Mid-circuit measurement and classical feed-forward are essential primitives for dynamic-circuit teleportation on superconducting quantum processors. However, the error associated with measurement-conditioned corrective operations remains poorly understood when evaluated with respect to individual measurement branches. In this paper, we present a framework for characterizing feed-forward error in dynamic circuit teleportation without losing valuable information related to its behavior across separate branches. We analyze three approaches to applying measurement-conditioned corrections: (i) physical application, (ii) post-processing adjustments, and (iii) a mitigated physical application which utilizes Bit-Flip Averaging (BFA)-based Probabilistic Readout Error Mitigation (PROM). We experimentally reconstruct branch Choi operators via an entangled reference qubit, and validate our physical-application and post-processing Choi-shadow estimators against full tomography of the branch Choi operators. We perform experiments on two physical qubit layouts which differ greatly in mid-circuit measurement readout error, and observe a reversal in the relative order in branch qualities obtained from the post-processing and PROM mitigation strategies. In one physical layout with higher measurement readout error, the operational feed-forward penalty is relatively modest (approximately 0.02-0.03) and PROM produces higher branch qualities than post-processing for every branch. In a separate layout with lower readout error, the operational feed-forward penalty increases to roughly 0.07, and post-processing exceeds PROM for all branch qualities. Our characterization framework can reveal branch-specific error structure and mitigation behavior that state-of-the-art outcome-averaged analyses fail to expose.

We develop a one-dimensional Newtonian reduction for uniformly rotating cold white dwarfs in which the angle-averaged centrifugal support is represented by an effective anisotropic term. From the stationary Euler equation, using \(\langle\sin^2θ\rangle=2/3\), the rotational contribution becomes $ Δ_{\rm rot}(r)=\frac{1}{3}ρ(r)Ω^2 r^2 . $ The mapping keeps the spin frequency explicit while preserving a one-dimensional hydrostatic system. With the Chandrasekhar degenerate-electron equation of state, we compute sequences over \(ρ_c\in[10^6,10^{11}]~{\rm g\,cm^{-3}}\) for rotation proxies \(f=Ω/Ω_{K,0}(ρ_c)\leq0.35\). The high-density readout shows monotonic increases of mass and radius with \(f\), with a percent-level mass shift for the largest retained proxy. Applicability is checked on the rotating configurations through sub-Keplerian diagnostics and the bulk-interior measure \(\mathcal{A}_{10^{-2}}\). We further compare the reduced rotational correction with an auxiliary quasi-two-dimensional reconstruction and a static isotropic Tolman--Oppenheimer--Volkoff reference sequence. These scale checks show that the reduced model remains useful for controlled trend-level surveys in the slow-rotation regime, while rotational and static relativistic corrections can both become percent-level effects at high central density. The construction provides a transparent Newtonian benchmark for future axisymmetric and relativistic rotating white-dwarf calculations.

We present fast-vollib, an open-source Python library that provides high-performance European option pricing, implied volatility (IV) computation, and Greeks under the Black-76, Black-Scholes, and Black-Scholes-Merton models. The library is designed as a drop-in alternative to the de-facto-standard py_vollib and py_vollib_vectorized packages, with pluggable PyTorch and JAX execution backends, a CUDA fused-kernel Triton contribution for batched IV workloads, and a compatibility-first public API. In addition to a vectorized Halley-method IV solver, fast-vollib ships an experimental, fully-vectorized implementation of Jäckel's "Let's Be Rational" (LBR) algorithm with NumPy/Numba, torch.compile, JAX, and Triton single-pass GPU kernels for batched option chains. This note announces the library and describes its public API surface, with source, documentation, and packaging artifacts available at: GitHub (https://github.com/raeidsaqur/fast-vollib), Docs (https://raeidsaqur.github.io/fast-vollib/), PyPI (https://pypi.org/project/fast-vollib/).

Exact density-functional theory is recast here as two parallel exact ensemble variational hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in exact noninteracting ensemble theory. The Kohn-Sham construction links the two on a common admissible density class. In this recasting, Levy-Lieb, Hohenberg-Kohn, and Kohn-Sham formulations appear as constrained specializations of broader ensemble variational structures. Fractional particle number and fractional occupations enter naturally in the same ensemble setting, while piecewise linearity, one-sided chemical potentials, derivative discontinuity, and Janak-type relations emerge as consequences of the underlying variational geometry. We also clarify several distinctions that are often compressed together in standard expositions, including functional domain versus representability class, density reproduction versus spectral interpretation, and the relation between state-space realization and density-level supporting-potential structure.

