \quad 2\le p<\infty. $$ The exact rate of convergence of $d(a,b,p,ε)$ is established and the ``almost extremal'' function is found.

A bicoloration of a graph $G=(V,E)$ is a map $β:V\to\{-1,1\}$. A local inversion at a vertex $v$ complements the subgraph induced by the neighbors of $v$ and simultaneously reverses the colors of all neighbors of $v$. Sabidussi (Discrete Mathematics, 1987) showed that every bicolored graph on $n$ vertices without isolated vertices admits a color reversal using at most $6n+3$ local inversions, and that any two bicolorings of such a graph can be transformed into each other using at most $9n$ local inversions. Recently, Porte, Sandeep, and Santra (CALDAM 2026) improved these bounds to $4n-3$ and $\lfloor(11n-3)/2\rfloor$, respectively. We prove the tight bound $3n$ by showing that, for every graph on $n$ vertices without isolated vertices, any bicoloring can be transformed into any other bicoloring using at most $3n$ local inversions. We also show that this bound is best possible: for complete graphs and stars on $n$ vertices, at least $3n$ local inversions are required to reverse the colors of all vertices. Moreover, the proof of the upper bound is constructive: given two bicolorings, it produces, in polynomial time, a sequence of at most $3n$ local inversions transforming one into the other.

This paper addresses the problem of quantitative rapid stabilization via the linear quadratic (LQ) theory. Specifically, for non-self-adjoint parabolic equations, by virtue of the LQ theory, we derive the quantitative rapid stabilization by selecting a special cost functional and combining it with a quantitative observability inequality. Furthermore, this approach reveals the equivalence between the quantitative rapid stabilization and the quantitative observability inequality for linear systems. In addition, we apply this framework to the Navier--Stokes equations and establish the quantitative rapid stabilization around nontrivial steady states. Finally, we extend this methodology to finite-dimensional feedback laws in self-adjoint cases.

Modern enterprises face an accelerating onslaught of API-targeted threats amid a rapidly expanding attack surface. Record volumes of software vulnerabilities continue to accelerate dramatically, with 28,818 CVEs disclosed in 2023 (a 38% jump from 2022) and 40,009 CVEs in 2024 (another 38% increase), while the average time-to-exploit (TTE) of new flaws shrank to mere days (approximately 5 days in 2023, down from 32 days in 2021). At the same time, API usage dominates web traffic and has become a primary vector for breaches - 99% of organizations experienced API security incidents in the last year, with 22% suffering actual data breaches via APIs (based on industry vendor research). This paper proposes a comprehensive "security-first" framework for API pipeline development, leveraging Zero-Trust Architecture principles within DevSecOps practices to counter these trends. We introduce a five-pillar approach encompassing Governance & Planning, Secure Design, Continuous Testing, Pipeline Controls, and Runtime Protection, aligned with industry standards (OWASP API Security Top 10 2023, NIST Secure Software Development Framework) and recent cybersecurity advisories. The results show significant improvements in vulnerability mitigation and breach prevention (e.g., 30% reduction in security incidents and 40% fewer post-release vulnerabilities in representative case studies), highlighting the positive impact of proactive security integration. The paper concludes with a discussion on implementation challenges, the evolving threat landscape, and recommendations for organizations to adopt a security-first pipeline with Zero-Trust to fortify API development against current and future threats.

As large language models (LLMs) are increasingly deployed with highly heterogeneous workloads, chunked-prefill execution has emerged as a mainstream serving architecture. Balancing scheduling fairness and latency stability in such environments is critical; otherwise, severe head-of-line blocking and request starvation will degrade user experience. However, existing systems rely on rigid First-Come, First-Served (FCFS) policies and static token budgets, leading to fairness degradation and unpredictable latency jitter. To address these issues, we propose a fairness-aware and latency-controllable scheduling framework for chunked-prefill LLM engines. Specifically, we design a lightweight aging-based scheduling policy that dynamically calculates priorities using accumulated waiting time and remaining prefill work. Furthermore, we develop Latency-Prediction-Based Request Scheduling (LPRS) and Active Prefill Control (APC) to replace static budgets with target-time constraints and actively regulate prefill concurrency. We evaluated our scheduling framework on NVIDIA GPUs and Ascend accelerators using real-world workloads. Results show the aging policy reduces mean end-to-end latency by over 10\% compared to FCFS. Moreover, LPRS and APC significantly reduce P99 tail latency and suppress prefill fragmentation, confirming that the structural prefill control and the temporal latency constraints are fundamentally complementary. All codes have been released in Github.

