We report a direct, maskless electron beam-induced etching (EBIE) process for diamond in air, enabling high-precision patterning without lithography or plasma processing. Through a comprehensive analysis of electron-gas, electron-diamond, and gas-surface interactions in the SEM environment, we demonstrate that etching is predominantly governed by low-energy secondary electrons, which drive gas dissociation and radical generation. The resulting oxygen- and nitrogen-based radicals chemisorb on the diamond surface, form volatile carbon-containing species, and desorb under continued electron irradiation, enabling controlled material removal. The process exhibits two distinct regimes: a molecule-limited regime governed by gas flux and an electron-limited regime controlled by current density. Etch depths up to 212 nm and lateral resolution down to 200 nm are achieved. Time-dependent anisotropy is observed, with (100) surfaces transitioning to (111)-faceted morphologies, enhancing etch yield. These results establish a general secondary electron-driven mechanism for EBIE in gas environments, providing a maskless, damage-free nanofabrication route for diamond semiconductor and other chemically inert materials.

In many practical and numerical inverse problems, the exact data log-likelihood is not fully accessible, motivating the use of surrogate models. We study heteroscedastic nonparametric nonlinear regression problems with Gaussian errors and establish contraction results for posterior distributions arising from a surrogate log-likelihood constructed from proxy error variances, an approximate forward map, and an appropriate Gaussian process prior. Under general assumptions on the approximation quality, we show that the resulting surrogate posterior is statistically reliable and contracts about the true parameter at rates comparable to those of the exact posterior. The analysis leverages consistency properties of the (penalised) MLE to effectively handle heteroscedastic noise and to control the impact of likelihood approximation errors. We apply the framework to PDE-constrained inverse problems for a reaction-diffusion equation and the two-dimensional Navier-Stokes equation. In the latter case, we consider misspecified viscosity and forcing terms as well as Oseen-type linearization models, highlighting the relevance of our results for numerical analysis applications.

In this paper, a rate-splitting multiple access (RSMA) based joint optimization framework for the space-air-ground integrated network (SAGIN) is proposed, where the satellite and base stations employ uniform planar array (UPA) antennas for signal transmission, and unmanned aerial vehicles (UAVs) relay the satellite signals. Earth stations (ESs) and user equipments (UEs) receive signals from satellite and base stations (BSs), respectively, resulting in mutual interference. We first model the channels and signals in this scenario and analyse the interference at BSs and UEs. Then, We formulate a joint optimization problem aimed at maximizing the weighted sum-rate, involving beamforming, RIS-UAV deployment and phase shifts, and rate splitting. However, this problem is highly non-convex. To tackle this challenge, we apply a block coordinate descent (BCD) approach to decompose the problem and employ the weighted minimum mean square error (WMMSE) method to transform the non-convex objective function. For the rate-splitting sub-problem, a greedy algorithm is proposed and a successive convex approximation (SCA) algorithm is used for beamforming. Besides, the alternating direction method of multipliers (ADMM) algorithm is employed for the RIS phase-shift problem with unit-modulus constraints, and an exhaustive search method is adopted for the complex UAV positioning and orientation. Simulation results validate that the proposed algorithm achieves superior performance in terms of user weighted sum-rate.

The paper investigates the approximation of the symmetric Total Variation functional on graphs. Such an approximation is given in terms of a discrete and symmetric finite difference model defined on point clouds obtained by randomly sampling a reference probability measure. We identify suitable scalings of the point distribution that guarantee an almost surely $Γ$-convergence to an anisotropic weighted symmetric Total Variation.

We consider finite configurations of particles and holes sampled according to Bernoulli product measure and with a second class particle added to a random position. The stabilization time is the number of steps needed to reach an ordered state under discrete time TASEP dynamics with parallel update. We describe the additional time of stabilization caused by the presence of the second class particle.

Under a thermodynamic gradient, for example, the concentration or temperature gradients, the colloidal particles immersed in the solvent can exhibit a directional migration along or against the gradient -- phoresis, a cross transport effect. When the solvent is an odd fluid, where the time-reversal and parity symmetries are broken microscopically, the odd transport phenomenon is allowed. This means an odd phoresis may appear: the colloidal particle migrates perpendicularly to the thermodynamic gradient. Here, we realize the odd diffusiophoresis and odd thermophoresis for a colloidal particle immersed in a two-dimensional odd fluid by performing mesoscale fluid simulations. We further provide the flow field driven by the diffusiophoretic force, which is quantitatively consistent with the numerical solutions of the corresponding odd fluid dynamics equations.