The ferroelectric nematic (NF) phase and related polar liquid-crystalline phases form a new class of strongly polarized yet fluid soft matter. Well-recognized heliconical ferroelectric phases such as NTBF and SmC_P^H exist, but their electro-optic functionality in smectic systems has been largely unexplored. Here, we report a newly designed single-component achiral molecule exhibiting a hierarchical polar phase sequence: SmAF-NTBF-HEC-SmC_P^H. The key feature of the SmC_P^H phase is its ability to form a stable macroscopic orientation without any alignment layers and to enable continuous, reversible pitch modulation over a wide spectral range at ultralow electric fields, approximately one-third of those required for conventional heliconical nematics. The system exhibits characteristic electro-optic properties in the sub-kilohertz range, differentiating it from heliconical materials controlled by dielectric-elastic balance at higher frequencies. In addition, the SmC_P^H phase's polar heliconical smectic structure facilitates enhanced second-harmonic generation via favorable phase matching, thereby establishing a simple and robust platform for low-voltage photonic applications.

Snapshot full-Stokes polarimetry across multiple wavelengths remains challenging because conventional architectures rely on multiplexed measurements and bulky optics. We present an end-to-end framework that reconstructs RGB full-Stokes images from a snapshot sensor measurement. The system jointly optimizes a differentiable single-layered metasurface frontend with a U-Net backend. A metasurface modeled by the multilayer perceptron (MLP) is employed to encode the full-Stokes polarization information. On a real-world dataset, the system achieves a 27.06 dB peak signal-to-noise ratio (PSNR) and 0.7172 structural similarity index measure (SSIM) for monochromatic imaging at the specific wavelength (0.44 μm), and 23.35 dB/0.5643 for RGB-achromatic imaging. These results show that end-to-end optical-digital co-design enables high-performance snapshot full-Stokes polarization imaging with a compact footprint and a high compression ratio.

The field of multiobjective evolutionary algorithms (MOEAs) often emphasizes its popularity for optimization problems with conflicting objectives. However, it is still theoretically unknown how MOEAs perform compared with typical approaches outside this field. This paper conducts such a systematic theoretical comparison on problem classes with different degrees of conflict. With OneMaxMin$_k$ depicting $k\in[0..n]$ degrees of conflict, we show the difficulties of two typical non-MOEA approaches, the scalarization (weighted-sum) and {the} $ε-$constraint approach. We prove that for any set of weights, the set of optima formed by {the} scalarization approach cannot cover its full Pareto front for $k>2$. Although constrained problems constructed from $ε-$constraint approach ensure the full coverage, general ways (via exterior or nonparameter penalty functions) to solve these constrained problems encounter difficulties. The nonparameter penalty function way cannot guarantee the full coverage, and the exterior way covers the Pareto front with expected $O(\max\{k,1\}n\ln n)$ number of function evaluations, but only with careful settings of $ε$ and $r$ ($r>1/(ε+1-\lceil ε\rceil)$). In contrast, MOEAs efficiently solve OneMaxMin$_k$ without careful designs. We prove the same expected runtime of $O(\max\{k,1\}n\ln n)$ for the (G)SEMO, MOEA/D, NSGA-II, and SMS-EMOA. Our brief discussions on a bi-objective LeadingOnes variant with different degrees of conflict show similar findings.

Power electronic converters are fundamental building blocks of both AC and DC microgrids, enabling the integration of renewable energy sources, energy storage systems, electronic loads, and electric vehicles. In contrast, converter control in DC microgrids has developed along the path of droop control, which is widely adopted for decentralized DC-bus voltage regulation and power sharing. Although these control strategies share certain characteristics, their similarities remain largely unexplored due to the distinct physical domains in which they operate. To bridge this gap, we introduce a novel perspective based on the concept of duality to reveal the underlying isomorphism between the two control approaches. We show that AC grid-forming and DC I--V droop control are duals of each other in several aspects, including: (i) the small-signal model of the converter; (ii) the inner current control structure; (iii) power-sharing mechanisms based on the AC swing equation and DC capacitor power balance; and (iv) disturbance signals and dynamic response. Theoretical analysis, validated through simulations on simple converter setups, illustrates these dualities and provides new insights towards a unified control design.

