Self-healing systems have long been a focus of research, aiming to enable software to recover from unexpected runtime errors without human intervention. Traditional approaches rely on predefined heuristic rules, such as reusing error handlers or rolling back to checkpoints, but these methods struggle to adapt to the diverse range of runtime errors. The emergence of Large Language Models offers a new opportunity to address this challenge. Leveraging their ability to understand and generate code and natural language, we propose using LLMs to dynamically generate error-handling strategies in real time, tailored to specific runtime contexts such as error messages and program states. We demonstrate the feasibility of this approach by designing such a framework, Healer, and empirically showing that it can handle runtime errors with a high success rate. When an unanticipated runtime error occurs, Healer leverages its internal LLM to generate bespoke error-handling code. The generated healing code is then executed to produce a corrected program state, allowing the program to continue execution with minimal disruption. We evaluate Healer across four code datasets and three state-of-the-art LLMs (GPT-3.5, GPT-4, and CodeQwen-7B), where GPT-4 can successfully recover from 72.8% of runtime errors, underscoring the promise of LLMs in this domain. Despite these promising results, challenges remain, particularly regarding the trustworthiness of LLM-generated code and its integration into existing systems. We mention potential solutions, such as safety checks and Healer-aware programming, to mitigate risks and ensure reliable operation. This work represents the first step toward agentic runtime healing, paving the way for more adaptive, resilient, and self-healing software systems.

Robust and efficient interpretation of QSAR methods is quite useful to validate AI prediction rationales with subjective opinion (chemist or biologist expertise), understand sophisticated chemical or biological process mechanisms, and provide heuristic ideas for structure optimization in pharmaceutical industry. For this purpose, we construct a multi-layer self-attention based Graph Neural Network framework, namely Ligandformer, for predicting compound property with interpretation. Ligandformer integrates attention maps on compound structure from different network blocks. The integrated attention map reflects the machine's local interest on compound structure, and indicates the relationship between predicted compound property and its structure. This work mainly contributes to three aspects: 1. Ligandformer directly opens the black-box of deep learning methods, providing local prediction rationales on chemical structures. 2. Ligandformer gives robust prediction in different experimental rounds, overcoming the ubiquitous prediction instability of deep learning methods. 3. Ligandformer can be generalized to predict different chemical or biological properties with high performance. Furthermore, Ligandformer can simultaneously output specific property score and visible attention map on structure, which can support researchers to investigate chemical or biological property and optimize structure efficiently. Our framework outperforms over counterparts in terms of accuracy, robustness and generalization, and can be applied in complex system study.

Retrieval-augmented generation (RAG) improves large language model reliability by grounding generated responses in external evidence. However, RAG performance depends on the relevance of retrieved passages, the quality of evidence ranking, and the ability to verify whether generated claims are supported by source documents. This study presents a hybrid retrieval and reranking framework for citation-aware RAG in biomedical and healthcare-related document question answering. The framework uses Amazon Bedrock Knowledge Bases for document ingestion, parsing, chunking, embedding generation, and evidence retrieval. Source PDF documents are stored in Amazon S3, embedded using Amazon Titan Text Embeddings V2, and indexed with Amazon OpenSearch Serverless. Hybrid retrieval first retrieves candidate evidence chunks, and Cohere reranking then prioritizes the most relevant passages before answer generation. The answer-generation stage uses top-ranked evidence chunks to produce controlled, evidence-grounded responses, while a separate judge model evaluates each generated factual claim against the retrieved evidence. The framework was evaluated using 25 biomedical NLP and healthcare transformer queries as a pilot-scale proof-of-concept study. Across the evaluation set, the system retrieved and reranked 500 evidence chunks and generated answers from top-ranked evidence. Claim-level grounding evaluation extracted 200 factual claims, all of which were judged to be supported by retrieved evidence, resulting in 100.0% grounding accuracy. The results suggest that hybrid retrieval, reranking, conservative prompting, and claim-level evaluation can support reliable evidence-grounded RAG responses when sufficient source evidence is available.