We study rings of real-valued continuous functions in terms of pseudocomplementation conditions on various lattices attached to their prime spectrum. We fully characterize pseudocomplementation in all cases and have an almost complete characterization of relative pseudocomplementation.

Exciton condensation, characterized by uniform phase coherence across macroscopic length scales, has enabled the discovery of a variety of excitonic states, greatly enriching our understanding of correlated many-body physics. More exotic quantum phenomena are anticipated when the phase factor develops spatial dependence. However, whether excitonic condensates with spatially modulated phase profiles can emerge spontaneously remains an open question. In this work, we uncover novel forms of excitonic density waves featuring nontrivial phase patterns in twisted semiconductor bilayers. Remarkably, we show that kinetic frustration inherent to these systems stabilizes excitonic condensates arranged into a vortex-antivortex lattice. This represents a class of correlated states previously unknown in two-dimensional semiconductors, wherein the phase degrees of freedom of exciton condensates play a defining role. Such states spontaneously break both time-reversal and inversion symmetries, leading to non-reciprocal exciton transport, an effect we term the excitonic diode effect. Furthermore, we compute and identify characteristic impurity-induced states in these unconventional condensates, providing distinct signatures for their experimental detection.

With the emergence of data-driven approaches in science, there is growing interest in their application to manufacturing, particularly in surface precision engineering. However, generating large datasets required for model training is often impractical experimentally due to high costs and the time-intensive nature of measurements. High-fidelity synthetic datasets offer a viable alternative if they can be generated both efficiently and accurately. To address this challenge, this paper presents an efficient framework for generating accurate 3D surface topographies and roughness indicators in milling operations using numerical methods. First, a conventional topography prediction model is developed based on the forward solution method (FSM). Building on this, an optimized computational algorithm is proposed to establish an efficient FSM with significantly improved performance. The model is validated against two independent sets of experimental results, assessing both prediction accuracy and computational efficiency. The results demonstrate acceptable prediction errors and an average computational speedup of 42.2x. The proposed open-source model provides a generalizable framework for large-scale analysis, enabling the generation of extensive datasets for data-driven surrogate modeling.

Tidal interactions shape the evolution of close-in giant planets and internal gravity-wave breaking offers an efficient pathway for dynamical-tide dissipation, although its population-wide impact remains poorly constrained. We aim to quantify wave-breaking tidal dissipation for 550 hot Jupiters, accounting for stellar-parameter uncertainties. We also aim to identify the most promising systems for detecting orbital decay through transit timing.\\ Stellar masses, radii, and ages were homogeneously redetermined from spectroscopic and photometric data using an isochrone fitting. For each system, these parameters were propagated through a dedicated \texttt{MESA} model grid to calculate the tidal quality factor, wave-breaking probability, orbital decay rate, transit-timing diagnostics and destruction timescales.\\ Wave breaking is predicted to be largely inactive in pre-intermediate-age main sequence (pre-IAMS) stars. The tidal quality factor for systems undergoing wave breaking peaks between $10^6$ and $10^7$, consistent with population-level inferences. About 43\% of planets, primarily with periods $\lesssim3.5$~d, are expected to inspiral on the main sequence, providing a physical explanation for the observed tendency of hot Jupiters to orbit younger stars. A further 41\% inspiral during post-main-sequence evolution within the stages considered. Systems with periods $\lesssim 1$~d, which could in principle experience the strongest tidal forcing, are unlikely to trigger wave breaking, leaving planets on stable orbits. Conversely, the most rapidly inspiralling systems with high wave-breaking probability might display measurable orbital-period shortening only over multi-decade baselines, eluding immediate detection. In contrast, the demographic imprint of wave breaking on occurrence rates should emerge more readily, with the first signs already visible in current population statistics.

We consider a nonlinear parabolic equation of fractional order in space and propose its numerical discretization. The fractional derivative is defined through a functional analytic setting, rather than the traditional definition of fractional derivatives such as the Riemann-Liouville derivative. Numerical experiments are reported and some conjectures are presented.

In this paper, by the technique of inverse relations and comparing coefficients, we establish some generalized forms of Andrews' q-series identity and two new Bailey pairs and q-identities closely related to Andrews-Warnaar's sum identity for partial theta functions.

Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and configuration. However, constructing graphs that preserve high-level properties across a broad range of graph classes remains a challenging problem. We present a novel evolutionary approach to evolve graphs based on the Laplacian graph spectra descriptor. This descriptor can be used as part of a fitness function to evaluate graphs according to their desired high-level properties. Our evolutionary algorithm evolves graphs towards this descriptor in order to obtain graphs having properties that are consistent with it but are different from each other in terms of non-spectral graph metrics, such as path length, clustering coefficient and betweenness centrality. Our experimental results show that our approach is successful for different classes of graphs and a wide range of Laplacian graph spectra.

Iterative model-based image reconstruction in photoacoustic tomography (PAT) enables principled incorporation of detector physics, object-related priors, and complex acquisition strategies. However, for three-dimensional (3D) imaging scenario, the computational cost is often dominated by repeatedly solving wave equations. We propose a fast forward model for planar detection geometries that exploits transverse shift invariance. This symmetry enables to compute the full acoustic field from a 3D object, as a result of a set of 2D convolutions with depth-dependent impulse responses. This formulation yields a FFT-based forward operator and its corresponding discrete adjoint operator, making iterative reconstruction faster without calling partial differential equation (PDE) solvers at each iteration. We validate the model against commonly used PDE solver under matched discretization and boundary settings, and demonstrate accelerations of up to 2 orders of magnitude for iterative reconstructions from experimental all-optical photoacoustic datasets.

We consider a family of nonlinear oscillators, which is the autonomous case of the two-dimensional projective connection. We construct several classes of these oscillators that are simultaneously integrable and metrisable. This leads to families of (super)integrable two-dimensional metrics that are parametrized by arbitrary functions. In the superintegrable case we obtain an explicit expression for the unparametrized geodesics. In the integrable case we present two families of metrics with transcendental first integrals. We introduce the concept of generalized Darboux integrability in the context of both projective equations and geodesic flows. We demonstrate that the constructed integrable metrics are generalized Darboux integrable. In addition, we establish a direct connection between relative Killing vectors and invariants of the projective vector fields that are linear in the first derivative. Finally, we compute the dimensions of the projective Lie algebra for the obtained metrics, which allows us to distinguish previously known integrable cases from new ones.

Conventional service design methods are valuable for improving healthcare experience, but are limited in scale and information capture. Based on a constructed database of 2,320 stories from patients and carers with multiple long-term conditions (MLTC), this paper shows how real-life experiences can be used to inform healthcare service redesign. By combining the richness of qualitative insight with the breadth and representativeness of large-scale data, it identifies "Continuity of care", "Care coordination", and "Temporal - Access to services" as the priority redesign opportunities for MLTC.

Powder snow avalanches are highly dynamic, multiphase gravity-driven flows typically composed of a dense basal layer overlain by airborne layers in which snow particles are suspended within a turbulent air phase. Despite extensive work on related systems such as pyroclastic density currents and turbidity currents, all gravity current communities face a fundamental limitation: the lack of direct, high-resolution particle-scale field data. Here, we present the first direct optical observations of individual particle motion inside the airborne layers of a natural powder snow avalanche using high-speed imaging. The flow is segmented into three regions: an initial short living surge, a highly dynamic suspension phase, and a final wake. Across these phases, we quantify flow velocity and turbulence characteristics, including integral length scales, and use image intensity as a proxy for particle concentration. We identify fluctuations exceeding the turbulent integral scale and use linear stability analysis to link them to Kelvin-Helmholtz-type shear instabilities. Observed changes in clustering behavior, stratification, and the decoupling of particles from the flow mark the transition from an unstable suspension layer characterized by a high level of turbulent activity to a stable one dominated by passive snow settling. Together, these findings provide the first empirical constraints on turbulence and instability dynamics in airborne avalanche layers, with direct implications for the refinement of numerical avalanche models and closure schemes in multiphase gravity current simulations.