We study the moduli spaces of rational curves on cubic hypersurfaces in characteristic $\neq2,3$. As a result, we prove that for every integer $d\geq1$ the Kontsevich moduli space of stable maps on a smooth cubic hypersurface $X$ of degree $d$ is irreducible if the dimension of $X$ is greater than or equal to $4$.

Distributional learning provides a useful framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-interface clause systems (FICSs). We formulate FICSs explicitly and study the corresponding learning problem under positive presentations and membership queries. We consider a bounded class of graph languages satisfying the finite context property (FCP) under a bounded-degree assumption. The bounds are expressed by the degree bound $Δ$ together with five structural parameters $m,s,t,w$, and $d$, which control the clause-system structure, interface ranks, and local head-frame complexity. The learning algorithm constructs hypotheses from ordered boundary representations induced by the observed positive examples. These representations make explicit the interface information needed to compare contexts and to test candidate clauses by membership queries. We prove that target contexts eventually appear in the observed sample, target clauses are reconstructed over the corresponding predicate representatives, and spurious non-fact clauses are eventually excluded. Consequently, for every fixed parameter tuple, the target language is identifiable in the limit from positive data and membership queries. We also prove that the learner has polynomial-time update on $\FICSLFCP_Δ(m,s,t,w,d)$: at each stage, only polynomially many ordered boundary representations, predicate symbols, clause candidates, and membership queries are needed. Overall, the paper gives a parameterized reformulation of distributional learning for interface-based graph languages in a fixed-interface setting.

This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces dimensionality offline by encoding solution snapshots using a multi-linear Tucker factorization, so that a reduced basis which varies nonlinearly with PDE parameters can be rapidly constructed online and used in a Galerkin ROM. Two novel extensions of this strategy, tailored to the cases of structured PDEs and sparse parameter sampling, are presented: the construction of reduced bases orthonormalized with respect to a general discrete inner product, and the interpolation of encoded states via radial basis functions. Basic representation and ROM error estimates are presented demonstrating the validity of these modifications, and the approach is challenged on examples where monolithic-basis ROMs are known to struggle, including a realistic instance of Maxwell's equations in 3D. Results suggest that the proposed nonlinear basis ROM can effectively mitigate linear restrictions on Kolmogorov $n$-width while improving upon previous tensorial ROM technology, particularly in the highly nonlinear and data-limited regimes characteristic of practical use cases.

We study the asymptotic behavior at infinity of solutions to the supercritical Lagrangian mean curvature equation \[ \sum_{i=1}^n \arctan λ_i(D^2u)=θ+f(x) \] on exterior domains in \(\mathbb R^n\), \(n\ge 2\), where \(|θ|>((n-2)π)/2\). The perturbation \(f\) is assumed to be locally Lipschitz near infinity and to satisfy a decay condition with rate \(β>0\). The main new ingredient is a scale-dependent difference quotient argument, combined with a nonlocal potential method, which avoids differentiating \(f\) twice and yields quantitative Hessian convergence under only Lipschitz regularity. We establish optimal asymptotic expansions in all dimensions and for all decay rates \(β>0\), including the critical logarithmic cases. This improves previous results requiring higher regularity of \(f\) and faster decay in \cite{BJ2026}.

Force fields are usually formulated directly in nuclear configuration space, whereas density functional theory is naturally formulated in terms of external potentials, densities, and variational duality. We show that exact force fields are variationally induced by DFT: the Born-Oppenheimer potential-energy surface is the pullback of the external-potential energy functional along the map from nuclear configurations to Coulomb potentials. In the Lieb formulation of density functional theory, the density is the first functional derivative of the energy with respect to the external potential, while the density-density response function is the second. Pulling these derivative objects back to nuclear configuration space yields the force and the nuclear Hessian, together with explicit terms induced by the nuclear-generated potential and the nuclear-nuclear repulsion. The resulting picture places force fields, density functional theory, and response theory within a single derivative hierarchy. The purpose of the present work is conceptual rather than algorithmic.

