We explore phenomenological constraints on, and future muon collider sensitivities to, the parameter spaces of various muonphilic portals to fermionic asymmetric dark matter (ADM). Both WEFT-level dimension-6 effective operators and two UV models based on gauged $L_μ- L_τ$ are considered. One of the latter features a vector coupling to the dark matter and the other an axial vector coupling. The ADM criterion that at least $99\%$ of the dark matter relic density is asymmetric is also imposed. We identify which of these scenarios are currently allowed by direct detection and collider constraints, and then determine how much more of the parameter space could be probed by 3 and 10 TeV muon colliders with 1 ab$^{-1}$ of data. For the UV models, the constraints from $g-2$ of the muon are included. The future sensitivity curves due to neutron star heating considerations are also depicted. We present results for both the few-GeV dark matter mass regime motivated by ADM approaches to the $Ω_b \simeq Ω_\text{DM}/5$ coincidence problem, and for larger masses in the context of more general ADM.

In this paper, we show that the equational theory of relational Kleene algebra with the \emph{graph loop} operator (a.k.a.~\emph{fixset}) is \textsc{PSpace}-complete. Here, the graph loop is the unary operator that restricts a binary relation to the identity relation. We further show that this \textsc{PSpace}-completeness still holds by extending the terms with top, tests, converse, and nominals, over relational models. Notably, for Kleene algebra with tests (KAT), while the equational theory of relational KAT with antidomain is \textsc{ExpTime}-complete, we show that the equational theory of relational KAT with domain is \textsc{PSpace}-complete, thereby resolving a problem left open in previous works. To this end, we introduce a novel automaton model on relational structures (graphs), called \emph{loop-automata}. Loop-automata extend nondeterministic finite automata with a transition type that tests whether the current vertex has a loop. Using this model, we can give a polynomial-time reduction from the equational theories above to the language inclusion problem for 2-way alternating automata.

A methodology is developed to extract $d$ invariant features $W=f(X)$ that predict a response variable $Y$ without being confounded by variables $Z$ that may influence both $X$ and $Y$. The methodology's main ingredient is the penalization of any statistical dependence between $W$ and $Z$ conditioned on $Y$, replaced by the more readily implementable plain independence between $W$ and the random variable $Z_Y = T(Z,Y)$ that solves the [Monge] Optimal Transport Barycenter Problem for $Z\mid Y$. In the Gaussian case considered in this article, the two statements are equivalent. When the true confounders $Z$ are unknown, other measurable contextual variables $S$ can be used as surrogates, a replacement that involves no relaxation in the Gaussian case if the covariance matrix $Σ_{ZS}$ has full range. The resulting linear feature extractor adopts a closed form in terms of the first $d$ eigenvectors of a known matrix. The procedure extends with little change to more general, non-Gaussian / non-linear cases.

We study opinion formation in a society where agents interact on a modular network generated using a stochastic block model (SBM). Opinion dynamics is modeled through the Biswas-Chatterjee-Sen (BChS) kinetic exchange model, in which agents undergo pairwise interactions that could be positive or negative. By tuning the relative strength of intra- and inter-group connectivity inherent to the SBM, as well as the disagreement probability, we identify distinct collective phases. In particular, we observe a robust regime with strong intragroup ordering but no global consensus, in addition to fully ordered and disordered states. In the particular case of two modules, we observe an anti-ferromagnetic type ordering with the increase of negative interaction between the groups. We show approximate analytical calculations and numerical results of it. These results demonstrate how modular interaction structure can qualitatively alter collective opinion dynamics and hinder consensus formation.

The concept of trimming, embedding, or immersing geometries into a computational background mesh has gained considerable attention in recent years, particularly in isogeometric analysis (IGA). In this approach, the physical domain is represented independently from the computational mesh, allowing the latter to be generated more easily compared with body-fitted meshes. While this facilitates the treatment of complex geometries, it also introduces challenges, such as ill-conditioning of the stiffness matrix caused by small cut elements and difficulties in accurately enforcing boundary conditions. A recently proposed technique to address these issues is the Shifted Boundary Method (SBM), which represents the computational domain solely through uncut elements and enforces boundary conditions via a Taylor expansion from a surrogate boundary to the true boundary. Previous studies have shown that, for Neumann boundary conditions, the flux evaluation requires additional derivatives in the Taylor expansion, effectively reducing the order of convergence by one. In this work, we investigate for the first time the performance of SBM combined with Truncated Hierarchical B-splines (THB-splines) under various local refinement strategies. In particular, we propose local p- and k-refinement schemes for THB-splines and compare them with local h-refinement and the unmodified SBM. Furthermore, we propose an enhanced shift operator that incorporates mixed partial derivatives, in contrast to the standard operator. The study assesses accuracy, stability, and computational efficiency for benchmark problems on trimmed domains. The results highlight how different refinement strategies affect convergence behavior in trimmed IGA formulations using SBM and demonstrate that targeted degree elevation can mitigate the Neumann boundary limitations of the standard method.