As machine learning as a service (MLaaS) gains increasing popularity, it raises two critical challenges: privacy and verifiability. For privacy, clients are reluctant to disclose sensitive private information to access MLaaS, while model providers must safeguard their proprietary models. For verifiability, clients lack reliable mechanisms to ensure that cloud servers execute model inference correctly. Decision trees are widely adopted in MLaaS due to their popularity, interpretability, and broad applicability in domains like medicine and finance. In this context, outsourcing decision tree evaluation (ODTE) enables both clients and model providers to offload their sensitive data and decision tree models to the cloud securely. However, existing ODTE schemes often fail to address both privacy and verifiability simultaneously. To bridge this gap, we propose $\sf PVODTE$, a novel two-server private and verifiable ODTE protocol that leverages homomorphic secret sharing and a MAC-based verification mechanism. $\sf PVODTE$ eliminates the need for server-to-server communication, enabling independent computation by each cloud server. This ``non-interactive'' setting addresses the latency and synchronization bottlenecks of prior arts, making it uniquely suitable for wide-area network (WAN) deployments. To our knowledge, $\sf PVODTE$ is the first two-server ODTE protocol that eliminates server-to-server communication. Furthermore, $\sf PVODTE$ achieves security against \emph{malicious} servers, where servers cannot learn anything about the client's input or the providers' decision tree models, and servers cannot alter the inference result without being detected.

The dependence of surface-enhanced Raman scattering (SERS) spectra on the precise axial position of the laser focus relative to a solid nanostructured substrate has received little to no attention in the literature. Here we show this dependence is both real and physically meaningful. Through vertical (Z-axis) scans varying the distance between the laser focus and a planar SERS substrate, we find that the SERS signal intensity follows a Lorentzian axial profile that peaks consistently above the physical sample surface. More significantly, the relative intensities of different spectral regions, i.e. SERS bands and background, vary non-monotonically and non-uniformly along the Z axis, meaning that band intensity ratios are focus-dependent. Finite-Difference Time-Domain (FDTD) simulations attribute these effects to plasmonic near-field responses specific to the focused and defocused beam interacting with the nanostructured metal surface. These findings reveal a previously overlooked source of spectral distortion in solid-substrate SERS measurements, with direct implications for the design and interpretation of quantitative assays based on band intensity ratios.

In this paper, we provide examples to show that for $1 \leq k \leq n/2$, solutions to $k$-Hessian equations $S_k(D^2u)=1$ in the exterior of a strictly convex domain need not be quasiconvex, when prescribing quadratic growth at infinity. Additionally, we give a new proof for the quasiconvexity of harmonic functions in such exterior domains that decay to zero at infinity.

Efficient thermal management in high-power electronic devices requires cooling channel designs that provide high heat removal while satisfying strict spatial and manufacturing constraints. This study presents a two-stage hierarchical topology optimization framework for cooling channels based on the Moving Morphable Components (MMC) method. The optimization is performed sequentially: in the first stage, only wall components are optimized to establish the global flow network and insignificant components are removed; in the second stage, the global structure is fixed and fin components are optimized to improve local thermal performance. The method is coupled with a two-layer thermofluid model using the Brinkman approximation and solved with the adjoint sensitivity approach. Across multiple inlet pressure conditions, the proposed framework consistently generates designs with clear functional separation. The results demonstrate that exploring such clearly separated structures through a two-stage optimization strategy leads to a further reduction in the objective function. Compared with simultaneous MMC optimization and conventional density-based topology optimization, the proposed method produces geometries that are more interpretable, controllable, and suitable for manufacturing.

Magnetic van der Waals (vdW) materials are promising for memory and logic applications because of their highly tunable magnetic properties and compatibility with vdW heterostructure devices. However, in conventional plan-view measurements, coupling between magnetic textures in stacked layers is difficult to resolve because the magnetic signal is integrated over the sample thickness. Here, these interactions are quantified in Fe$_3$GeTe$_2$ (FGT)/graphite/FGT heterostructures using cross-sectional Lorentz transmission electron microscopy and electron holography, enabling reconstruction of the local magnetic field within and between the layers. Domain alignment weakens with increasing FGT separation, yielding a dipolar coupling length scale of $λ= 34 \pm 4$ nm for the cross-sectional geometry studied here, corresponding to the average separation at which domain misalignment first emerges. This length scale coincides with an approximately 50\% reduction in the interlayer magnetic field relative to bulk FGT. Surface effects result in canting of the magnetic moments away from the easy axis up to $\sim$100 nm from a surface. Finally, the domain walls are narrow ($\sim$9 nm), while micromagnetic simulations reproduce the observed textures without invoking Dzyaloshinskii-Moriya interaction. These results quantify the internal and stray fields in stacked vdW magnets and guide the design of devices that require controllable coupling between magnetic textures.