Exploits are widely used to check whether library vulnerabilities appear in different versions and to mark affected version ranges. Exploit-based checks sometimes fail because exploits stop running on many versions after API or environment changes. Commit-based methods, such as SZZ-style analysis, sometimes miss the right introduce commits and spread labels incorrectly along long version chains. These problems leave many affected versions unlabeled or wrongly labeled and make manual exploit failure analysis very expensive and impractical at scale. We present ATTAIN, a trace-driven diff analysis framework with three modules to assess vulnerability presence across evolving library versions. The modules are trace construction, diff exploration, and affected-version judgment. The trace construction module executes an exploit across historical library versions and compares their behaviors to capture cross-version execution divergences. Using these divergences, the diff exploration module guides an LLM through a finite-state tool loop to autonomously search over version changes and collect vulnerability-relevant diff hunks. The affected-version judgment module reasons over the collected evidence to determine whether the vulnerability exists in each version and outputs the affected version range. We evaluate ATTAIN on an extensive dataset comprising 224 CVEs and 25,943 library versions across 128 libraries. ATTAIN achieves an F1-score of 93.24%, outperforming the commit-based methods V-SZZ and LLM4SZZ by 116.28% and 33.30%, respectively. ATTAIN uses short tool-guided prompts and a fixed number of iterations, keeping token usage low. It matches or surpasses existing methods on frequent CWE types, including cases where exploit runs fail for non-vulnerability reasons or commit messages do not clearly delimit affected versions.

We implement GPU acceleration of collinear and noncollinear density functional theory (DFT) calculations in the numerical atomic orbitals (NAOs) code OpenMX by offloading matrix multiplications and eigenvalue solves (plus selected auxiliary steps) to cuBLAS/cuSOLVER and OpenACC. Benchmarks on the Pegasus supercomputer (per node: a 48-core Intel Xeon Platinum 8468 CPU and one NVIDIA H100 GPU) compare GPU-accelerated and CPU-only runs under identical settings. For a 512-atom collinear case on two nodes (two GPUs total), the GPU-accelerated calculation achieves a 2.02 times speedup over a CPU-only run on two nodes (96 CPU cores total); for a 384-atom noncollinear case on two nodes (two GPUs total), the speedup is 2.60 times over two CPU-only nodes (96 cores). These results demonstrate practical GPU-accelerated DFT in an NAO-based code for both collinear and noncollinear calculations.

We study the behaviour of the smallest possible constant $d_n$ in weighted Hardy inequality $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2 k^ε\le d(n,ε)\,\sum_{k=1}^{n}{a_k^2}\,k^ε$$ The exact rate of convergence of $d_n$ is established and the ``almost extremal'' sequence is found.

Numerical computation of stochastic control problems under partial observation is challenging because the dynamic programming formulation is naturally posed on the conditional distribution of the hidden state. We propose particle-based methods that replace this infinite-dimensional filtering state by a finite-dimensional weighted particle system, building on recent limit theory for mean-field control with common-noise-adapted controls. We prove, under suitable assumptions, convergence of the fully discretized particle approximation to the original continuous-time partially observed control problem. The particle reformulation is high-dimensional but permutation-invariant, a structure that can be exploited by symmetric neural network architectures. We develop two deep learning algorithms: a direct optimization method for feedback controls and a Deep BSDE method for particle problems admitting a backward stochastic differential equation representation. We also extend the computational framework to partially observed mean-field control problems, which have been studied theoretically but remain less developed numerically. Numerical experiments on a linear--quadratic benchmark, a nonlinear partially observed mean-field control problem, and two financial applications, portfolio liquidation and asset allocation, demonstrate the accuracy and practical utility of the approach.

For a variational problem in a Banach space with quadratic kinetic term and a lower semicontinuous potential, existence of a minimizer is restored by replacing the norm of the space with an equivalent one, arbitrarily close to the original. The form of the problem is preserved; only the norm is perturbed. This extends a result of Ivanov and Zlateva from the convex to the lower semicontinuous case.

A function $f \colon X^k \to X$ on a finite set embeds into a polynomial of total degree $d$ over a commutative ring $R$ if there is an injection $j \colon X \to R$ and a polynomial $g$ of total degree at most $d$ with $j \circ f = g \circ j^k$, where $j^k$ applies $j$ in each coordinate. These are the transition functions of $k$-neighbour cellular automata, and the injection $j$ is an enlargement of the alphabet that preserves the transitions. We prove three results, all verified in Lean~4 with Mathlib~\cite{bacik2026finbin}. Every unary function $f \colon X \to X$ embeds into a polynomial of total degree $1$. Every binary Kronecker delta embeds into a polynomial of total degree $4$. For every $d$ there is a binary function that does not embed into any polynomial of total degree $d$.

