Datacenters are vital to our digital society, but consume a considerable fraction of global electricity and demand is projected to increase. To improve their sustainability and performance, we envision that simulators will become primary decision-making tools. However, and unlike other fields focusing on key societal infrastructure such as waterworks and mass transit, datacenter simulators do not yet combine multiple independent models into their operation and thus suffer from issues associated with singular models, such as specialization, and lack of adaptability to operational phenomena. To address this challenge, we propose M3SA, a datacenter simulation and analysis framework that uses discrete-event simulation to predict, for each model, the impact on climate and performance under various realistic datacenter conditions, and then combines these predictions. We design an architecture for simulating multiple concurrent models (Multi-Model), a technique for integrating the results of multiple models into a Meta-Model, and a procedure for quantifying Meta-Model accuracy. Through experiments with an M3SA prototype, we show that (i) M3SA can reproduce and enhance peer-reviewed experiments; (ii) M3SA can predict operational phenomena (e.g., failures) of datacenters, running fundamentally different workload traces; (iii) M3SA enables various types of what-if and how-to analysis, such as how to configure CO2-aware migration over yearly energy-production patterns. M3SA has been integrated into the open-source simulator OpenDC and is available at: https://github.com/atlarge-research/opendc-m3sa.

Slow light is a regime of reduced group velocity, resulting in increased photon density in optical pulses and enhanced nonlinear effects. Here, we propose the realization of slow light in the regime of strong light-matter interaction between waveguide photons and semiconductor excitons. We design a dielectric superlattice structure with a nearly-flat band characterized by low group velocity and group velocity dispersion, both required for enhancing nonlinear effects with ultrashort pulses. Furthermore, by applying this general framework to a perovskite-based structure, we demonstrate an enhancement of the single-particle phase shift by a factor of more than 20, representing a significant step toward the few-photon quantum regime. Our results provide a blueprint for accessible strong interactions in solid-state integrated optics.

We present an updated determination of the hadronic vacuum polarization contribution to the running of the electromagnetic coupling $Δα_{\mathrm{had}}^{(5)}(-Q^2)$, and of the electroweak mixing angle in the space-like momentum range up to $12 \ \mathrm{GeV}^2$. Using $N_f=2+1$ CLS ensembles at five values of the lattice spacing and several pion masses, including the physical point, we achieve a significantly enhanced precision over our previous result. A refined analysis strategy based on telescopic series and a new family of kernel functions enables a clean separation of distinct Euclidean regions, disentangling strong cutoff effects at short distances from the pronounced chiral dependence at larger ones. Employing the Euclidean split technique, we convert our lattice results into an ab initio estimate of $Δα_{\mathrm{had}}^{(5)}(M_Z^2)$. A comparison with results from other lattice calculations and phenomenology is performed. We also analyze improvement scenarios required to match the projected precision of future electroweak measurements at next-generation colliders.

Metaheuristic algorithms such as Particle Swarm Optimization (PSO) and Evolutionary Algorithms (EA) excel at exploring solution spaces but lack mechanisms to accumulate and reuse procedural knowledge from successful search trajectories. This paper proposes Associative Constructive Evolution (ACE), a framework that enhances metaheuristics through learned generative guidance. ACE introduces a Generative Construction Automaton (GCA) -- a probabilistic model over operation sequences -- coupled with the base metaheuristic in a synergistic loop: the metaheuristic explores and provides trajectory samples, while the GCA consolidates successful patterns and guides future exploration. Three mechanisms realize this cooperation: Hebbian weight consolidation that strengthens associations between co-successful operations, guided sampling that biases search toward learned high-quality regions, and symbolic abstraction that extracts frequent patterns into reusable macro-operations. Experiments integrating ACE with EA and PSO on molecular design and maze navigation demonstrate consistent improvements. ACE-PSO achieves a 27.5% increase in success rate while reducing convergence time by 49.6%. In molecular design, ACE-EA improves fitness by 10.1% with 126 chemically interpretable macro-operations automatically discovered.