DC microgrids are converter-based electrical networks that are increasingly being used in various applications, including data centers and industrial distribution systems. A central challenge in their operation is maintaining the DC-bus voltage within predefined limits while ensuring overall system stability. Although a wide variety of converter control algorithms has been proposed to achieve these objectives, the literature lacks a clear and physically interpretable framework for evaluating their effectiveness and for classifying and comparing them. Moreover, the grid-forming versus grid-following distinction that exists in AC systems has largely been unexplored in DC microgrids. To address this gap, this paper introduces three novel impedance-based indices that can be used to quantify the voltage-forming and current-forming behavior of a converter. The indices also provide a basis for defining the desired converter behavior that yields superior DC-bus voltage regulation performance. Simulation results illustrate the application of the framework to several representative control strategies and highlight the strengths and limitations of these control algorithms.

We establish a sharp point-sphere incidence bound in finite fields for point sets exhibiting controlled additive structure. Working in the framework of \((4,s)\)-Salem sets, which quantify pseudorandomness via fourth-order additive energy, we prove that if \(P\subset \mathbb{F}_q^d\) is a \((4,s)\)-Salem set with \(s\in \big( \frac{1}{4}, \frac{1}{2} \big]\) and \(|P|\ll q^{ \frac{d}{4s}}\), then for any finite family \(S\) of spheres in \(\mathbb{F}_q^d\), \[ \bigg| I(P,S)-\frac{|P||S| }{q} \bigg| \ll q^{\frac{d}{4}}\,|P|^{1-s}\,|S|^{\frac{3}{4}}. \] This estimate improves the classical point-sphere incidence bounds for arbitrary point sets across a broad parameter range. The proof combines additive energy estimates with a lifting argument that converts point-sphere incidences into point-hyperplane incidences in one higher dimension while preserving the \((4,s)\)-Salem property. As applications, we derive refined bounds for unit distances and sum-product type phenomena, and we extend the method to \((u,s)\)-Salem sets for even moments \(u\ge4\).

We investigate an analytic theory of force-dipole hydrodynamics in a viscous membrane coupled to an infinite surrounding fluid, focusing on quenched (orientation-fixed) dipoles. While the single-dipole flow exhibits the known Saffman crossover from a near-field $v\sim r^{-1}$ to a screened far-field $v\sim r^{-2}$, we show that this crossover induces a qualitatively new reorganization of dipole--dipole interactions. For two identical quenched dipoles, the near-field dynamics is exactly solvable and effectively one-dimensional, with a fixed line of centers and linear evolution of the squared separation. In the far field, the system remains integrable but becomes intrinsically two-dimensional, with coupled radial and angular dynamics and an exact first integral. For pullers, the angular dynamics drives alignment toward an attracting manifold, leading to universal late-time collapse $R\sim (t_c-t)^{1/3}$, in contrast to the near-field scaling $R\sim (t_c-t)^{1/2}$. The Saffman crossover thus reorganizes the Hamiltonian phase-space structure of dipolar interactions and produces a transition from effectively one-dimensional to fully coupled dynamics, providing a minimal framework for aggregation in viscous fluid membranes.

Non-Markovian dynamics arise when a system is coupled to a bath with finite correlation time, producing memory effects that allow the bath to temporarily store and return excitations. However, how memory modifies irreversibility, and whether it can be exploited to improve thermodynamic performance, is not well established. We address this question using a Markovian embedding of generalized Langevin dynamics, in which bath memory is encoded in auxiliary modes and irreversible dissipation is represented by a residual Markovian bath. Here we show that this embedding naturally induces a decomposition of the entropy production of the original non-Markovian system into two parts: the entropy production of the embedded Markovian dynamics, which quantifies the memoryless irreversible contribution, and a nonnegative memory contribution associated with correlations between the system and auxiliary modes. This decomposition establishes a hierarchy of entropy production under Markovian embedding and provides a thermodynamic interpretation of memory effects. The resulting hierarchy yields finite-time thermodynamic bounds for non-Markovian systems, including entropic bounds, thermodynamic uncertainty relations, speed limits, and power-efficiency trade-offs, revealing how memory effects modify heat engine performance and current precision.