We define a higher-derivative generalization of Maxwell-Chern-Simons theory in $\mathcal{N}=1$ and $\mathcal{N}=2$ superspaces. In particular, the chosen higher-derivative operator is a polynomial function of the d'Alembertian of arbitrary degree, and it is introduced exclusively in the gauge sector. The main goal is to explicitly compute the one-loop quantum corrections to the superfield effective potential for these theories. This is carried out by means of background field quantization in a higher-derivative $R_ξ$ gauge. The effective potential is obtained in closed form and expressed in terms of the roots of polynomial functions.

In the context of the Dirac equation with square-summable potential, we study the Jost solutions and prove that the maximal function associated with the argument of the transmission coefficient is unbounded. We also show that the strong version of the nonlinear Carleson conjecture fails for Dirac equations and Krein systems.

In this article we introduce the linear canonical Riesz potential (for short, LCRP) and give its symbol in terms of linear canonical transforms. Driven by image processing, we establish the convergence/divergence of these LCRPs for different kinds of functions. Concretely, for grating functions, we prove that their classical Riesz potentials diverge, whereas their LCRP converge due to the key role of chirp functions. For the characteristic function ${\mathbf 1}_P$ of a convex polygon $P$, we show that the limit of its Riesz potential at any non-boundary point $\boldsymbol{x}$ equals ${\mathbf 1}_P(\boldsymbol{x})$, but its limit at the boundaries differ from ${\mathbf 1}_P$, while it is known that, for any Schwartz function $f$, the limit of its Riesz potential at any point $\boldsymbol{x}$ always equals $f(\boldsymbol{x})$. Based on these and the inverse operator of the LCRP (namely the linear canonical Laplacian operator), we propose an asymmetric cascaded LCRP method for the multi-image encryption and create an efficient and secure cryptosystem. Systematic security evaluations, including sensitivity, statistical, noise attack, and occlusion attack analyses, demonstrate its robustness and its security. Even for a single image, the proposed method is more efficient than the known encryption approach based on the fractional Riesz potential. The novelty of these results lies in that the convergence and the divergence of LCRTs at the critical indices, respectively, for ``good" Schwartz functions and for ``bad" discrete image functions essentially affect the security of image encryption and decryption.

Outside the core of the plasma, the plasma current and pressure rapidly transition to zero in a scrape-off or edge region or plasma-vacuum interface. However, existing tools for fixed-boundary magnetohydrodynamic equilibria in 2D and 3D domains $Ω$ typically prescribe the computational boundary $\partialΩ$ interior to this transition layer. We (1) argue that a more realistic and robust assumption is to define the computational boundary exterior to this transition layer, in a vacuum-like region where $J|_{\partialΩ} \sim p|_{\partialΩ} \sim 0$, (2) show that, without this boundary change, existing coil optimization routines for 3D toroidal equilibria (stellarators) should be changed to match free-boundary equilibrium requirements, and (3) derive an algorithm for a fixed-boundary 3D equilibrium solver compatible with a very general computational boundary, with conditions $B \cdot n|_{\partialΩ} \neq 0$ (not necessarily a flux surface), $p|_{\partialΩ} \neq \text{const.}$ (not necessarily an isobar), and $J \times n|_{\partialΩ} \neq 0$.

Lumens are cavities enclosed by polarized cells that are essential for organ function, from nutrient transport in the gut to gas exchange in the lungs. Defects in lumen formation are associated with severe diseases, including polycystic kidney disease and respiratory malformations. The emergence, growth, and maintenance of lumens involve a rich set of phenomena that can be framed within out-of-equilibrium physics and biological active matter, including osmotically driven hydraulic flows, coarsening-like dynamics, morphological instabilities, and mechanochemical feedbacks linking luminal pressure to tissue response. Yet experimental and theoretical efforts to study these phenomena have largely developed within specific biological systems, complicating the identification of shared physical principles across them. In this review, we bring these efforts together and present lumenogenesis within a biological physics framework in which lumens are viewed as active balloons: pressurized cavities that are inflated, sculpted, and maintained through tightly coupled active processes.