We consider the geometric problem of determining the maximum number $n_q(r,h,f;s)$ of $(h-1)$-spaces in the projective space $\operatorname{PG}(r-1,q)$ such that each subspace of codimension $f$ does contain at most $s$ elements. In coding theory terms we are dealing with additive codes that have a large $f$th generalized Hamming weight. We also consider the dual problem of the minimum number $b_q(r,h,f;s)$ of $(h-1)$-spaces in $\operatorname{PG}(r-1,q)$ such that each subspace of codimension $f$ contains at least $s$ elements. We fully determine $b_2(5,2,2;s)$ as a function of $s$. We additionally give bounds and constructions for other parameters. For the computational results we partially use extensive integer linear programming computations.

The cryogenic approach to the search for the neutron electric dipole moment--performing the experiment in superfluid liquid helium--holds promise for a substantial increase in sensitivity, potentially enabling a sensitivity level of $10^{-28}$ e-cm. A crucial component in realizing such an experiment is the high voltage and electrode system capable of providing an electric field of 75 kV/cm. This, in turn, requires an electric potential of 635 kV to be applied to the high voltage electrode, while simultaneously satisfying other experimental constraints, such as those on heat load and magnetic noise requirements. This paper describes the outcome of a comprehensive development program addressing these challenges. It outlines the system requirements, discusses new insights into relevant physical phenomena, and details selected technical solutions with their corresponding experimental demonstrations and expected performance. The results collectively demonstrate the successful development of the necessary technology for the high-voltage and electrode system for this approach.

We develop an age-structured hydrodynamic (HD) theory which describes the collective behavior of $N\gg 1$ anomalously diffusing particles under stochastic renewal resetting. The theory treats the age of a particle -- the time since its last reset -- as an explicit dynamical variable and allows for resetting rules which introduce global inter-particle correlations. The anomalous diffusion is modeled by the scaled Brownian motion (sBm): a Gaussian process with independent increments, characterized by a power-law time dependence of the diffusion coefficient, $D(t)\sim t^{2H-1}$, where $H>0$. We apply this theory to three different resetting protocols: independent resetting to the origin (model~A), resetting to the origin of the particle farthest from it (model~B), and a scaled-diffusion extension of the ``Brownian bees" model of Berestycki et al, Ann. Probab. \textbf{50}, 2133 (2022). In all these models non-equilibrium steady states are reached at long times, and we determine the steady-state densities. For model A the (normalized to unity) steady-state density coincides with the steady-state probability density of a single particle undergoing sBM with resetting to the origin. For model B, and for the scaled Brownian bees, the HD steady-state densities are markedly different: in particular, they have compact supports for all $H>0$. The age-structured HD formalism can be extended to other anomalous diffusion processes with renewal resetting protocols which introduce global inter-particle correlations.

Transient grating spectroscopy (TGS) is a material characterization technique based on laser-induced thermoelastic excitation of thermal and acoustic gratings. On opaque samples, these gratings are dynamic surface displacements that reflect the sample's elastic and thermal properties, enabling both types of parameters to be determined from a single experiment. Here, we develop a detailed finite element model (FEM) of the TGS experiment that fully captures the coupling between the thermal and mechanical fields, as well as the optical detection of surface displacement using a heterodyning approach. Using custom-designed two-dimensional elements, the model is particularly suitable for analyzing TGS measurements on anisotropic media, for which analytical theory is insufficient. The simulation captures not only the anisotropic relaxation of the thermoelastic field but also several acoustic features that arise at very short (ultra-transient) timescales and provide additional information about the elastic properties of the examined material. The model offers new opportunities for the in silico testing of various modifications of TGS experiments and their applications to a broad class of materials.