A data-driven reduced-order modelling framework is proposed for wall-bounded turbulent flows to forecast the intermittent near-wall dynamics over extended time horizons from sparse sensor measurements. The approach combines a $β$-VAE-GAN, which compresses high-dimensional flow fields into a low-dimensional latent space, with a sensor-conditioned Transformer that forecasts the evolution of the latent variables. The temporal module employs Easy Attention, a static time-mixing operator that replaces the learnable query-key mechanism of standard self-attention at reduced computational cost, combined with an adapted AdaLN-Zero modulation mechanism for sensor-based conditioning. Evaluated on the Minimal Flow Unit ($Re_τ= 200$) at $y^+ = 14$, the compression stage recovers $87\%$ of the turbulent kinetic energy within a four-dimensional latent space, exceeding the standard $β$-VAE baseline by more than $10\%$. The latent dimensions autonomously encode the characteristic timescales of the flow, with specific coordinates capturing the low-frequency signature of the near-wall regeneration cycle ($T^+ \approx 1724$), establishing the physical interpretability of the learnt representation. The sensor-conditioned Transformer maintains accurate forecasts over $17{,}288\,t^+$ from an initialisation window of only $128\,t^+$, whilst end-to-end inference reconstructs $82\%$ of the turbulent kinetic energy. The principal limitation is the attenuation of rare, extreme-amplitude events, a consequence of the encoder prioritising the most statistically recurrent flow states within the low-dimensional bottleneck. Nevertheless, the framework accurately reproduces the alternating active and quiescent phases of the regeneration cycle, demonstrating its suitability as a surrogate model for the intermittent dynamics of wall-bounded turbulence.

Unplanned grid-connected (GC)/stand-alone (SA) transitions commonly occur in AC microgrids during protection trips, manual breaker operation, or low-bandwidth supervisory communication. Under such unplanned transitions, a grid-forming inverter must support the local-load voltage in stand-alone operation and regulate the desired power/current injection in grid-connected operation. Existing P--Q droop-based seamless-transfer methods often rely on planned transition commands, supervisory islanding detection, or pre-synchronization interval, which may prevent timely voltage/current support during unplanned bidirectional transitions. To address this problem, this paper proposes a seamless contraction-control (SCC) framework for target dynamics. Using the SCC, contraction-based grid-connected current-control and stand-alone voltage-control laws are proposed. With the new control laws, the inverter achieves transient stability and converges to the target trajectory with a prescribed convergence rate. Furthermore, a breaker-status observer is proposed to infer the grid-connected/stand-alone mode from voltage measurements on both sides of the breaker, eliminating the need for a dedicated pre-synchronization interval or supervisory islanding detection process and enabling timely voltage/current support during unplanned transitions. Experimental results validate that the proposed method achieves stand-alone voltage support, stable grid-connected current injection under symmetrical/unsymmetrical grid-voltage sag and phase-jump disturbances, and unplanned bidirectional transitions.

Living organisms, from bacteria to humans, are more likely to survive if their traits enhance fitness. In populations well adapted to their environmental niches, natural selection proceeds via rarely beneficial mutations. But when a catastrophe wipes out niche diversity, sudden adaptation often follows. Here, we present a data-validated theory of natural selection in the wake of catastrophe and unveil a simple law that emerges during recovery: the mean fitness relaxes inversely with time, with a prefactor proportional to the number of traits coupled to the post-catastrophe environment. We put our approach to test using experimental fitness landscapes measured following antibiotic administration to E. coli. The resulting mean trait adaptation is not described by gradient ascent on a fitness landscape, instead it follows an algorithm known as Levenberg-Marquardt optimization. Near fitness peaks, evolutionary trajectories are biased against greediness - from an optimization perspective, post-catastrophic selection is optimistic.

We have studied the higher-twist distributions of the proton, including T-even and T-odd transverse momentum-dependent parton distributions (TMDs). Under the umbrella of the light-front framework, we have chosen two distinctive approaches of quark-spectator systems for comparison, one inspired by the soft-wall AdS/QCD and another with a dipolar form factor at the nucleon-quark-diquark vertex. The comprehensive picture at higher-twist provided by both T-even and T-odd TMDs not only aids deeper insights into the internal structure of the proton in the quark sector but also provides an interpretation of different components of the energy-momentum tensor in quantum chromodynamics. Hence, using these standard parton distribution functions, further predictions regarding the physical insights of gravitational TMDs in momentum space are also provided.