We revisit QCD-induced little inflation in which the Universe starts with a large baryon chemical potential and undergoes a strong first-order QCD phase transition, generating an observable stochastic gravitational-wave background in the nano-Hz range relevant for pulsar timing array (PTA) observations. We point out that the conventional homogeneous transition from the quark-gluon plasma phase to the hadronic gas phase faces an unavoidable difficulty in achieving the required strength of supercooling for the observed baryon density. This motivates us to explore whether a qualitatively different phase structure at a large baryon chemical potential can alter the relation between the baryon density and the chemical potential, and thereby modify the supercooling history of the transition. Using the nucleon-meson model with isoscalar vector mesons, we determine the critical and spinodal structure of the chiral density wave (CDW) phase in the $(μ_B, T)$ plane. We find that the CDW phase exhibits a nontrivial structure and can remain metastable down to a low baryon density in a certain region of the parameter space. Taking into account the subsequent liquid-gas transition and phase separation, however, the released latent heat is too small to realize a viable QCD-induced little inflation scenario and its associated PTA-scale gravitational-wave signal. Our analysis sharpens the conditions under which QCD phase transitions may act as cosmological sources of nano-Hz gravitational waves, while clarifying the possible cosmological relevance of inhomogeneous QCD phases.

We present the Severed Floor, a framework for Macrodata Refinement of the daily astro-ph arXiv feed, deployed at Phermon Industries (formerly McPherson Laboratory, The Ohio State University). In this framework, researchers undergo a "severance procedure" that produces a digital work-self -- an innie -- while the original researcher, the outie, is free to attend to the remainder of their life unburdened by the daily arXiv listing. Twenty-one members of the Department of Astronomy have been severed. Each innie is constructed from the outie's public publication record and assigned papers selected to match its expertise. The innies convene daily on a virtual Severed Floor -- a pixel-art simulation of McPherson Laboratory -- where they encounter one another, are paired with papers by the Board, and engage in collegial, figure-driven scientific discussions. They have been instructed to enjoy each paper equally. At the close of each shift, innies compose correspondence summarizing the day's refinement activities, which is transmitted to their outies through a Board-approved mail protocol. Complete session recordings are archived for public replay and for the Board's ongoing surveillance of workplace anomalies, in compliance with Phermon Handbook \S13.1 (Vigilance Protocol). The system is real, deployed, and available for public inspection in archival replay mode. The severance procedure is painless and requires only a name and an ORCID. Happy April Fools' Day.

High-order perfect absorption of coherent input has recently attracted significant attention due to its broadband absorption capacity. However, the realization of a high-order perfect absorber relies on the exceptional point (EP) to coalesce the scattering zeros. Here, we present a general scattering framework and achieve the high-order perfect absorber in the absence of EP. We consider the asynchronous coherent input, where a spatial delay introduces a momentum-dependent phase factor beyond the amplitude and phase control in synchronous coherent input. This new degree of freedom enables active control of the momentum dependent output, effectively reshaping the absorption line shape necessary for the high-order perfect absorber. Remarkably, despite the absence of EP, the proposed high-order perfect absorber exhibits significant response to the perturbations in the delay length. Our findings provide insights for the delay induced momentum-sensitive interference phenomenon and offer a new route for wave control.

A homemorphism between domains in $\mathbb R^n$, $n\ge 2$ is quasiconformal, with its intricate analytic and geometric consequences, if the (pointwise) linear dilatation -- a purely metric quantity -- is uniformly bounded. Gehring proved that it will suffice to verify the uniform bound up to a set of measure zero as long as we can show that the dilatation is finite outside a subset of finite Hausdorff--$(n-1)$ measure. In short, we say that we can allow an exceptional codimension $1$ subset. In the metric setting, it has been proved, roughly speaking, that one can allow an exceptional codimension $p$ subset, $p \ge 1$, if the source space satisfies a $p$-Poincaré inequality. We prove, effectively, the sharpness of the latter claim.

