To support rapid AI advances and broaden access to large-scale computing resources for under-resourced institutions at the Mid-South, we established the first regional mid-scale GPU cluster at the University of Memphis (UofM), iTiger. We present and analyze efforts of infrastructure management and computational support for educators, students, and researchers across scientific and engineering disciplines, such as precision agriculture, smart transportation, and health informatics. We outline our initiatives to broaden cluster adoption on research and education, such as seed grant programs, workshop trainings, course integration, and other outreach activities. We also identify challenges and further discuss findings of GPU infrastructure adoptions among college students and multidisciplinary researchers. The insights will indicate how to effectively and broaden infrastructure adoption and integrate into research and workforce developments.

We investigate the phenomenological prospects of the Two Higgs Doublet and Complex Singlet Scalar Extension (2HDMS) in the context of dark matter (DM) and Higgs phenomenology. The 2HDMS provides an enlarged Higgs sector along with a DM candidate. In this work, we perform an exhaustive scan to find representative benchmarks which are consistent with all theoretical and experimental constraints. We choose benchmarks with light, intermediate and massive DM masses and in some cases, also accommodate the 95 GeV excess in $b\bar{b}$ and $γγ$ channels observed at the Large Electron-Positron Collider (LEP) and Large Hadron Collider (LHC). We focus on the relevant signatures at the LHC and at proposed future lepton colliders including electron-positron and muon colliders. Using a cut and count analysis, we show that while the High Luminosity LHC (HL-LHC) may give a hint of new physics, future lepton colliders prove to be efficient discovery probes for the 2HDMS.

We establish two global boundedness results for weak solutions to generalized Schrödinger-type double phase problems with variable exponents in $\mathbb{R}^N$ under new critical growth conditions optimally introduced in [26, 32]. More precisely, for the case of subcritical growth, we employ the De Giorgi iteration with a suitable localization method in $\mathbb{R}^N$ to obtain a-priori bounds. As a byproduct, we derive the decay property of weak solutions. For the case of critical growth, using the De Giorgi iteration with a localization adapted to the critical growth, we prove the global boundedness. As an interesting application of these results, the existence of weak solutions for supercritical double phase problems is shown. These results are new even for problems with constant exponents in $\mathbb{R}^N$.

Random geometric graphs defined on Euclidean subspaces, also called Gilbert graphs, are widely used to model spatially embedded networks across various domains. In such graphs, nodes are located at random in Euclidean space, and any two nodes are connected by an edge if they lie within a certain distance threshold. Accurately estimating rare-event probabilities related to key properties of these graphs, such as the number of edges and the size of the largest connected component, is important in the assessment of risk associated with catastrophic incidents, for example. However, this task is computationally challenging, especially for large networks. Importance sampling offers a viable solution by concentrating computational efforts on significant regions of the graph. This paper explores the application of an importance sampling method to estimate rare-event probabilities, highlighting its advantages in reducing variance and enhancing accuracy. Through asymptotic analysis and numerical studies, we demonstrate the effectiveness of our methodology, contributing to improved analysis of Gilbert graphs and showcasing the broader applicability of importance sampling in complex network analysis.

The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasi-crystal phase. Additionally, a potential intermediate hexatic phase with quasi long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.

Current noisy intermediate-scale quantum (NISQ) devices remain limited in their ability to perform accurate quantum chemistry simulations due to restricted numbers of high-fidelity qubits and short coherence times. To overcome these challenges, we introduce the perturbative variational quantum eigensolver (VQE-PT), a hybrid quantum-classical algorithm that augments VQE with perturbation theory to account for electron correlation effects beyond a compact active space. Within this framework, the effective Hamiltonian in the active space is solved by VQE, and the perturbative energy correction is computed from reduced density matrices, thereby avoiding any increase in circuit depth or qubit overhead. We benchmark the proposed algorithm through numerical simulations on HF and N$_2$, demonstrating systematic improvements over standard VQE within compact active spaces. Furthermore, we perform an experimental realization on the Quafu superconducting quantum processor for $\rm F_2$, where, in conjunction with robust error mitigation strategies, the method achieves high accuracy (a mean absolute error of 1.2 millihartree) along the potential energy surface. These results demonstrate VQE-PT as a practical and resource-efficient pathway for incorporating dynamic correlation in quantum chemistry simulations.