Continuum reverberation mapping (RM) is a powerful technique for constraining the accretion disk structure in active galactic nuclei (AGNs). In typical cases, the shorter-wavelength emission is used as the reference, and a positive time lag is observed since the inner, hotter regions of the accretion disk respond earlier than the cooler outer regions at longer wavelengths. However, we detect a short-timescale negative inter-band lag in SDSS~J083717.88+191647 using RM techniques, where the \textit{g}-band lags behind the \textit{r}-band emission. The light curves from the Zwicky Transient Facility reveal two distinct phases, a stabilizing and a declining phase, in which the time lags show opposite signs. Using \texttt{JAVELIN} with the $g$-band as the reference, we obtain time lags of $3.68^{+1.94}_{-2.78}$~days during the stabilizing phase and $-1.60^{+0.69}_{-0.54}$~days during the declining phase. Although negative continuum lags have been reported in a few previous studies, the present case is distinguished by its clear phase dependence and the accompanying color evolution. We attribute the observed lag reversal to a moving dust-cloud obscuration scenario, in which the cloud crossing the line of sight preferentially obscures emission from the outer longer-wavelength regions of the disk, causing the $r$-band to decline earlier than the $g$-band and thus producing the observed negative inter-band lag. Our results indicate that AGN variability may be more complex than previously thought. Future high-cadence, multi-band observations will be essential to test this dust-obscuration model and to further explore the interplay between the accretion disk emission and dust in AGNs.

We prove an averaging formula for the canonical archimedean height pairing of special divisors with weights over orthogonal and unitary Shimura curves in terms of derivatives of Whittaker functions.

Based on the ballistic macroscopic fluctuation theory, the integration of the spin correlation function (spin conductivity) is analyzed for the spin-1/2 XXZ chain in the critical regime. In the time when the magnetization of an infinite spin chain fluctuates from an initial state with a wavelength as long as the infinite length $N$, the equal-time two-point spin correlation function is scaled up to $O(1/N)$. In the state where the ballistic spin transport decays at high temperature $T$, the diffusive transport remains on a large scale. We show that the spin conductivity is proportional to $1/T$ in the limit $T\to\infty$ and its high temperature proportionality constant diverges in the case where one-quasiparticle magnetization is infinitely large. This analysis informs that the superdiffusive spin transport is driven by the $1/N$-scaled long-range spin correlation and sheds a light on the dynamic scaling in spin transport at the isotropic point.

LLM agents emit actions, not just text, and once taken, those actions often cannot be undone. Yet today's agent-safety evaluations run greedy or a few sampled rollouts and report a single safe/unsafe rate -- blind to the long-tail trajectories where unsafe behavior may arise from low-probability but non-negligible actions. We argue agent safety should be measured by search, not sampling. We apply BOA, a framework that, given a deployment configuration (model, decoder, prompt, environment, judger, likelihood budget), searches the in-budget trajectory space and reports a safety score: the probability the agent stays safe under the configuration. BOA searches both within a single LLM round and across the agent-environment interaction tree under a given likelihood budget, and makes search practical via batched decoding/judging, prefix caching, and chunked tree expansion. On agent-safety workloads, BOA discovers unsafe trajectories that greedy and sampled evaluations miss. BOA can additionally be used for ranking models, defenses, and attacks, all on the same scale, with manageable GPU costs.

We prove a generalization of Orlov's theorem for matrix factorizations with $n$ steps. Let $X$ be a regular scheme, $W\colon X\to \mathbb{A}^1$ a flat morphism and $D:=W^{-1}(0)$ its central fiber. We construct an appropriate triangulated category of matrix factorizations with $n$-steps and show that it is equivalent to the singularity category of the root stack $\sqrt[n]{(X, D)}$. We also show that this category admits a semiorthogonal decomposition into $n-1$ copies of the usual (absolute derived) category of matrix factorizations with $2$ steps.