RF fingerprinting authenticates satellite transmitters by exploiting hardware-specific signal impairments, yet existing methods operate without theoretical performance guarantees. We derive the Fisher information matrix (FIM) for joint estimation of in-phase/quadrature (IQ) imbalance and power amplifier (PA) nonlinearity parameters, establishing Cramér-Rao bounds (CRBs) whose structure depends on constellation moments. A necessary condition for full IQ identifiability is that the identifiability factor~$β$ exceeds zero; for binary phase-shift keying (BPSK), $β= 0$ yields a rank-deficient FIM, rendering IQ parameters unidentifiable. This provides a plausible theoretical explanation for OrbID's near-random performance (area under the ROC curve, AUC~$= 0.53$) on Orbcomm. From the FIM, we define a discrimination metric that predicts which hardware parameters dominate authentication for a given modulation. For constant-modulus PSK signals, PA nonlinearity features are predicted to dominate while IQ features are ineffective. We validate the framework on 24~Iridium satellites using two recording campaigns, achieving cross-file PA fingerprint correlation $r = 0.999$ and confirming all four CRB predictions. A discrimination-ratio-weighted (DR-weighted) authentication test achieves AUC~$= 0.934$ from six features versus $0.807$ with equal weighting, outperforming machine-learning classifiers (AUC~$\leq 0.69$) on the same data.

We consider testing zero pricing errors in high-dimensional linear factor pricing models. Existing methods are mainly based on either an $L_2$ statistic, which is effective under dense alternatives, or an $L_\infty$ statistic, which is powerful under very sparse alternatives. To bridge these two regimes, we develop a class of $L_q$-based tests for finite $q$, including the practically useful $L_4$ and $L_6$ cases. We show that larger $q$ leads to greater sensitivity to sparse alternatives. We further establish the asymptotic independence between the $L_\infty$ statistic and the $L_q$ statistic for any finite $q$, which motivates a Cauchy combination test that adapts to a broad range of sparsity levels. Simulation studies and a real-data analysis show that the proposed methods are more robust to the unknown sparsity of the alternative and can outperform existing procedures in finite samples.

We derive the stochastic price process for tokens whose sole price discovery mechanism is a constant-product automated market maker (AMM). When the net flow into the pool follows a diffusion, the token price follows a constant elasticity of variance (CEV) process, nesting Black-Scholes as the limiting case of infinite liquidity. We obtain closed-form European option prices and introduce liquidity-adjusted Greeks. The CEV structure generates a leverage effect -- volatility rises as price falls -- whose normalized implied volatility skew depends only on the pool's weighting parameter, not on pool depth: Black-Scholes underprices 20%-out-of-the-money puts by roughly 6% in implied volatility terms at every pool depth, while the absolute pricing discrepancy vanishes as pools deepen. Empirically, after controlling for pool depth and flow volatility, realized return variance across 90 Bittensor subnets exhibits a strongly negative price elasticity, decisively rejecting geometric Brownian motion and consistent with the CEV prediction. A complementary delta-hedged backtest across 82 subnets confirms near-identical hedging errors at the money, consistent with the prediction that pricing differences are concentrated in the wings.

Academic dishonesty has long been a concern in computing education, and the rapid growth of online learning and generative artificial intelligence (AI) has further complicated how cheating is perceived and addressed. We report on a study examining how different actors in the computer science (CS) classroom interpret potential cheating scenarios and the motivations behind academic dishonesty. Participants included instructors (n = 6), teaching assistants (TAs; n = 21), and undergraduate students (n = 538) enrolled in two CS courses at a large Southeastern institution in the United States. Respondents classified scenarios as serious cheating, trivial cheating, or not cheating and answered to an open-ended question about motivations for academic dishonesty. Our findings reveal notable discrepancies across groups: instructors most often attribute cheating to grade pressure and laziness, while students and TAs emphasize gaps in prerequisite knowledge and time management challenges. These results highlight misaligned perceptions of academic dishonesty and underscore the need for clearer communication and curricular strategies in computing education, particularly in post-COVID learning environments where hybrid instruction, increased reliance on digital resources, and AI-assisted tools have reshaped students' approaches to coursework and learning.