Model documentation plays a crucial role in promoting transparency and responsible development of AI systems. With the rise of Generative AI (GenAI), open-source platforms have increasingly become hubs for hosting and distributing these models, prompting platforms like Hugging Face to develop dedicated model documentation guidelines that align with responsible AI principles. Despite these growing efforts, there remains a lack of understanding of how developers document their GenAI models on open-source platforms. Through interviews with 13 GenAI developers active on open-source platforms, we provide empirical insights into their documentation practices and challenges. Our analysis reveals that despite existing resources, developers of GenAI models still face multiple layers of uncertainties in their model documentation: (1) uncertainties about what specific content should be included; (2) uncertainties about how to effectively report key components of their models; and (3) uncertainties in deciding who should take responsibilities for various aspects of model documentation. Based on our findings, we discuss the implications for policymakers, open-source platforms, and the research community to support meaningful, effective and actionable model documentation in the GenAI era, including cultivating better community norms, building robust evaluation infrastructures, and clarifying roles and responsibilities.

Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an engineering method to reduce the executing time for randomized algorithms using dynamic circuits, i.e., quantum circuits involving intermediate measurement and feedback processes. The main idea is to generate the probability distribution defining a target randomized algorithm on a quantum computer, instead of a classical computer, which enables us to implement a variety of static circuits on a single dynamic circuit with many measurements. We applied the proposed method to the task of random Pauli measurement for one qubit on an IBM superconducting device, showing that a 14,000-fold acceleration of executing time was observed compared with a conventional method using static circuits. Additionally, for the problem of estimating expectation values of 28- and 40-qubit hydrogen chain models, we successfully applied the proposed method to realize the classical shadow with 10 million random circuits, which is the largest demonstration of classical shadow. This work significantly simplifies the execution of randomized algorithms on real quantum hardware.

Integrated coherent sources of ultra-violet (UV) light are essential for a wide range of applications, from ion-based quantum computing and optical clocks to gas sensing and microscopy. Conventional approaches that rely on UV gain materials face limitations in terms of wavelength versatility; in response frequency upconversion approaches that leverage various optical nonlinearities have received considerable attention. Among these, the integrated thin-film lithium niobate (TFLN) photonic platform shows particular promise owing to lithium niobate's transparency into the UV range, its strong second order nonlinearity, and high optical confinement. However, to date, the high propagation losses and lack of reliable techniques for consistent poling of cm-long waveguides with small poling periods have severely limited the utility of this platform. Here we present a sidewall poled lithium niobate (SPLN) waveguide approach that overcomes these obstacles and results in a more than two orders of magnitude increase in generated UV power compared to the state-of-the-art. Our UV SPLN waveguides feature record-low propagation losses of 2.3 dB/cm, complete domain inversion of the waveguide cross-section, and an optimum 50% duty cycle, resulting in a record-high normalized conversion efficiency of 5050 %W$^{-1}$cm$^{-2}$, and 4.2 mW of generated on-chip power at 390 nm wavelength. This advancement makes the TFLN photonic platform a viable option for high-quality on-chip UV generation, benefiting emerging applications.

Existing mortality forecasting methods focus on age-specific mortality rates, which lie in an unconstrained space and overlook the distributional nature of life-table death counts. Few studies have developed and compared forecasting methods that model the shape and dynamics of the age distribution of deaths, especially at the subnational level, where data quality varies greatly. This paper presents several forecasting methods to model and forecast the subnational age distribution of death counts. The age distribution of death counts has many similarities to probability density functions, which are non-negative and have a constrained integral, and thus live in a constrained nonlinear space. To address the nonlinear nature of objects, we implement a cumulative distribution function transformation that is scale-free and has additional monotonicity. Using subnational Japanese life-table death counts from the Japanese Mortality Database (2025), we evaluate the forecast accuracy of the transformation and forecasting methods. The improved forecast accuracy of life-table death counts implemented here will be of great interest to demographers in estimating regional age-specific survival probabilities and life expectancy, and to actuaries as a foundation for exploring potential applications in determining annuity prices for various ages and maturities.

The operational calculus associated with Hermite numbers has been shown to be an effective tool for simplifying the study of special functions. Within this context, Hermite polynomials have been viewed as Newton binomials, with the consequent possibility of establishing previously unknown properties. In this article, this method is extended to study the lacunary Hermite polynomials and obtain novel results concerning their generating functions, recurrence relations, differential equations and certain integral transforms. The proposed method is systematically applied to a variety of evolution equations. Furthermore, this idea is extended to combinatorial interpretation of these polynomials, broadening their applicability in mathematical analysis and discrete structures.