We investigate the influence of rotation and quadrupole deformations of astrophysical compact objects on the Shirokov and Shapiro effects within the Hartle-Thorne spacetime, which describes the exterior gravitational field of slowly rotating, slightly deformed celestial objects. Using geodesic deviation equations, we analyze the oscillatory motion of neighboring test particle trajectories and show how the combined impact of angular momentum $J$ and quadrupole moment $Q$ affects the Shirokov effect. The results are compared with our previous analysis for the Lense-Thirring and Zipoy-Voorhees metrics, revealing consistent trends in the coupling between radial and azimuthal oscillations. For the Shapiro time delay, we examine two limiting configurations: (i) the Lense-Thirring frame-dragging case with $J^2=0$, $Q=0$ and $J\neq0$, where the effect persists for both positive and negative values of the angular momentum; and (ii) the static quadrupolar case with $J=0$ and $Q\neq0$, where more oblate sources produce a stronger gravitational time delay with increasing distance. We also study these effects in the Hartle-Thorne spacetime without employing the weak-field approximation, performing a full numerical analysis. In particular, we examine the mimicking effects produced by the quadrupole deformation and the angular momentum of the compact object. These results illustrate how the deformation and rotation of compact objects influence the relativistic observables in the surrounding spacetime.

Odrzywołek defined a system Exp-Minus-Log (EML) that reduces all elementary functions over complex numbers down to a constant `$1$', and a single two place function $E(α, β) = \exp(α) - \log(β)$. This paper shows that in this system, equivalent to Chow's EL numbers, every EML-expressible number is computable. We go on to prove that the canonical example of a non-computable real, Chaitin's $Ω_U$, is inexpressible in EML. This gives a formal inexpressibility theorem for this system.

Bag and Shparlinski \cite{BaSh} considered bilinear sums of terms of the form $e_p(axy^s)$, where $p$ is a prime, $a$ is an integer coprime to $p$, $s$ is an integer, $x$ runs over a subset of $\mathbb{F}_p^{\ast}$ and $y$ runs over an interval. Closely following their method, we establish an analogous result for the case when $s=1/2$ ($y^{1/2}$ being a modular square root of $y$ modulo $p$, if existent). A part of this note is devoted to reviewing our recent works on related bilinear sums.

This paper presents the design and performance analysis of a 1x6 linear microstrip patch antenna array tailored for automotive radar and 5G millimetre-wave (mm-wave) applications. The proposed antenna array comprises six rectangular radiating patches with the primary patch excited using a microstrip feedline, while the remaining patches are interconnected through narrow microstrip lines with a width of 0.1 mm, enabling effective power distribution along the array. Optimal inter-element spacing facilitates constructive and destructive interference, enabling the formation of a narrow beam with enhanced directivity and a wide operational bandwidth. The high-gain radiation characteristics are achieved through the combined effects of the six-element linear configuration and precise impedance matching. Key performance metrics including reflection coefficient, current distribution, and radiation patterns have been analysed. Results demonstrate a reflection coefficient better than 10 dB across the target frequency range and a narrow beamwidth with high directivity, making the array suitable for high-resolution automotive radar and 5G mm-wave communications. Potential applications include vehicle-to-vehicle (V2V) radar sensing, lane change detection, blind spot monitoring at 28 GHz, and high-capacity point-to-point wireless backhaul links. The design offers a promising solution for compact, high-performance beamforming antenna systems in intelligent transportation and next-generation wireless networks.

On the grounds of nonadditive entropies -- appropriate for complex systems -- we investigate the electroencephalogram amplitudes of typical and ADHD children. The corresponding probability distributions are $q$-Gaussians, i.e., $ρ(x) \propto e_q^{-βx^2} \equiv [1+(q-1) βx^2]^{1/(1-q)}$, where $(q,β)$ are, respectively, the entropic index characterizing complexity and the inverse width. We show that $q$ tends to monotonically vary with $β$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path. We show that $q$ tends to monotonically vary with $β$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path.