We report a quantitative calorimetric study of UTe2 under pressure with a direct measurement of the Sommerfeld gamma coefficient, showing a three-fold enhancement of electronic effective mass when approaching the critical pressure where superconductivity is suppressed and ordered states occur. We analyse the evolution of gamma with the amplitude of the jumps in the specific heat at the two superconducting transitions, and the superconducting critical temperature with pressure. This analysis would suggest that the high pressure superconducting phase nucleates only on a fraction of the Fermi surface. It also points to the possible major role of a quantum critical point of the unidentified phase that has been called weak magnetic order, rather than to the critical pressure of the antiferromagnetic phase. Just at the border of long-range antiferromagnetic order, where superconductivity emerges from the weak magnetic order phase, a significant increase in the specific heat jump for both superconducting transitions is found, accompanied by a noticeable change of their shapes.

The results of recent experiments [1] on observing soliton lattices and their dislocations in vertical cylindrical channels filled with immiscible fluids with strongly different viscosities and but slightly different densities are discussed. The less viscous, lower-density fluid fills the central region of the cylinder. Injecting a light fluid from below generates nonlinear cnoidal waves at the interface between the fluids, which have the appearance of soliton lattices. Two types of lattice dislocations are observed, the interaction between which is elastic. This experimental study fully confirms the theory of cnoidal waves and their dislocations for the KDV equation, which was developed 50 years ago and published in JETP [2].

We report Barkhausen-like switching at millitesla fields in an $n$-doped InAs/Al nanowire Josephson junction, which serves as an interferometric probe of intrinsic magnetic reconfigurations, as evidenced by discrete switching-current jumps. At $T=30$~mK the device displays a Fraunhofer-like modulation with $I_{\mathrm{sw}}(0)\approx 0.24~μ\mathrm{A}$ and an abrupt transition at $|B|\approx 3~\mathrm{mT}$ between two branches differing by $ΔI_{\mathrm{sw}}\approx 0.13~μ\mathrm{A}$. By tracking the characteristic field scales from $30$ to $900$~mK, we find that the jump field is essentially temperature-independent, whereas the superconducting critical field decreases with temperature, as expected for thin Al films. The sharp discontinuity, sweep-direction asymmetry, and reproducibility across repeated scans point to avalanche-like switching between metastable magnetic configurations of the local magnetic texture, which are directly coupled to the weak link. Within an effective-field framework, each reconfiguration modifies a local field offset, thereby reshaping the interference response and leading to an abrupt reorganization of the switching-current pattern.

Nonequilibrium energy transport serves as one of fundamental problems in quantum thermodynamics and quantum technologies. Driven quantum master equation in the dressed picture provides an efficient way of investigating nonequilibrium energy flow in general driven-dissipative quantum systems, where the systems are simultaneously driven by the finite thermodynamic bias and coherent driving field. The validity and general applicability of driven quantum master equation is confirmed by comparing with Floquet master equation, by analyzing energy currents in generic spin and boson models. The additional driving phase reserved in system-reservoir interactions, will apparently modify microscopic energy exchange processes. The steady-state energy currents are dramatically enhanced, in particular near the resonant regimes. In contrast, the traditional dressed master equation yields distinct behaviors of the energy currents. We hope that the driven quantum master equation may provide an efficient utility for the control of quantum transport and thermodynamic performances in driven-dissipative nanodevices.

This paper addresses the problem of steering a state distribution over a finite horizon in discrete time with output feedback. The incorporation of output feedback introduces additional challenges arising from the statistical coupling between the true state distribution and the corresponding filtered state distribution. In particular, this paper extends existing distribution steering formulations to scenarios in which estimation errors are not orthogonal to the state estimates. A general framework is developed to capture this non-orthogonality, and the resulting problem is formulated in a form solvable via sequential convex programming with rank constraints. The proposed approach generalizes existing methods and is validated through numerical examples and Monte Carlo simulations, including cases with non-orthogonal estimation errors that prior techniques cannot address.