Perturbation theory for asymptotically stable systems has received sustained attention, leading to many criteria that preserve stability under uncertainty. A limitation of classical stability analysis, however, is that it is inherently equilibrium-dependent. Contractive systems, by contrast, are defined independently of any equilibrium and admit a rich set of robustness bounds. In this letter, we develop new time-varying perturbation conditions for contractive dynamics that preserve incremental exponential stability of the perturbed system and, in specific regimes, guarantee asymptotic convergence to solutions of the nominal dynamics. As an application, we propose a safety filter for steering a nominally contractive system to a desired equilibrium while avoiding an unsafe set, and we present an example illustrating advantages of the proposed method over existing approaches.

Let $X$ be a compact complex surface. We prove that the skew product associated to a Borel probability measure $μ$ on $\operatorname{Aut}(X)$ admits a unique invariant measure of maximal fiber entropy, assuming that $μ$ satisfies a logarithmic integrability condition and that $\operatorname{supp}(μ)$ generates a non-elementary subgroup of $\operatorname{Aut}(X)$. We describe this measure canonically in terms of the random limit currents constructed by Cantat and Dujardin, and show that its fiber entropy is equal to the Furstenberg exponent of the associated random action on cohomology. Under an exponential moment assumption, we prove that it is mixing.

Alloys inevitably contain interphase boundaries, whose energetics govern nucleation processes and precipitate morphology. In Cu-Ni-Si alloys, Mn addition markedly changes grain boundary (GB) precipitation behavior. While GB precipitation of stable Ni$_2$Si in Mn-free alloys is associated with degraded mechanical properties, Mn addition instead promotes film-shaped Mn$_6$Ni$_{16}$Si$_7$ (G-phase) precipitation, which is correlated improved mechanical properties. However, the atomic origin of the contrasting GB phase selection and morphology remains unclear. Here we perform machine-learning interatomic potential (MLIP) calculations to investigate the effect of interphase-boundary atomic structure on GB precipitates in Cu-Ni-Si alloys with and without Mn. The MLIP calculations reliably reproduce DFT-level energetics for interfacial bonding and microstructural configurations, and further predict that Mn addition favors GB precipitation of Mn$_6$Ni$_{16}$Si$_7$ rather than Ni$_2$Si. Experimentally, Mn-free alloys are observed to exhibit irregularly-shaped Ni$_2$Si precipitates with open-boundary-like Cu/Ni$_2$Si interfaces, whereas Mn-added alloys exhibit film-like G-phase at GBs. Large-scale atomistic interface calculations reveal that the coherent interface structure between Cu and Ni$_2$Si favors the formation of plate-like strained Ni$_2$Si precipitates in the matrix. Upon coarsening and stress release, an out-of-phase coherent-like interface can form at GBs, generating a local repulsive region that gives rise to surface-like open-boundary structures and explains the irregular morphology of GB stable Ni$_2$Si precipitates. In contrast, Cu/Mn$_6$Ni$_{16}$Si$_7$ interfaces remain predominantly incoherent with moderate boundary energies and no pronounced repulsive regime, thereby stabilizing continuous interfacial contact and explaining film-shaped GB precipitation.

We study high-dimensional linear regression under a general symmetric convex constraint. Rather than imposing a specific sparsity-inducing penalty, we start from an arbitrary sign-symmetric and permutation-invariant convex body $K\subseteq \mathbb R^p$ and construct the sparse convexification hierarchy \[ K^{(s)} = \operatorname{conv}\{v\in K:\|v\|_0\le s\}. \] We propose a penalized least-squares estimator that searches over this hierarchy and adapts to the best sparse convex approximation of the target. Under standard sub-Gaussian assumptions on the random design and noise, we prove an oracle inequality showing that the estimator adapts to the best sparse convex approximation of the target. For an $s$-sparse target, the result yields a squared-error rate governed by the effective sparse dimension $s\log(ep/s)$, the noise level $σ$, and the Euclidean diameter $d_s$ of the sparse convexification $K^{(s)}$. The method applies broadly to symmetric norm balls and can be implemented using oracle access to the Minkowski functional of $K$. As a special case, the framework yields a consistency result for the constrained Lasso.