Nonlocal modifications of gravity derive from corrections to the quantum gravitational stress tensor which grow nonperturbatively strong during primordial inflation and may persist to the current epoch. Phenomenological constructions have been given that realize MOND in gravitationally bound systems and, separately, reproduce all the cosmological phenomena usually ascribed to dark matter, including the cosmic microwave background radiation, baryon acoustic oscillations and linearized structure formation. In this work we exhibit a single model that interpolates between the two regimes.

Healthcare has become exceptionally sophisticated, as wearables and connected medical devices revolutionize remote patient monitoring, emergency response, medication management, diagnosis, and predictive and prescriptive analytics. Internet of Things and Cloud computing integrated systems (IoT-Cloud) facilitate sensing, automation, and processing for these healthcare applications. While real-time response is crucial for alleviating patient emergencies, protecting patient privacy is paramount in data-driven healthcare. In this paper, we propose a multi-layer IoT, Edge, and Cloud architecture to enhance emergency healthcare response times by distributing tasks based on response criticality and data permanence requirements. We ensure patient privacy through a Differential Privacy framework applied across several machine learning models: K-means, Logistic Regression, Random Forest, and Naive Bayes. We establish a comprehensive threat model identifying three adversary classes and evaluate Laplace, Gaussian, and hybrid noise mechanisms across varying privacy budgets, with supervised algorithms achieving up to 83.6% accuracy. The proposed hybrid Laplace-Gaussian noise mechanism with adaptive budget allocation provides a balanced approach, offering moderate tails and better privacy-utility trade-offs for both low and high-dimension datasets. At the practical threshold of $\varepsilon$=5.0, supervised algorithms achieve 80-81% accuracy while reducing attribute inference attacks by up to 18% and data reconstruction correlation by 70%. We further enhance security through Blockchain integration, which ensures trusted communication through time-stamping, traceability, and immutability for analytics applications. Edge computing demonstrates 8$\times$ latency reduction for emergency scenarios, validating the hierarchical architecture for time-critical operations.

We study Wilson loops on the Coulomb branch of $N = 4$ super-Yang-Mills theory, by solving for minimal surfaces that connect the contour on the boundary with the D3-brane in the bulk of AdS$_5 \times S^5$. The circular loop undergoes the Gross-Ooguri transition as a function of the radius and angular separation, and we fully map its phase diagram. As a byproduct we find evidence that the expectation value of the straight line is tree-level exact.

The computational complexity of calculating phase diagrams for multi-parameter models significantly limits the ability to select parameters that correspond to experimental data. This work presents a machine learning method for solving the inverse problem - forecasting the parameters of a model Hamiltonian for a cuprate superconductor based on its phase diagram. A comparative study of three deep learning architectures was conducted: VGG, ResNet, and U-Net. The latter was adapted for regression tasks and demonstrated the best performance. Training the U-Net model was performed on an extensive dataset of phase diagrams calculated within the mean-field approximation, followed by validation on data obtained using a semi-classical heat bath algorithm for Monte Carlo simulations. It is shown that the model accurately predicts all considered Hamiltonian parameters, and areas of low prediction accuracy correspond to regions of parametric insensitivity in the phase diagrams. This allows for the extraction of physically interpretable patterns and validation of the significance of parameters for the system. The results confirm the promising potential of applying machine learning to analyze complex physical models in condensed matter physics.

Following the AI Seoul Summit in 2024, twelve AI companies published frontier AI safety frameworks (Frameworks) outlining their approaches to managing catastrophic risks from advanced AI systems. Emerging legislation increasingly treats these Frameworks as external accountability mechanisms, incorporating them into reporting requirements. But what do the Frameworks actually commit each company to do? This study assesses 12 Frameworks, using 65 weighted criteria, across four dimensions: risk identification, risk analysis \& evaluation, risk treatment, and risk governance. Our criteria adapt established risk management principles from other high-risk industries (e.g. aviation, nuclear power) to the frontier AI context, following Campos et al. (2025). Overall scores range from 34% (Anthropic) to 8% (Cohere), with a median of 18%. Many aspects are missing or under-specified. These low scores may be natural given the nascency of AI risk management compared to industries with decades of practice. Nonetheless, current Frameworks are limited as accountability functions, with vague commitments that make it difficult to predict company decisions, assess whether planned responses are adequate, or determine whether commitments have been kept. Still, higher scores appear feasible within current constraints: a company adopting all leading practices currently adopted across their peers would score 54%, which is triple the current median.