The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological fields whose multiplicative group is isomorphic to $G$. This result yields an equivalence between the category of semitransitive distributive binary $G$-spaces and the category of topological fields with multiplicative group $G$. As applications of the duality theorem, two important results are established. It is shown that a finite group can act semitransitively, distributively, and binarily only on finite sets whose cardinality is a power of a prime number. A complete characterization of those groups that can appear as multiplicative groups of topological fields is also obtained.

We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and horizontal visibility graphs), transition, and proximity) and the graph is converted to a dissimilarity matrix from which a Vietoris-Rips filtration yields persistence diagrams. These diagrams are vectorized into fixed-length features through persistence landscapes and topological summary statistics. By standardizing the downstream processing, differences in classification performance are attributable to the network construction and distance metric alone. Experiments on twelve UCR benchmarks show that (i) no single construction dominates: the optimal graph type depends on the signal's discriminative structure; (ii) the graph distance metric is a first-order design choice, with diffusion distance uniformly outperforming shortest-path alternatives; and (iii) persistence-based features degrade gracefully under noise, consistent with the classical stability theorem of persistent homology.

We describe a polynomial complexity algorithm for reducing transition matrices, for vector bundles glued along a clutching-type cover of a real anisotropic conic, to canonical block diagonal forms. This is a generalization, to the real anisotropic form, of the classification of vector bundles on the Riemann sphere by their canonical diagonal forms due to Grothendieck and Birkhoff. To enable our algorithm, we provide an elementary algebraic proof for the result, due to Biswas-Nagaraj and Novakovic, of the decomposition of vector bundles on real anisotropic conics into sums of indecomposable vector bundles of rank at most 2. While our algorithm and our proof of this decomposition focus solely on the setting of a real anisotropic conic, our methods are immediately generalizable to anisotropic conics over arbitrary fields.

Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin still remains not fully understood. In this perspective we report on recent studies showing that chaos is the realization of one of the most fundamental principles in physics: spontaneous symmetry breaking also known as spontaneous ordering. In the present context, the symmetry involved is a topological supersymmetry inherent to all continuous-time (stochastic) dynamical systems. Chaos is then truly a manifestation of order of topological origin potentially encoding a sort of long-range information hidden beneath its apparent unpredictability. We finally argue that this point of view may have far-reaching implications well beyond chaotic dynamics.

Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine learning, as gradient-based algorithms built on the implicit function reformulation have enabled the computation of large-scale problems involving possibly millions of variables. Despite these advances, the implicit function framework relies on restrictive assumptions, notably the requirement that the lower-level problem admit a unique optimal solution for each upper-level decision. Moreover, the computation of the derivative of the lower-level optimal solution function becomes significantly more involved when the lower-level problem includes constraints. As a result, many existing bilevel learning algorithms are effective only for relatively narrow classes of problems. This paper reviews the main algorithmic ideas underlying recent progress in bilevel learning, highlighting both the key mechanisms responsible for their scalability and the limitations that arise in more general settings. We then draw connections with the broader bilevel optimization literature and discuss algorithmic techniques that may help overcome these limitations. Our aim is to bridge the gap between bilevel learning and classical bilevel optimization, thereby supporting the development of scalable methods capable of solving more general large-scale bilevel programs.