Inverse design has transformed vast physical parameter spaces into a substrate for emergent functionality, raising the tantalizing prospect of relocating intelligence from the digital domain into the physical world itself. Nowhere is this prospect more consequential than in sensing, where the analog-to-digital interface imposes a fundamental bottleneck: information not captured by the hardware is irrevocably lost to any downstream algorithm. Existing approaches improve information capture through either sensor hardware optimization or adaptive measurement strategies operating on fixed hardware, but rarely both in concert. A principled migration of intelligence from digital to physical demands their joint optimization: the sensing geometry must be co-designed with a policy that determines what to measure next. We formulate this co-design as joint dynamic programming (joint-DP), a unified optimization over sensor geometry and a Bellman-optimal adaptive measurement policy. The outer hardware gradient is obtained through differentiable dynamic programming with a sharp Bellman maximum. A hierarchy of relaxations extends the framework from small discrete POMDPs to freeform photonic topologies with more than $10^5$ design pixels.

A conjecturally complete list of connected components of complements of discriminant varieties (aka wave fronts) of smooth function singularities of type $X_{10}^3$ and $X_{10}^1$ is presented; it are the first examples of not semi-quasihomogeneous plane function singularities. It is shown that the complements of discriminants of singularities of classes $X_9^{\pm}$ and $X_{10}^1$ have non-trivial 1-dimensional homology groups, in contrast to all simple singularity classes.

We introduce a framework within which a large class of joint equidistribution problems can be studied and resolved with effective error terms. This involves proving a higher dimensional and $μ$-analogue of the Erdös-Turán inequality, and utilizing the theory of the Hardy-Krause (H-K) variation from analysis, where, in particular, we formulate a technique to approximate a broad class of relevant functions by functions of bounded H-K variation. Our main focus will be on the vertical Sato-Tate problem for spaces of cusp forms and for families of elliptic curves over finite fields. In particular, we obtain novel results concerning the distribution of arithmetic relations, and, more generally, multi-dimensional functions of Fourier coefficients and Frobenius traces.

We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary conditions parametrized by an integer $n$, corresponding to different velocity distributions imposed at the boundaries, generalizing the standard flux-weighted Maxwellian scheme. By combining Liouville's theorem with the boundary injection rule, we derive an explicit analytical expression for the stationary distribution function. This framework provides a direct link between microscopic boundary dynamics and macroscopic stationary profiles. We show that thermal equilibrium is recovered only for the standard flux-weighted injection method, while for all other cases the system relaxes to manifestly non-thermal stationary states. The resulting density and temperature profiles exhibit non-trivial spatial structures, including non-monotonic behaviour and temperature gradients induced by the boundary conditions alone. Analytical predictions for stationary moments are obtained in closed form for representative cases and are nicely reproduced by particle-based numerical simulations.

We study dynamic pricing where a seller repeatedly interacts with a strategic, non-myopic buyer who has a fixed private valuation and discounts future utility. Prior work focused exclusively on posted-price mechanisms, where the seller gives a take-it-or-leave-it offer. For our first result, we show that menu mechanisms consisting of allocation-payment contracts achieve $O(T_γ)$ regret, where $T_γ$ is the buyer's effective discounted time horizon. We also establish a $Ω(T_γ)$ lower bound, demonstrating the bound is tight. Considering the geometric discounting buyer with a constant discount factor, our bound is $O(1)$, while prior bounds using posted-price mechanisms incur an unavoidable $Ω(\log\log T)$ factor in regret. Our second contribution is more conceptual in nature. The problem of dynamic pricing sits at the intersection of two paradigms: learning with strategic agents in computer science / machine learning and revelation-principle-based mechanism design in economics, yet their relationship has remained unclear. We establish a fundamental equivalence: indirect learning-based mechanisms and direct revelation mechanisms achieve identical optimal regret. The adaptive, data-driven algorithms of online learning and explicit type elicitation are two languages towards solving the same problem.