We introduce a fun problem that can be considered as a variant of the classic birthday problem, the Bottleneck Birthday Problem (BBP). It is stated as: what is the maximum number of people we have to choose so that no day of the year has more than r >= 1 birthdays incident on it with probability at least 1/2? We provide a survey of techniques used in the literature on occupancy and load balancing problems to derive recurrence relations for exact computation of the probability, and the number of people keeping probability fixed at a threshold. Further, we show that restricted Stirling numbers of the second kind can be used to derive an additional recurrence, in a novel way. We provide complexity comparisons and numerical results from an implementation of the recurrences.

We propose a model-independent test of CP violation in the scalar sector. We consider a heavy neutral scalar $h_2$ with tree-level couplings at the $h_2 V V$ and $h_2 h_1 Z$ vertices (with $V=W^{\pm},Z$), alongside the 125~GeV SM-like Higgs boson $h_1$. At future muon colliders (MuC), we exploit vector-boson-fusion (VBF) production of $h_2$ followed by the decay $h_2 \to Z h_1$. In our framework, observing the single process $V V \to h_2 \to Z h_1$ implies both relevant couplings are nonzero, which is sufficient to establish CP violation in the scalar sector. We simulate signal and backgrounds at $\sqrt{s}=3~(10)$~TeV with integrated luminosity $L=0.9~(10)~\mathrm{ab}^{-1}$. We then present the expected discovery sensitivities across the $(c_2,c_{12})$ parameter space (with the coupling parameters $c_{2}$ and $c_{12}$ defined in the text) for multiple $m_{h_2}$ hypotheses.

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher interconnectivity among degrees of freedom. In particular, the discretization with tensor-product B-splines or NURBS of degree $p$ on a mesh with $n$ elements per parametric direction leads to symmetric positive-definite systems of the form $K\mathbf{u} = \mathbf{F}$, where the matrix bandwidth and condition number scale unfavorably with both $p$ and spatial dimension $d$. To address the computational challenges posed by such systems, especially in three-dimensional or high-order scenarios, Krylov subspace methods with specialized preconditioners become essential. This paper investigates the efficacy of algebraic multigrid (AMG) preconditioners tailored for IgA-based discretizations, with a focus on performance in modern high-performance computing (HPC) environments. Leveraging the Parallel Sparse Computation Toolkit (PSCToolkit), we explore distributed-memory and GPU-accelerated strategies for solving large-scale problems. The study assesses algorithmic efficiency and scalability across a range of benchmark tests. The results demonstrate that AMG preconditioners can achieve robust and scalable performance, confirming their potential as practical solvers for large IgA systems in engineering and scientific applications.

To enhance the performance of aerial-ground networks, this paper proposes an integrated sensing and communication (ISAC) framework for multi-UAV systems. In our model, ground base stations (BSs) cooperatively serve multiple unmanned aerial vehicles (UAVs), employing a dynamic time-division strategy where beam scanning for sensing precedes data communication in each time slot. To maximize the sum communication rate while satisfying a mission-level cumulative radar mutual information (MI) requirement, we jointly optimize the UAV trajectories, communication and sensing power allocation, and the time-division ratio. The resulting highly coupled non-convex optimization problem is efficiently solved using an alternating optimization (AO) and successive convex approximation (SCA) framework, which yields a non-decreasing objective sequence and convergence to a finite objective value under the adopted surrogate-based iterative procedure. Extensive simulation results demonstrate that our proposed joint design significantly outperforms benchmark schemes with static trajectories, partially optimized resources, or non-cooperative single-BS transmission. Furthermore, a comprehensive sensitivity analysis reveals the distinct mechanisms by which sensing thresholds and the number of UAVs influence resource allocation and spatial organization, highlighting the critical importance of dynamic, multi-dimensional resource management for effectively navigating the sensing-communication trade-off in low-altitude economies.