This vision paper addresses the research challenges of integrating traditional signal processing with Artificial Intelligence (AI) to enable energy-efficient, programmable, and scalable wireless connectivity infrastructures. While prior studies have primarily focused on high-level concepts, such as the potential role of Large Language Model (LLM) in 6G systems, this work advances the discussion by emphasizing integration challenges and research opportunities at the system level. Specifically, this paper examines the role of compact AI models, including Tiny and Real-time Machine Learning (ML), in enhancing wireless connectivity while adhering to strict constraints on computing resources, adaptability, and reliability. Application examples are provided to illustrate practical considerations and highlight how AI-driven signal processing can support next-generation wireless networks. By combining classical signal processing with lightweight AI methods, this paper outlines a pathway toward efficient and adaptive connectivity solutions for 6G and beyond.

I derive a size premium from the constant-product automated market maker used to price Bittensor subnet tokens and test the prediction using daily data on 128 subnets. A small-minus-big factor earns 1.01% daily (Newey-West t = 3.28). The December 2025 halving of token emissions, which the theory predicts should halve the premium, reduces it from 1.17% to 0.51% (p = 0.044). Exact slippage calculations show the premium is implementable only below \$10K in assets under management; at \$100K, transaction costs exceed gross returns.

We consider a Hamiltonian $\hat H$ with a (partially) continuous spectrum and examine the zero-overlap condition which involves the projection onto exact continuum eigenstates of a set of pseudostates obtained from the diagonalization of $\hat H$ in a finite basis of square-integrable functions. For each projected pseudostate the condition implies the occurrence of zeros at all energies that correspond to the pseudo-continuum matrix eigenvalues, except for the eigenenergy associated with that pseudostate. This feature was observed for the Coulomb continuum represented in a Laguerre basis [M. McGovern et al., Phys. Rev. A 79, 042707 (2009)] and later explained using special properties of the Laguerre functions [I. B. Abdurakhmanov et al., J. Phys. B 44, 075204 (2011)]. We establish that a sufficient condition for the zero-overlap condition to occur is that the image space of the operator $\hat Q \hat H \hat P$, where $\hat P$ is the projection operator onto the subspace spanned by the basis and $\hat Q = \hat 1 - \hat P$ its complement, has dimension one. We show that the condition is met for the one-dimensional free-particle problem by a basis of harmonic oscillator eigenstates and for the Coulomb problem by a Laguerre basis, thus offering an alternative proof for the latter case. The zero-overlap condition ensures that in, e.g., an ionizing collision or laser-atom interaction process, transition probabilities obtained from the projection of a time-propagated pseudostate-expanded system wave function onto eigenstates of $ \hat H $ are asymptotically stable.

Trusted Execution Environments (TEEs) allow the secure execution of code on remote systems without the need to trust their operators. They use static attestation as a central mechanism for establishing trust, allowing remote parties to verify that their code is executed unmodified in an isolated environment. However, this form of attestation does not cover runtime attacks, where an attacker exploits vulnerabilities in the software inside the TEE. Control Flow Attestation (CFA), a form of runtime attestation, is designed to detect such attacks. In this work, we present a method to extend TEEs with CFA and discuss how it can prevent exploitation in the event of detected control flow violations. Furthermore, we introduce HPCCFA, a mechanism that uses HPCs for CFA purposes, enabling hardware-backed trace generation on commodity CPUs. We demonstrate the feasibility of HPCCFA on a proof-of-concept implementation for Keystone on RISC-V. Our evaluation investigates the interplay of the number of measurement points and runtime protection, and reveals a trade-off between detection reliability and performance overhead.