We introduce the two-factor Quintic Ornstein-Uhlenbeck (OU) model, where volatility is modelled as a degree-five polynomial of the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian motion, each mean-reverting at a different speed. We demonstrate that the model effectively captures the volatility surfaces of SPX and VIX while aligning with the skew-stickiness ratio (SSR) across maturities ranging from a few days to over two years. Furthermore, it is consistent with key empirical stylized facts, notably reproducing the Zumbach effect.

Let $χ^λ_μ$ be the value of the irreducible character $χ^λ$ of the Hecke algebra of the symmetric group on the conjugacy class of type $μ$. The usual Murnaghan-Nakayama rule provides an iterative algorithm based on reduction of the lower partition $μ$. In this paper, we establish a dual Murnaghan-Nakayama rule for Hecke algebras of type $A$ using vertex operators by applying reduction to the upper partition $λ$. We formulate an explicit recursion of the dual Murnaghan-Nakayama rule by employing the combinatorial model of ``brick tabloids", which refines a previous result by two of us (J. Algebra 598 (2022), 24--47).

In this paper, we explore the application of ensemble optimal control to derive enhanced strategies for pharmacological cancer treatment, and we tackle the problem of the long-term management of the disease, i.e., when the complete eradication of the tumor is not achievable. In particular, we focus on moving beyond the classical clinical approach of giving the patient the maximal tolerated drug dose (MTD), which does not properly exploit the fight among sensitive and resistant cells for the available resources. Here, we employ a Lotka-Volterra model to describe the competing subpopulations, and we enclose this system within the ensemble control framework. In the first part, we establish general results suitable for application to various cancers. Then, we carry out numerical simulations in the setting of prostate cancer treated with androgen deprivation therapy, yielding a computed policy that is reminiscent of the medical `active surveillance' paradigm. Finally, inspired by the numerical evidence, we propose a variant of the celebrated adaptive therapy (AT), which we call `Off-On' AT.

Multiscale homogenization of woven composites requires detailed micromechanical evaluations, leading to high computational costs. Data-driven surrogate models based on neural networks address this challenge but often suffer from big data requirements, limited interpretability, and poor extrapolation capabilities. This study introduces a Hierarchical Physically Recurrent Neural Network (HPRNN) employing two levels of surrogate modeling. First, Physically Recurrent Neural Networks (PRNNs) are trained to capture the nonlinear elasto-plastic behavior of warp and weft yarns using micromechanical data. In a second scale transition, a physics-encoded meso-to-macroscale model integrates these yarn surrogates with the matrix constitutive model, embedding physical properties directly into the latent space. Adopting HPRNNs for both scale transitions can avoid nonphysical behavior often observed in predictions from pure data-driven recurrent neural networks and transformer networks. This results in better generalization under complex cyclic loading conditions. The framework offers a computationally efficient and explainable solution for multiscale modeling of woven composites.

We establish comparison maps between the classical algebraic $K$-theory of algebras over a field and its analogue $K^c$, an algebraic $K$-theory for coalgebras over a field. The comparison maps are compatible with the Hattori--Stallings (co)traces. We identify conditions on the algebras or coalgebras under which the comparison maps are equivalences. Notably, the algebraic $K$-theory of the power series ring is equivalent to the $K^c$-theory of the divided power coalgebra. We also establish comparison maps between the $G$-theory of finite dimensional representations of an algebra and its analogue $G^c$ for coalgebras. In particular, we show that the Swan theory of a group is equivalent to the $G^c$-theory of the representative functions coalgebra, reframing the classical character of a group as a trace in coHochschild homology.

For a balanced pair $(\mathcal{X},\mathcal{Y})$ in an abelian category, we investigate when the chain homotopy categories ${\bf K}(\mathcal{X})$ and ${\bf K}(\mathcal{Y})$ are triangulated equivalent. To this end, we realize these chain homotopy categories as homotopy categories of certain model categories and give conditions that ensure the existence of a Quillen equivalence between the model categories in question. We further give applications to cotorsion triples, Gorenstein projective and Gorenstein injective modules, as well as pure projective and pure injective objects.