We prove explicit one-lag finite-$N$ lower bounds for $\mathbb P(\bigcup_{k=1}^N A_k)$ using only the marginal probabilities and a selected-lag dependence coefficient of the event-generated $σ$-fields. Each finite statement uses one fixed coefficient convention, either ambient or finite restricted, rather than a limiting mixing assumption. In the $φ$ case, a residue-class blocking argument and a one-sided approximate-independence inequality yield a free spacing parameter $L\ge0$, spacing coefficient $1/(L+1)$, and residual terms governed by $φ(L+1)$. In the $α$ case, we give a simpler one-lag additive-correction bound based on strong-mixing covariance control. We compare these blocking estimates with the Chung--Erdős second-moment bound and with variance criteria for strongly mixing sequences, emphasizing that the $α$-mixing estimate is not intended to replace full-rate variance bounds when the complete decay profile is available. A windowed rate corollary and a second-order Bonferroni refinement parallel the corresponding $m$-dependent finite-sample results. The coefficient $1/(L+1)$ is sharp as a universal spacing constant only in the zero-residual sense: the full mixing classes contain $L$-dependent block constructions with $φ(L+1)=0$ and $α(L+1)=0$ that asymptotically attain the corresponding bound. This sharpness statement does not assert optimality of the residual penalties.

This paper proposes a consistency-model-based channel estimation algorithm for multiple-input multiple-output (MIMO) systems. The proposed algorithm employs a consistency model (CM) to learn the angle-domain channel distribution and uses the trained CM as a plug-and-play (PnP) generative prior for MIMO channel estimation. The proposed algorithm alternates between a pilot-observation-based data-consistency update and a CM-prior-based denoising update. In addition, the proposed algorithm adaptively selects the penalty parameter according to residual energy and residual whiteness, and adjusts the CM denoising level according to the observed signal-to-noise ratio (SNR), thereby avoiding the performance degradation caused by fixed inference schedules under varying observation conditions. Simulation results show that the proposed algorithm not only reduces the number of inference steps by 50%--90, but also achieves high estimation accuracy and favorable cross-dataset performance.

Large nonlinear recurrent neural networks with random couplings generate rich, potentially chaotic activity and are of interest in neuroscience and other fields. A key object encoding the structure of activity is the $N \times N$ covariance matrix. Recent work proposed an ansatz in which, at large $N$ and for typical quenched couplings, this covariance matrix matches that of a linear network with the same couplings, driven by independent noise. We derive this ansatz using a two-site cavity method that gives access to the joint statistics of activities at a pair of sites without disorder averaging. Specifically, we decompose each unit's activity into a linear response to its local field and a nonlinear residual; using the cavity method, we show that cross covariances of residuals at distinct sites are strongly suppressed, so that the residuals act as independent noise driving a linear network. In an alternative derivation, we construct a self-consistent equation for the covariance matrix in which non-Gaussian contributions supply cross terms that, in a linear network, would correspond to an external drive. Higher-order cross-site moments admit a Wick decomposition into pairwise covariances at leading order, reducing them to the linear-equivalent ansatz. We confirm the results in simulations and discuss their neuroscience implications.

Incorporating chiral organic cations into organic-inorganic hybrid materials has been shown to enable the inorganic sublattice to display chiroptical properties. We report a new two-dimensional magnetic ($S=1/2$) chiral metal halide material, (R)- and (S)-$(C_4H_9FN)_2CuCl_4$ (where $(C_4H_9FN)^+$ is 3-fluoropyrrolidinium), which consists of Cu-Cl inorganic layers separated by $(C_4H_9FN)^+$ organic cations. The presence of the chiral $(C_4H_9FN)^+$ organic cation induces formation of chiral magnetic order, even though the inorganic sublattice itself is nearly structurally centrosymmetric. We also report the racemic variant, containing an equal amount of (R)- and (S)- cations, which shows no evidence of chiral magnetic order. When the magnetic susceptibility is measured perpendicular to inorganic Cu-Cl layer propagation direction, an antiferromagnetic phase transition at Néel temperature $T_N = 2.23~K$ is observed in both the chiral and racemic materials, and the existence of the magnetic phase transition is supported by specific heat capacity measurements. Field-induced magnetic chirality is observed through the existence of a second-order magnetoelectric effect in the chiral variant, while no magnetoelectric signal is observed for the racemic material, indicating the absence of magnetic chirality. Our findings demonstrate that materials exhibiting chiral magnetic order can be created through the incorporation of a chiral cation into an organic-inorganic hybrid magnetic material, potentially allowing for the design of tailored materials that combine chiral magnetism with other desirable optical and electronic properties that come from structural chirality.