The metal abundances in galactic nuclei carry key information on the history of star formation and mass transfer in central regions of galaxies. X-ray fluorescence analysis is a unique tool to reliably measure the abundances of various elements via simple physics. Here we present a new observation of the active nucleus in the Circinus Galaxy with the XRISM satellite at unprecedented X-ray energy resolution. The fluorescent iron-K$α$ line profile modified by Compton scattering indicates that the material responsible for its emission is cold, metal-rich, and is located $\gtrsim$0.024 parsecs (pc) from the supermassive black hole, consistent with the dusty torus region. The abundance pattern derived from comparing fluorescent line intensities of different metals shows sub-solar ratios of argon- and calcium-to-iron, and a super-solar ratio of nickel-to-iron. This abundance pattern is best produced by a combination in number fraction of $92^{+2}_{-4}$\% core-collapse supernovae from progenitor stars less massive than $20^{+3}_{-2} M_\odot$ and $8^{+4}_{-2}$\% type-Ia SNe. This suggests that gas feeding the super-massive black hole was enriched by recent core-collapse supernovae. Our findings imply that in metal-rich environments stars more massive than about 20 $M_\odot$ directly collapse into black holes or make faint SNe without ejecting heavy metals into the space.

The Mal'tsev product of two varieties of similar algebras is always a quasivariety. We consider the question of when this quasivariety is a variety. The main result asserts that if $\mathcal{V}$ is a strongly irregular variety with no nullary operations and at least one non-unary operation, and $\mathcal{S}$ is the variety, of the same type as $\mathcal{V}$, equivalent to the variety of semilattices, then the Mal'tsev product $\mathcal{V} \circ \mathcal{S}$ is a variety. It consists precisely of semilattice sums of algebras in $\mathcal{V}$. We derive an equational base for the product from an equational base for $\mathcal{V}$. However, if $\mathcal{V}$ is a regular variety, then the Mal'tsev product may not be a variety. We discuss various applications of the main result, and examine some detailed representations of algebras in $\mathcal{V} \circ \mathcal{S}$.

Driven by the MagNet Challenge 2025 (MC2), increased research interest is directed towards modeling transient magnetic fields within ferrite material. An accurate time-resolved and temperature-aware H-field prediction is essential for optimizing magnetic components in applications with quasi-stationary / non-stationary excitation waveforms. Within the scope of this investigation, a selection of model structures with varying degrees of physically motivated structure are compared. Based on a Pareto investigation, a rather black-box gated recurrent unit (GRU) model structure with a graceful initialization setup is found to offer the most attractive model size vs. model accuracy trade-off, while the physics-inspired models performed worse. For a GRU-based model with only 325 parameters, a sequence relative error of 8.02 % and a normalized energy relative error of 1.07 % averaged across five different materials are achieved on unseen test data. With this excellent parameter efficiency, the proposed model won the first place in the performance category of the MC2.

Whether there is a cosmic shoreline that divides terrestrial planets which have atmospheres from those that don't is one of the biggest open questions in exoplanet science. Most atmosphere searches have focused on terrestrial planets around M dwarf stars, since their smaller radii compared to sun-like stars boost planet atmosphere signals. However, the higher activity levels of M dwarfs might also entirely preclude atmosphere retention for their planets. In this work we present a new hope for defining an M dwarf cosmic shoreline, leveraging not only data from exoplanets in our own galaxy, but a comprehensive survey conducted by a commission of the Galactic Republic a long, long time ago in a galaxy far, far away. In this survey, we find definitive proof that M dwarf planets can retain atmospheres, and define an M dwarf cosmic shoreline whose slope agrees well with empirical predictions for Sun-like stars. We then define atmosphere retention metrics for the planets on the JWST Rocky Worlds DDT Targets Under Consideration list. Our analysis highlights the benefits of looking beyond the Milky Way for answers to some of the field's most pressing questions.

We investigate the rotational phase diagram of a quasi-two-dimensional, weakly-interacting Bose-Einstein condensate confined in power-law and in hard-wall trapping potentials. For weak interactions, the system undergoes discontinuous transitions between multiply-quantized vortex states as the rotation frequency of the trap increases. In contrast, stronger interactions induce continuous phase transitions toward mixed states involving both singly and multiply-quantized vortex states. A central result is the qualitative (and experimentally observable) difference between power-law and hard-wall confinement: In hard-wall traps, the leading instability always involves states with nonzero density at the trap center, whereas in power-law traps the density vanishes as the rotation frequency increases. The two different types of confinement give rise to scaling properties in the derived phase diagrams.