Gravitational waves emitted after neutron star binary coalescences and the information they carry about dense matter are a high-priority target for next-generation detectors. Even though such detectors are expected to observe millions of signals, detectable postmerger emission will remain rare. In this work, we explore postmerger detectability and inference through an alternative detector readout scheme for data dominated by quantum-noise, which is the case above $1$\,kHz: photon-counting. In such a readout, signals and noise become quantized into discrete distributions corresponding to the detection of single photons measured in a chosen basis of modes. Through simulated data, we demonstrate that photon counting can be efficient even for weak signals. We find ${\sim}1$ in 100 signals with a postmerger signal-to-noise ratio of 0.2 can result in a single photon and thus be detected. Furthermore, after $2\times10^4$ signals -- equivalent to $10^{-2}$ to $1.5$ years of observation -- photon counting results in a twofold improvement in the measurement of the radius of a $1.6\,M_\odot$ neutron star. Constraints can be further tightened if the detector classical noise is reduced. Photon counting offers a promising alternative to traditional homodyne readout techniques for extracting information from low signal-to-noise ratio postmerger signals.

It is well-established that human activity is driving extreme weather patterns, and that these extreme events influence human behaviour. However, few models allow for human behaviours and the climate to dynamically interact. The models presented in this paper expand on previous work and serve as an initial framework to extend current models by using a dynamic social-climate feedback loop. First, we introduce a social model to determine the conditions under which a committed minority can overturn a pre-established social convention. Second, we modify an existing climate model to include climatic variability. Lastly, we formulate a social-climate feedback model to study the interplay between human behaviour and the climate. Our results demonstrate that the social-climate feedback loop may be important in accurately predicting future temperatures, in contrast to the standard approach where human behaviour is a priori. Additionally, we find that a committed minority plays a vital role in shifting public opinion towards climate action and that the time at which the social convention of climate inaction is overturned has a large impact on future temperatures.

The memory-burden effect stabilizes the evaporating Primordial Black Holes (PBHs) before its complete decay. This also suppresses the evaporation flux via the entropy factor to the $k$-th power and circumvents severely astrophysical and cosmological constraints, such that it opens a new mass window for PBH Dark Matter lighter than $10^{15}$ g which has entered the memory-burden phase in the present epoch. In this study, we propose two scenarios to probe PBHs in the earlier semiclassical phase that evaporate at unsuppressed rates. The first scenario considers gravitons, emitted semiclassically from PBHs, propagating across the recombination epoch, then the magnetic field in the cosmological filaments converts them into photons via the Gertsenshtein effect. The second scenario relies on the PBHs mergers today, reproducing young semiclassical black holes with unsuppressed evaporation, but it is highly model dependent and has no sufficient theory support. For phenomenology studies, we perform computations of the extragalactic photon spectrum from PBHs emission according to these scenarios. The upper limits on the fractional abundance of PBH are obtained by comparing with the sensitivities of gamma-ray observations. The graviton-photon conversion scenario excludes the mass window $7.5\times 10^5\,{\rm g} \leq M_{\rm PBH}\leq 4.4\times 10^7\,{\rm g}$ with $f_{\rm PBH}|_{T_ϕ}\geq 1$ and $k=1$, assuming the optimistic magnetic field $B_0=100$ nG. Meanwhile, the merging scenario, which is insensitive on $k$, restricts PBH Dark Matter lighter than $2.2\times 10^{11}$ g.

An induced additive action on a projective variety $X\subseteq\mathbb{P}^n$ is a regular action of the group $\mathbb{G}_a^n$ on $X$ with an open orbit that can be extended to a regular action on $\mathbb{P}^n$. Such actions are known to correspond to pairs $(A, U)$, where $A$ is a local algebra and $U$ is a generating subspace lying in the maximal ideal. This paper studies additive actions on projective toric varieties, with a particular focus on toric surfaces. We prove that for any linearly normal toric variety equipped with a torus-normalized additive action, the associated pair consists of a monomial algebra and a subspace spanned by variables. Also we describe pairs that correspond to additive actions on toric surfaces in low-dimensional projective spaces.