Despite their ubiquity, the rich physics present in a plasma sheath has inhibited the development of a generally applicable description of this critical region. The present study utilizes a physics-informed neural network (PINN) to evaluate a hierarchy of models of the plasma sheath. Unlike traditional deep learning methods, PINNs use the governing PDEs to constrain the predictions of a neural network, and thus do not require any experimental or simulation data to train. In this work, we utilize a PINN to identify the parametric solution to fluid models of different physics fidelity of the plasma sheath. While the offline training time of the PINN is often longer than a traditional solver, once trained, the PINN is able to efficiently predict the sheath profiles across a broad range of parameter regimes, thus yielding an effective surrogate of the plasma sheath.

We show that spectral features of primordial gravitational-wave backgrounds (GWB) can directly reconstruct \textit{Lagrangian} parameters of beyond-the-Standard-Model (BSM) particles, for any transient gravitational-wave production mechanism, independent of the specific source of gravitational waves. Sufficiently long-lived particles generically induce a temporary period of early matter domination in the thermal history of the Universe, which imprints two characteristic frequencies in any primordial GWB corresponding to the onset and end of this epoch. These frequencies are determined by the initial abundance, mass, and decay rate of the species. Once the underlying model and initial abundance are specified, the observed spectral features directly determine the particle mass and decay rate. We find that gravitational-wave observations probe regions of parameter space both complementary to and far beyond the reach of upcoming laboratory searches for long-lived particles. Remarkably, frequencies in the nanohertz band, where a stochastic signal has recently been reported by pulsar timing arrays, map directly onto decay lengths accessible in upcoming long-lived-particle (LLP) searches.

The standard $Λ$CDM model has been highly successful in describing cosmic microwave background (CMB) observations. Nevertheless, a set of large-scale statistical anomalies persists in temperature anisotropies across WMAP and Planck. CMB $E$-mode polarization offers an independent probe of these anomalies, circumventing the look-elsewhere effect inherent in temperature-only analyses. In this paper, we forecast the capability of the Ali CMB Polarization Telescope (AliCPT), a ground-based CMB experiment in the Northern Hemisphere, to detect such anomalies in large-scale $E$-mode polarization. Using 1000 unconstrained simulations processed with the NILC component separation method, we evaluate four anomaly estimators: dipole modulation, lack of large-angle correlations, quadrupole-octopole alignment, and point-parity asymmetry. Our analysis considers two noise levels for AliCPT, the goal configuration of the Simons Observatory (SO) Large Aperture Telescope (LAT) alone, and a joint AliCPT+SO configuration. For dipole modulation, we validate the local variance estimator on modulated simulations with an input amplitude $A_d = 0.07$, and find that the combined AliCPT+SO dataset is likely to detect the injected $E$-mode modulation at a 99% confidence level. Tests of the full suite of anomaly statistics on unconstrained isotropic simulations indicate that AliCPT alone, owing to its limited sky coverage, might introduce systematic biases or enlarged uncertainties, especially for quadrupole-octopole alignment and point-parity asymmetry. The combination with SO largely restores the statistical distributions to those expected in an ideal full-sky scenario, thereby establishing a near-cosmic-variance benchmark for upcoming anomaly investigations.

We perform a canonical analysis of the Holst model for General Relativity, within the framework laid out in arXiv:2401.07307 and arXiv:2010.07725, distinguishing our approach by setting the Barbero parameter to $β=0$ and leaving the lapse and shift functions unconstrained. The $β= 0$ choice is of particular interest because it is viable across all dimensions, providing a necessary foundation for extending the Loop Quantum Gravity formalism beyond $3+1$ dimensions. Through field decomposition and the projection of the field equations, we derive a system of 37 equations (10 differential constraints, 21 algebraic constraints, and 6 evolution equations) exactly matching the 37 field components to be determined. Moreover, leaving the gauge unfixed reveals that three equations, which are typically identically satisfied under normal evolution, are actually differential constraints whose triviality depends on specific gauge choices. The resulting framework remains fully consistent with the standard $3+1$ decomposition of the Einstein equations without requiring any constraints on the lapse and shift functions.