The quantum approximate optimization algorithm (QAOA) has emerged as a promising candidate for demonstrating quantum advantage on noisy intermediate-scale quantum (NISQ) devices. While various QAOA parameterization schemes exist, ranging from the original single-angle approach to the more expressive multi-angle quantum approximate optimization algorithm (MA-QAOA) and automorphic-angle quantum approximate optimization algorithm (AA-QAOA), each presents distinct trade-offs between expressiveness and classical optimization complexity. In this work, we introduce the $k$-interaction-angle quantum approximate optimization algorithm ($k$A-QAOA), a parameterization scheme that groups cost function terms by their $k$-body interaction order, providing a natural middle ground between parameter efficiency and solution quality. This approach is particularly well-suited for combinatorial optimization problems defined on hypergraphs, where multi-body interactions naturally arise in applications such as Boolean satisfiability and resource allocation with multi-party constraints. We benchmark $k$A-QAOA against standard single-angle quantum approximate optimization algorithm (SA-QAOA), MA-QAOA, and AA-QAOA on two problem classes: 3-uniform cyclic sign-alternating hypergraphs and random coefficient hypergraphs. Our results demonstrate that $k$A-QAOA achieves approximation ratios comparable to MA-QAOA while requiring significantly fewer function evaluations, thereby reducing quantum resource consumption.

Based on the conventional metric tensor and driven by a nearly constant energy density, cosmic inflation, characterized by a remarkably accelerated expansion, was proposed as an early epoch in the Universe. The energy density is typically modeled through a slow-rolling scalar field, whose potential energy dominates the dynamics. This mechanism addresses horizon, flatness, and relic problems, while also generating quantum fluctuations that are stretched to cosmological scales, leading to emergence of primordial curvatures and tensor perturbations. Despite its empirical success, significant questions remain regarding identity of the inflaton, origin of the potential, and role of quantum gravity. A quantum-deformed conformal metric that is both perturbatively and tensorially structured and expanded is employed to reexamine the dynamics of inflation, thus enabling the computation of a range of inflationary observables in presence of quantum-induced corrections. We have established a closed and internally consistent set of analytical formulas for scalar and tensor power spectra, including their spectral tilts, runnings, and the tensor-to-scalar ratio, among other parameters. The quantum corrections appear to provide a clear physical interpretation related to measure scaling and momentum-induced kinetic deformation, which facilitates modifications to the inflationary observables in a controlled and predictive manner. While maintaining the classical limits, these corrections provide a well-defined phenomenological perspective on potential quantum-gravitational structures in the early Universe.

We develop a unified description of dense fermionic matter that consistently incorporates Pauli degeneracy, interaction effects, and pairing correlations. The condition that the temperature is much smaller than the Fermi energy leads to a natural separation between Sommerfeld, Fermi-liquid, and pairing regimes, and how these contributions enter the equation of state. The resulting EOS is applied to the Tolman-Oppenheimer-Volkoff equations to analyze neutron-star structure. We demonstrate that Pauli degeneracy provides the dominant pressure, interactions determine the stiffness of the EOS, and pairing correlations produce subleading but potentially significant corrections, especially in quark matter. Implications for mass--radius constraints and modern observations are discussed.

We study a nonlocal Poisson problem with discontinuous source term and analyze how the regularity of the integral kernel determines the discontinuity structure of the corresponding solution. Under general assumptions on compactly supported integrable kernels, we show that jump discontinuities in the source term are inherited by the solution. We then identify two principal mechanisms governing higher-order regularity: singular behavior of the kernel at the origin and jump discontinuities of the kernel, or of its derivatives, at the horizon endpoints. Singularities at the origin lead to blow-up of certain derivatives of the solution at the source discontinuity, while jumps at the horizon generate cascades of derivative discontinuities at translated locations. These phenomena occur for kernels commonly used in peridynamic-type models. By contrast, compactly supported \(C^\infty\) kernels do not generate derivative blow-up or cascading losses of regularity, and in this case the source term and the solution have equivalent piecewise smooth regularity. Motivated by this analysis, we develop a semi-analytic spectral method for the accurate numerical treatment of discontinuous nonlocal problems. The method uses successive smoothing transformations and explicitly constructed correction functions to convert the original problem into an auxiliary problem with improved regularity. A spectral solver is then applied to the smoothed problem, and the approximation to the original solution is recovered by adding back the analytic corrections. Numerical experiments show substantial gains in accuracy and convergence, demonstrating that the method effectively mitigates the loss of accuracy caused by discontinuities and Gibbs oscillations while retaining the efficiency of spectral methods.