We consider time-optimal controls of a controllable linear system with a scalar control on a long time interval. It is well-known that if all the eigenvalues of the matrix describing the linear system dynamics are real then any time-optimal control has a bounded number of switching points, where the bound does not depend on the length of the time interval. We consider the case where the governing matrix has purely imaginary eigenvalues, and show that then, in the generic case, the number of switching points is bounded from below by a linear function of the length of the time interval. The proof is based on relating the switching function in the optimal control problem to the mean motion problem that dates back to Lagrange and was solved by Hermann Weyl.

Teleparallel Born-Infeld gravity (TBI) is a modified theory of gravity that aims to maintain second order field equations, leading to alternative scenarios for strong gravity and cosmological settings. In this study, we examine the impact of TBI gravity on the physical characteristics of thin (Novikov-Thorne) accretion disks, focusing on quantities such as flux, pressure, temperature, etc. We also examine the spectral luminosity, comparing it to disks around the Schwarzschild black holes. By comparing the theoretical predictions to observational data in the low frequency regime, we demonstrate the model's ability to match real astrophysical systems and distinguish subtle differences between TBI gravity and general relativity, with improved sensitivity. Furthermore, the results suggest that observations of X-ray spectra from the inner disk regions can provide valuable insights into the properties of TBI gravity, potentially offering constraints on this modified gravity theory through future astrophysical observations.

Mission critical applications, such as UAV-assisted IoT networks require risk-aware decision-making under dynamic topologies and uncertain channels. We propose meta-conservative quantile regression (M-CQR), a meta-offline distributional MARL algorithm that integrates conservative Q-learning (CQL) for safe offline learning, quantile regression DQN (QR-DQN) for risk-sensitive value estimation, and model-agnostic meta-learning (MAML) for rapid adaptation. Two variants are developed: meta-independent CQR (M-I-CQR) and meta-CTDE-CQR. In a UAV-based communication scenario, M-CTDE-CQR achieves up to 50% faster convergence and outperforms baseline MARL methods, offering improved scalability, robustness, and adaptability for risk-sensitive decision-making. Code is available at https://github.com/Eslam211/MA_Meta_ODRL

We introduce the meta-problem Sidestep$(Π, \mathsf{dist}, d)$ for a problem $Π$, a metric $\mathsf{dist}$ over its inputs, and a map $d: \mathbb N \to \mathbb R_+ \cup \{\infty\}$. A solution to Sidestep$(Π, \mathsf{dist}, d)$ on an input $I$ of $Π$ is a pair $(J, Π(J))$ such that $\mathsf{dist}(I,J) \leqslant d(|I|)$ and $Π(J)$ is a correct answer to $Π$ on input $J$. This formalizes the notion of answering a related question (or sidestepping the question), for which we give some motivations, and compare it to the neighboring concepts of smoothed analysis, certified algorithms, planted problems, edition problems, and approximation algorithms. Informally, we call hardness radius the ``largest'' $d$ such that Sidestep$(Π, \mathsf{dist}, d)$ is NP-hard. This framework calls for establishing the hardness radius of problems $Π$ of interest for the relevant distances $\mathsf{dist}$. We exemplify it with graph problems and two distances $\mathsf{dist}_Δ$ and $\mathsf{dist}_e$ (the edge edit distance) such that $\mathsf{dist}_Δ(G,H)$ (resp. $\mathsf{dist}_e(G,H)$) is the maximum degree (resp. number of edges) of the symmetric difference of $G$ and $H$ if these graphs are on the same vertex set, and $+\infty$ otherwise. We show that the decision problems Independent Set, Clique, Vertex Cover, Coloring, Clique Cover have hardness radius $n^{\frac{1}{2}-o(1)}$ for $\mathsf{dist}_Δ$, and $n^{\frac{4}{3}-o(1)}$ for $\mathsf{dist}_e$, that Hamiltonian Cycle has hardness radius 0 for $\mathsf{dist}_Δ$, and somewhere between $n^{\frac{1}{2}-o(1)}$ and $n/3$ for $\mathsf{dist}_e$, and that Dominating Set has hardness radius $n^{1-o(1)}$ for $\mathsf{dist}_e$. We leave several open questions.