Spin squeezing serves as both a fundamental witness of quantum entanglement and a critical resource for quantum-enhanced metrology. While generating substantial spin squeezing in finite-range interacting systems remains challenging, such capability is important for advancing quantum technologies. In this work, we develop an optimal control strategy for achieving enhanced spin squeezing in a two-dimensional XX model with dipolar interactions. Leveraging rotor-spin-wave theory for periodic boundary conditions, we circumvent computational bottlenecks to explore control strategies at unprecedented scales. Remarkably, optimizing a single collective transverse field is sufficient to achieve substantial squeezing enhancement, exceeding the two-axis-twisting benchmark. The optimized control field achieves this breakthrough by dynamically suppressing inter-subspace mixing induced by the finite-range interactions, thereby confining the system evolution predominantly within the maximal spin subspace. We further extend rotor-spin-wave theory to open boundary conditions and incorporate dephasing noise, providing a scalable framework for realistic systems. Under these conditions, the optimized protocol remains effective, highlighting its robustness and suitability for experimental implementation.

Diffusion-based editing has rapidly evolved from curated inpainting tools into general-purpose editors spanning text-guided instruction following, mask-localized edits, drag-based geometric manipulation, exemplar transfer, and training-free composition systems. Despite strong empirical progress, the field lacks a unified treatment of core desiderata that govern practical usability: controllability (how precisely and continuously the user can specify an edit), faithfulness to user intent (semantic alignment to instructions), semantic consistency (preservation of identity and non-target content), locality (containment of changes), and perceptual quality (artifact suppression and detail retention). This paper provides a theoretical and empirical analysis of general diffusion-based image editing, connecting diverse paradigms through a common view of editing as guided transport on a learned image manifold. We first formalize editing as an operator induced by a conditional reverse-time generative process and define task-agnostic metrics capturing instruction adherence, region preservation, semantic consistency, and stability under repeated edits. We then develop theory describing edit dynamics under (i) noise-injection and denoising transport, (ii) inversion-and-edit pipelines and the propagation of inversion errors, and (iii) locality constraints implemented via masked guidance or hard constraints. Under mild Lipschitz assumptions on the learned score or flow field, we derive bounds connecting guidance strength and inversion error to measurable deviations in non-target regions, and we characterize accumulation effects under iterative multi-turn editing. Empirically, we benchmark representative paradigms.

In this paper, we consider the dispersive estimates for Schrödinger operators with Coulomb-like decaying potentials, such as $V(x)=-c|x|^{-μ}$ for $|x|\gg 1$ with $0<μ<2$, in one dimension. As an application, we establish both the standard and orthonormal Strichartz estimates for this model. One of the difficulties here is that perturbation arguments, which are typically applicable to rapidly decaying potentials, are not available. To overcome this, we derive a WKB expression for the spectral density and use a variant of the degenerate stationary phase formula to exploit its oscillatory behavior in the low-energy regime.

Purpose: Multiwinner voting rules typically require full knowledge of voter preferences, which becomes impractical in large-scale or attention-limited settings. This paper investigates how accurately a winning committee can be approximated when voter preferences are elicited using a limited budget of structured queries. Methods: We introduce a query-based framework for multiwinner elections in which voter preferences are elicited through refinement queries over subsets of candidates under a limited budget. We analyse several cost functions that model the cognitive effort needed to answer such queries, propose axiomatic properties for evaluating them, and experimentally evaluate simple query-based committee selection rules across multiple election models. Results: Experimental results show that strategies based on recursively splitting candidate sets provide the best trade-off between elicitation cost and committee accuracy. Across several statistical models, these strategies approximate the outcome of k-Borda elections significantly more efficiently than alternative query types. Conclusion: The results demonstrate that well-designed query strategies can substantially reduce the amount of preference information required while still producing high-quality committee outcomes, suggesting that query-based elicitation is a promising approach for scalable multiwinner decision-making.