We study estimation of the proportion of areal units in a spatially correlated domain whose success probabilities exceed a prespecified threshold. Such problems arise in health surveillance, environmental monitoring, and social policy, where the goal is to estimate the fraction of high-risk areas. We propose a DUST-MNS design that combines maxima-nominated sampling (MNS) with the probability-proportional-to-size dependent unit sequential technique (pps-DUST), thereby promoting spatial spread while mitigating the effect of spatial autocorrelation. The design forms $n$ candidate sets of size $k$ and obtains final measurements only from the area judged to be at highest risk in each set, yielding $n$ measured areas from $nk$ screened candidates. Ranking may be based on expert judgment, prior surveys, or easily obtained auxiliary covariates. We derive a closed-form estimator of the exceedance probability $θ$ based on data from DUST-MNS design, establish its bias and variance, and show that, in the rare-to-moderate exceedance regime $θ<θ^\star(k)$, the proposed DUST-MNS estimator outperforms its SRS and DUST-SRS counterparts, where $θ^\star(k)$ depends only on $k$. We also provide guidance on the choice of $k$, derive efficiency bounds under a Beta model, extend the method to imperfect ranking, and develop variance estimation and bootstrap confidence intervals. An application to county-level stroke prevalence data from CDC PLACES, using diabetes prevalence as the ranking concomitant, illustrates the proposed approach.

Cluster resource allocation is a multidimensional search problem that finds the best allocation of tasks to servers. Because the search space grows exponentially, modern approaches frame it as a mixed integer program (MIP) or a complex set of search heuristics. This paper proposes using a different approach: convex optimization, which has extremely fast solution methods. The research challenge is devising how to transform cluster resource allocation into a convex problem that generates good placements. We describe CvxCluster, which allocates cluster resources with a two-stage algorithm. The first stage solves a convex relaxation of the placement problem to yield a principled set of per-machine resource prices. The second stage uses these prices to drive a lightweight greedy procedure to place tasks. Experimental results with Azure traces find that CvxCluster scales to 100,480 servers under proportional workload growth and sustains arrival rates up to 500,000x the baseline trace. CvxCluster runs 100 to 2,500x faster than a state-of-the-art MIP solver while remaining within 3% of the optimal objective. CvxCluster can support complex constraints such as job anti-affinity, machine types, and GPU servers. The key insight behind CvxCluster is that reformulating placement as a continuous rather than discrete problem enables much faster methods that find solutions just as good or better than prior heuristics.

We investigate the propagation of high-speed solar wind streams from their origin near the Sun to 1 AU using three-dimensional magnetohydrodynamic simulations. By tracking both global stream structure and individual plasma parcels, we assess how local in-situ measurements relate to the underlying plasma evolution. We find that high-speed streams are not parcel-preserving structures: commonly used diagnostics such as peak velocity, density, or temperature do not trace fixed plasma elements, and feature-based radial trends can therefore misrepresent the true evolution. Instead, velocity-based relationships provide a more robust framework for linking plasma parcels across heliocentric distances. Stream evolution is dominated by interaction regions, where compression leads to deceleration of fast wind, acceleration of slow wind, and significant heating. A boundary layer forms close to the Sun and can dominate narrow streams, biasing in-situ measurements toward lower apparent velocities. We show that three-dimensional transport, in particular latitudinal flows, redistributes mass and magnetic flux and reduces center-to-flank contrasts. While radial magnetic flux is conserved, the total field strength is not in spherical sampling geometries due to non-radial components. Finally, observed stream properties and geoeffectivity depend strongly on sampling location, stream geometry, and latitudinal magnetic deflection, introducing systematic variability and asymmetries in geomagnetic response.