As large language models (LLMs) advance and become widespread, students increasingly turn to systems like ChatGPT for assistance with writing tasks. Educators are concerned with students' usage of ChatGPT beyond cheating; using ChatGPT may reduce their critical engagement with writing, hindering students' learning processes. The negative or positive impact of using LLM-powered tools for writing will depend on how students use them; however, how students use ChatGPT remains largely unknown, resulting in a limited understanding of its impact on learning. To better understand how students use these tools, we conducted an online study $(n=70)$ where students were given an essay-writing task using a custom platform we developed to capture the queries they made to ChatGPT. To characterize their ChatGPT usage, we categorized each of the queries students made to ChatGPT. We then analyzed the relationship between ChatGPT usage and a variety of other metrics, including students' self-perception, attitudes towards AI, and the resulting essay itself. We found that factors such as gender, race, and perceived self-efficacy can help predict different AI usage patterns. Additionally, we found that different usage patterns were associated with varying levels of enjoyment and perceived ownership over the essay. The results of this study contribute to discussions about how writing education should incorporate generative AI-powered tools in the classroom.

Several generalizations of Vershik-Kerov limit shape problem are motivated by topological string theory and supersymmetric gauge theory instanton count. In this paper specifically we study the circular and linear quiver theories. We also briefly discuss the double-elliptic generalization of the Vershik-Kerov problem, related to six dimensional gauge theory compactified on a torus, and to elliptic cohomology of the Hilbert scheme of points on a plane. We prove that the limit shape in that setting is governed by a genus two algebraic curve, suggesting unexpected dualities between the enumerative and equivariant parameters.

The goal of this paper is to provide a definition for a notion of extended boundary at time and space-like infinity which, following Figueroa-O'Farril--Have--Prohazka--Salzer, we refer to as Ti and Spi. This definition applies to asymptotically flat spacetime in the sense of Ashtekar--Romano and we wish to demonstrate, by example, its pertinence in a number of situations. The definition is invariant, is constructed solely from the asymptotic data of the metric and is such that automorphisms of the extended boundaries are canonically identified with asymptotic symmetries. Furthermore, scattering data for massive fields are realised as functions on Ti and a geometric identification of cuts of Ti with points of Minkowksi then produces an integral formula of Kirchhoff type. Finally, Ti and Spi are both naturally equipped with (strong) Carrollian geometries which, under mild assumptions, enable to reduce the symmetry group down to the BMS group, or to Poincaré in the flat case. In particular, Strominger's matching conditions are naturally realised by restricting to Carrollian geometries compatible with a discrete symmetry of Spi.

We propose using a modified conductance-based method to study the mixing time of an important class of two-block Gibbs samplers, the data augmentation (DA) algorithm. %, which is of prominent interest in both theoretical and empirical research. Using this method, we prove the first non-asymptotic polynomial upper bounds on mixing times of three important DA algorithms: DA algorithms for Bayesian Probit regression (Albert and Chib, 1993, ProbitDA) and Bayesian Logit regression (Polson, Scott, and Windle, 2013, LogitDA), and Bayesian Lasso Regression (Park and Casella, 2008, Rajaratnam et al., 2015, LassoDA). Concretely, for ProbitDA and LogitDA, we demonstrate a tight bound that explicitly depends on the design matrix and prior covariance matrix. Under the assumption that data are independently generated from either a sub-Gaussian or log-concave distribution and properly scaled, the bound implies that with $η$-warm start, parameter dimension $d$, and sample size $n$, with high probability over data, the two algorithms require $\mathcal{O}\left(n\log \left(\frac{\log η}ε\right)\right)$ steps to obtain samples with at most $ε$ error in TV, KL, or $χ^2$ distance. Meanwhile, we show that under minimal data assumptions, LassoDA requires $\mathcal{O}\left(d^2(d\log d +n \log n)^2 \log \left(\fracηε\right)\right)$ steps to achieve $ε$-accuracy in TV distance. The results are generally applicable to settings with large $n$ and large $d$, including settings with highly imbalanced response data in Probit and Logit regression. We compare them with the best known guarantees of Langevin Monte Carlo and Metropolis Adjusted Langevin Algorithm. We evaluate our theoretical results using numerical examples, and discuss the mixing times of the three algorithms under feasible initialization.