The flux of extragalactic gamma rays is attenuated through interactions with optical and infrared photons of the extragalactic background light (EBL). The EBL is an isotropic, diffuse photon field that is difficult to measure directly at these wavelengths due to strong foreground emission. We present niebla, the first open-source code to compute the EBL from optical to far-infrared wavelengths using a phenomenological approach that accepts fully customizable inputs. This software enables a detailed modeling of the influence of EBL optical depth on gamma-ray observations and facilitates the distinction between different dust reemission models. The code models the optical background primarily from stellar emission, by evolving the spectrum of a single stellar population as a function of redshift, considering mean metallicity evolution and star formation rate density. Additional sources to the EBL can be provided by the user. The code already includes optional contributions from, e.g., stripped stars, intra-halo light, or the decay of axion dark matter. The optical emissivity is then absorbed by interstellar dust and reemitted in the infrared regime. We provide multiple prescriptions to model this process, using spectral dust templates or a combination of blackbodies. We provide three EBL models calculated with different dust reemission prescriptions, which have been fitted to various observational data sets. In addition, we showcase the versatility of our model through a simulated observation of the blazar Markarian 501 in a high-flux state with the LHAASO array. We find that the simulated VHE spectrum is highly sensitive to the photon density of the EBL at infrared wavelengths. Our model will therefore allow the community to distinguish between different dust reemission models and constrain EBL parameters with future observations.

For an ideal $\mathcal{I}$ in a $σ$-complete Boolean algebra $\mathcal{A}$, we show that if the Boolean algebra $\mathcal{A}\langle\mathcal{I}\rangle$ generated by $\mathcal{I}$ does not have the Nikodym property, then it does not have the Grothendieck property either. The converse however does not hold -- we construct a family of $\mathfrak{c}$ many pairwise non-isomorphic Boolean subalgebras of the power set $\wp(ω)$ of the form $\wp(ω)\langle\mathcal{I}\rangle$ which, when thought of as subsets of the Cantor space $2^ω$, belong to the Borel class $\mathbb{F}_{σδ}$ and have the Nikodym property but not the Grothendieck property, and a family of $2^\mathfrak{c}$ many pairwise non-isomorphic non-analytic Boolean algebras of the form $\wp(ω)\langle\mathcal{I}\rangle$ with the Nikodym property but without the Grothendieck property. Extending a result of Hernández-Hernández and Hrušák, we show that for an analytic P-ideal $\mathcal{I}$ on $ω$ the following are equivalent: 1) $\mathcal{I}$ is totally bounded, 2) $\mathcal{I}$ has the Local-to-Global Boundedness Property for submeasures, 3) $\wp(ω)/\mathcal{I}$ contains a countable splitting family, 4) $\mbox{conv}\le_K\mathcal{I}$. Moreover, proving a conjecture of Drewnowski, Florencio, and Paúl, we present examples of analytic P-ideals on $ω$ with the Nikodym property but without the Local-to-Global Boundedness Property for submeasures (and so not totally bounded). Exploiting a construction of Alon, Drewnowski, and Łuczak, we also describe a family of $\mathfrak{c}$ many pairwise non-isomorphic ideals on $ω$, induced by sequences of Kneser hypergraphs, which all have the Nikodym property but not the Nested Partition Property -- this answers a question of Stuart. Finally, Tukey reducibility of a class of ideals without the Nikodym property is studied.

Jupyter notebooks are widely used for machine learning (ML) prototyping. Yet, few debugging tools are designed for ML code in notebooks, partly, due to the lack of benchmarks. We introduce JunoBench, the first benchmark dataset of real-world crashes in Python-based ML notebooks. JunoBench includes 111 curated and reproducible crashes with verified fixes from public Kaggle notebooks, covering popular ML libraries (e.g., TensorFlow/Keras, PyTorch, Scikit-learn) and notebook-specific out-of-order execution errors. JunoBench ensures reproducibility and ease of use through a unified environment that reliably reproduces all crashes. By providing realistic crashes, their resolutions, richly annotated labels of crash characteristics, and natural-language diagnostic annotations, JunoBench facilitates research on bug detection, localization, diagnosis, and repair in notebook-based ML development.