Recently, Altavista, Anastasi, Angius and Uranga discussed a method to construct junctions and bouquets of different perturbative string theories. Following this analysis, we here argue that three non-tachyonic ten-dimensional heterotic string theories can be joined together at a nine-dimensional junction. This is done by creating a two-dimensional non-conformal $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theory with three asymptotic ends, each equipped with one of the worldsheet theories of the supersymmetric $E_8\times E_8$ theory, the supersymmetric $SO(32)$ theory, and the non-supersymmetric $SO(16)\times SO(16)$ theory, respectively. It is actually a special case of a more general construction involving an arbitrary $\mathbb{Z}_2$-symmetric theory $T$, its $\mathbb{Z}_2$-orbifold $T/\mathbb{Z}_2$, and the modified $\mathbb{Z}_2$-orbifold $(T\times q)/\mathbb{Z}_2$, where $q$ is a certain $\mathbb{Z}_2$-symmetric spin invertible theory.

Measurements of the combined CP asymmetries in $\kern 0.18em\overline{\kern -0.18em B}^0 \to D_s^- D^+$ and $\kern 0.18em\overline{\kern -0.18em B}_s^0 \to D_s^+ D^-$ decays are made using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9fb$^{-1}$. The measurements are found to be \begin{aligned} A_{CP}(\kern 0.18em\overline{\kern -0.18em B}^0 \to D_s^- D^+) &= 0.0009 \pm 0.0053 \pm 0.0040, \\ A_{CP}(\kern 0.18em\overline{\kern -0.18em B}_s^0 \to D_s^+ D^-) &= 0.103\phantom{0} \pm 0.053\phantom{0} \pm 0.010, \end{aligned} where the first and second uncertainties are statistical and systematic, respectively. This is the first measurement of this asymmetry in $\kern 0.18em\overline{\kern -0.18em B}_s^0$ decays, and the most precise measurement to date for $\kern 0.18em\overline{\kern -0.18em B}^0$ decays. Both measurements are found to be consistent with CP symmetry.

We investigate the production of the scalar meson $f_0(980)$ in proton--proton collisions at $\sqrt{s}=5.02$~TeV using the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport model supplemented with a $K\bar{K}$ coalescence afterburner. After conservatively tuning the UrQMD string-fragmentation parameters, the model reproduces the bulk charged-kaon production in the low-to-intermediate transverse-momentum region, providing the kaon phase-space distribution used as input for the coalescence calculation. In the present implementation, both charged and neutral kaon--antikaon pairs are considered, and each accepted $K\bar{K}$ pair is assigned to the isoscalar $f_0(980)$ and isovector $a_0(980)$ channels with an equal Monte Carlo probability. Using the updated integration analysis, we find that $Δp=0.4$~GeV/$c$ gives the best directly simulated agreement with the ALICE $p_T$ spectrum and integrated yield, while a linear interpolation between the neighboring points at $Δp=0.3$ and $0.4$~GeV/$c$ yields an interpolated optimum of $Δp^{\ast}\approx0.365$~GeV/$c$. Within this constrained hadronic coalescence framework, the measured $f_0(980)$ production is reasonably described, and the results are consistent with interpreting the $f_0(980)$ as a late-stage $K\bar{K}$ molecular configuration formed near kinetic freeze-out in small collision systems.

Conversion objectives in large-scale recommender systems are sparse, making them difficult to optimize. Generative recommendation (GR) partially alleviates data sparsity by organizing multi-type behaviors into a unified token sequence with shared representations, but conversion signals remain insufficiently modeled. While recent behavior-aware GR models encode behavior types and employ behavior-aware attention to highlight decision-related intermediate behaviors, they still rely on standard attention over the full history and provide no additional supervision for conversions, leaving conversion sparsity largely unresolved. To address these challenges, we propose RCLRec, a reverse curriculum learning-based GR framework for sparse conversion supervision. For each conversion target, RCLRec constructs a short curriculum by selecting a subsequence of conversion-related items from the history in reverse. Their semantic tokens are fed to the decoder as a prefix, together with the target conversion tokens, under a joint generation objective. This design provides additional instance-specific intermediate supervision, alleviating conversion sparsity and focusing the model on the user's critical decision process. We further introduce a curriculum quality-aware loss to ensure that the selected curricula are informative for conversion prediction. Experiments on offline datasets and an online A/B test show that RCLRec achieves superior performance, with +2.09% advertising revenue and +1.86% orders in online deployment.