This study explores the link between dietary behavior and the risk of nutritional deficiency dermatoses (NDD) in the Bicol region, where malnutrition remains a concern. Using regression analysis on FNRI data, it examines food purchase patterns, particularly riboflavin intake. Findings show an NDD risk prevalence of 15.75%, with Masbate and Camarines Sur contributing over half of cases. While rice (1590.93 g/day) and plant-based diets (523.30 g/day) are not rich in riboflavin, they still reduce NDD odds by 0.3% per gram. Riboflavin-rich foods like meat, eggs, and dairy lower risks by up to 3% per gram. The logistic regression model demonstrated strong performance (Nagelkerke = 0.765, accuracy = 94.1%, precision = 84.5%). Findings highlight the need for nutrition interventions, including enriched rice, better market access, and food diversity education to improve riboflavin intake and mitigate NDD risks.

Code search is essential for code reuse, allowing developers to efficiently locate relevant code snippets. The advent of powerful decoder-only Large Language Models (LLMs) has revolutionized many code intelligence tasks. However, their effectiveness for the retrieval-based task of code search, particularly compared to established encoder-based models, remains underexplored. This paper addresses this gap by presenting a large-scale systematic evaluation of eleven decoder-only LLMs, analyzing their performance across zero-shot and fine-tuned settings. Our results show that fine-tuned decoder-only models, particularly CodeGemma, significantly outperform encoder-only models like UniXcoder, achieving a 40.4% higher Mean Average Precision (MAP) on the CoSQA$^+$ benchmark. Our analysis further reveals two crucial nuances for practitioners: first, the relationship between model size and performance is non-monotonic, with mid-sized models often outperforming larger variants; second, the composition of the training data is critical, as a multilingual dataset enhances generalization while a small amount of data from a specific language can act as noise and interfere with model effectiveness. These findings offer a comprehensive guide to selecting and optimizing modern LLMs for code search.

The problem of detecting fake data inspires the following seemingly simple mathematical question. Sample a data point $X$ from the standard normal distribution in $\mathbb{R}^n$. An adversary observes $X$ and corrupts it by adding a vector $rt$, where they can choose any vector $t$ from a fixed set $T$ of the adversary's ``tricks'', and where $r>0$ is a fixed radius. The adversary's choice of $t=t(X)$ may depend on the true data $X$. The adversary wants to hide the corruption by making the fake data $X+rt$ statistically indistinguishable from the real data $X$. What is the largest radius $r=r(T)$ for which the adversary can create an undetectable fake? We show that for highly symmetric sets $T$, the detectability radius $r(T)$ is approximately twice the scaled Gaussian width of $T$. The upper bound actually holds for arbitrary sets $T$ and generalizes to arbitrary, non-Gaussian distributions of real data $X$. The lower bound may fail for not highly symmetric $T$, but we conjecture that this problem can be solved by considering the focused version of the Gaussian width of $T$, which focuses on the most important directions of $T$.

The impact of a management intervention on the soil organic carbon (SOC) stored in a given volume of soil is moderated by features that determine that soil's sequestration potential under that intervention. To maximize total SOC sequestration cost efficiently, interventions should be targeted to soils with the highest responses and lowest intervention costs. We present a framework for estimating SOC sequestration potentials and approximating efficient management policies. We review relevant sources of measurement uncertainty and formalize policy choice using potential outcomes. An optimal sequestration policy can be approximated by modeling SOC measurements as functions of covariates within each treatment group, using the fitted models to estimate SOC sequestration potential for each plot, and finding the policy that maximizes the average of those estimates. The modeling can use linear regression or other algorithms to learn relationships between features and SOC sequestration potential. We demonstrate this method using data from a study of compost amendments applied to California rangelands. We find that the plots exhibit treatment effects moderated by baseline SOC -- so targeting amendments to plots with lower baseline SOC would increase overall SOC sequestration rates. We evaluate these methods further in simulated field experiments. Refined policy estimates sequestered more SOC than uniform application of the single management policy estimated to have the largest average treatment effect, especially when SOC sequestration potential could be predicted from observed features. We conclude by discussing baseline SOC moderation, observational studies, inference, cost models, and broader policy uncertainties.

We investigate the role of energy-invariant assistants in energy extraction from quantum batteries. To this end, for energy extraction, we restrict ourselves to unitaries that jointly act on the battery and the assistant but preserve the energy of the assistant. We demonstrate that, in the presence of an energy-invariant assistant having the same dimension as the battery, all stored energy of the battery can always be extracted, transforming the battery into its ground state when an appropriate joint unitary and assistant state are employed. Additionally, we provide a necessary and sufficient condition for a battery to be unable to provide any energy, i.e., to be inactive, even when an energy-invariant assistant is present and prepared in an arbitrary but fixed state.