Balancing plasma performance and coil cost is a significant challenge when designing a stellarator power plant. Most current stellarator designs are produced through two-stage optimization: stage-1 for the equilibrium and stage-2 for a coil design that reproduces its magnetic configuration. Because few proxies connect both stages, two-stage optimization can produce plasmas that have high-quality physical properties but overly complex coils. In recent years, single-stage optimization has increasingly been used to optimize the plasma and coils simultaneously in order to improve the plasma-coil balance. However, all existing single-stage tools are specialized for filament coils, cannot model coil systems containing permanent magnets (PM) or dipole arrays, and continue to be challenged by numerical problems. The quasi-single-stage (QSS) optimization finds a middle-ground by integrating a coil optimization subproblem into stage-1 optimization. We present a flexible, differentiable coil complexity proxy based on the newly developed QUADCOIL coil optimization code. QUADCOIL is fast and can target realistic coil metrics and constraints that are unavailable to codes with comparable speed. We demonstrate the effectiveness and flexibility of the QUADCOIL proxy by presenting two QSS optimization studies. The first study produces a permanent magnet solution for the MUSE stellarator with 29% fewer magnets than previous solutions. The second study produces a coil solution for the ARIES-CS stellarator with 27% reductions in both peak and root-mean-square force.

Betas from spot regressions are central to asset pricing and risk management, as measures of systematic risk. This paper develops a new estimation and inference framework for spot regressions by leveraging high-frequency candlesticks, extending conventional (open-to-close) returns with intra-period high/low prices. Specifically, I construct candlestick-based estimators of regression parameters, including spot beta, by minimizing a quadratic risk under a fixed-k asymptotic framework. I then develop a feasible hypothesis testing procedure for spot betas with correct asymptotic size. Simulation results show that the proposed estimator reduces estimation risk relative to return-based estimators, especially in small samples, and the test achieves notably higher power. I apply the framework to assess the market neutrality of Bitcoin using 1-minute data on IBIT and SPY, finding deviations from neutrality, particularly in high-volatility periods.

The Wightman two-point function of any Hadamard state of a linear quantum field theory determines a corresponding Feynman propagator. Conversely, however, a Feynman propagator determines a state only if certain positivity conditions are fulfilled. Choosing a Feynman propagator to satisfy the correct positivity conditions involves a slightly subtle point that we address and resolve. Starting from a recent generalisation of the Duistermaat-Hörmander theory of distinguished parametrices to normally hyperbolic and Dirac-type operators acting on sections of hermitian vector bundles, we complete this work by showing how Feynman propagators can be chosen so as to define Hadamard states. The theories considered are: the complex bosonic field governed by a normally hyperbolic operator; the corresponding hermitian theory if the operator commutes with a complex conjugation; the Dirac fermionic theory governed by a Dirac-type operator, and the corresponding Majorana theory in the case where the operator commutes with a skew complex conjugation. The additional key ingredients that we supply are simple domination properties of self-adjoint smooth kernels.

We present a comprehensive investigation of reconstructions on $β$-Ga$_2$O$_3$(001) combining first-principles calculations with experimental observations. Using ab initio atomistic thermodynamics and replica-exchange grand-canonical molecular dynamics simulations, we explore the configurational space of possible reconstructions under varying chemical potentials of oxygen and gallium. Our calculations reveal several stable surface reconstructions, most notably a previously unreported 1$\times$2 reconstruction consisting of paired GaO$_4$ tetrahedra that exhibits remarkable stability across a wide range of experimental growth conditions. In this reconstruction, two Ga atoms share one oxygen bond and are separated by a distance of 2.64 Å along the [010] direction. High-angle annular dark-field scanning transmission electron microscopy imaging of homoepitaxially grown (001) layers is consistent with the predicted structure. Additional investigations of possible indium substitution at the surface sites, which can occur during metal-exchange catalysis growth, reveal a cooperative effect in In incorporation, with distinct stability regions for In-substituted structures under O-rich conditions. Our findings provide an understanding for controlling surface properties during epitaxial growth of $β$-Ga$_2$O$_3$(001).

Mechanical systems provide a unique test bed for studying quantum phenomena at macroscopic length scales. However, realizing quantum states that feature quantum correlations among macroscopic mechanical objects remains an experimental challenge. Here, we propose a quantum system in which two micro-electromechanical oscillators interact through a chain of Rydberg atoms confined in optical tweezers. We demonstrate that the coherent dynamics of the system generate entanglement between the oscillators. Furthermore, we utilize the tunability of the radiative decay of the Rydberg atoms for dissipative entanglement generation. Our results highlight the potential to exploit the flexibility and tunability of Rydberg atom chains to generate nonclassical correlations between distant mechanical oscillators.