Achieving coherent integration in distributed Internet of Things (IoT) sensing networks requires precise synchronization to jointly compensate clock offsets and radio-frequency (RF) phase errors. Conventional two-step protocols suffer from time-phase coupling, where residual timing offsets degrade phase coherence. This paper proposes a generalized hyper-plane regression (GHR) framework for joint calibration by transforming coupled spatiotemporal phase evolution into a unified regression model, enabling effective parameter decoupling. To support resource-constrained IoT edge nodes, a feature-level distributed architecture is developed. By adopting a linear frequency-modulated (LFM) waveform, the model order is reduced, yielding linear computational complexity. In addition, a unidirectional feature transmission mechanism eliminates the communication overhead of bidirectional timestamp exchange, making the approach suitable for resource-constrained IoT networks. Simulation results demonstrate reliable picosecond-level synchronization accuracy under severe noise across kilometer-scale distributed IoT sensing networks.

Large Language Models (LLMs) are now capable of resolving real-world GitHub issues. However, current approaches overapproximate the code context and suffer from two compounding problems: the prohibitive cost of processing massive inputs, and low effectiveness as noise floods the context window and distracts the model from the bug-fixing signal. Existing compression techniques fail to resolve this tension: generic compressors compromise the semantic integrity of code, while code-specific tools lack awareness of code structure and task context to preserve essential patch ingredients. To address this, we propose a novel framework consisting of two components. First, Oracle-guided Code Distillation (OCD), a context distillation algorithm that combines genetic search and delta debugging to systematically reduce code contexts to their minimal sufficient subsequence - retaining only the ingredients required for a successful fix. We use this distilled data to fine-tune SWEzze, a lightweight model that learns to compress code context at inference time, filtering noise and combating distraction while preserving fix ingredients. Evaluated on SWE-bench Verified across three frontier LLMs, SWEzze maintains a stable compression rate of about 6 times across models, reduces the total token budget by 51.8%-71.3% relative to the uncompressed setting, improves issue resolution rates by 5.0%-9.2%, and delivers the best overall balance among effectiveness, compression ratio, and latency compared with state-of-the-art context compression baselines.

We present an algorithm that enumerates all ideals of an input poset with constant delay in Gray code order, i.e., such that consecutively visited ideals differ in at most three elements. This answers a long-standing open problem posed by Pruesse and Ruskey, and improves upon previous algorithms by Pruesse and Ruskey, Squire, Habib, Medina, Nourine and Steiner, as well as Abdo. Using the same techniques, we also obtain an algorithm that enumerates all antichains of an input poset with constant delay such that successively visited antichains differ in at most three elements. As a key technical ingredient, we introduce a new potential-based analysis framework for recursive algorithms, which we call the Pyramid method. We show that this method subsumes the Push-out method of Uno. Beyond the present application, the Pyramid method is a general framework to analyze recursive algorithms and may thus be of independent interest.

Recently, several spectra have emerged, designed to encapsulate the distributional characteristics of non-Gaussian stationary processes. This article introduces parametric families of generalized spectra based on the characteristic function, alongside inference procedures enabling $\sqrt{n}$-consistent estimation of the unknown parameters in a broad class of parametric models. These spectra capture non-linear dependencies without requiring that the underlying stochastic processes satisfy any moment assumptions. Crucially, this approach facilitates frequency domain analysis for heavy-tailed time series, including possibly non-causal Cauchy autoregressive models and discrete-stable integer-valued autoregressive models. To the best of our knowledge, the latter models have not been studied theoretically in the literature. By estimating parameters across both causal and non-causal parameter spaces, our method automatically identifies the causal or non-causal structure of Cauchy autoregressive models. Furthermore, our estimator does not depend on smoothing parameters since it is based on the integrated periodogram associated with the generalized spectrum. As applications, we develop goodness-of-fit tests, moving average unit-root tests, and tests for non-invertibility. We study the finite-sample performance of the proposed estimators and tests via Monte Carlo simulations, and apply the methodology to estimation and forecasting of a measles count dataset. We evaluate finite-sample performance using Monte Carlo simulations and illustrate the practical value of the procedure with an application to measles case-count estimation and forecasting.