In the present paper, we propose Local Discontinuous Galerkin (LDG) approximations for a nonlinear system of $p$-Stokes type, having $(p,δ)$-structure. On the basis of the primal formulation, we prove well-posedness and stability (a priori estimates) of the methods under truly minimal regularity assumptions. We show that the first method possesses a pressure-robust and quasi-optimal error estimate, and discuss its consequences. Moreover, we propose a second method, for which we show a pressure-robust error estimate and prove convergence and convergence rates, which are optimal for linear ansatz functions for all $p\in (1,\infty)$ and $δ\geq 0$.

We establish an operational framework connecting the classical Kolmogorov--Arnold (KA) representation theorem to quantum information theory. By introducing and proving an algebraic, bounded-degree polynomial version of the theorem, we demonstrate that any target physical property of an unentangled multi-qubit product state can be exactly decomposed using a finite, fixed set of local <<inner>> observables and a shallow architecture of univariate polynomials. We further analyze the stability of this Quantum Kolmogorov--Arnold (QKA) representation under adversarial perturbations. In stark contrast to the pathological instabilities and severe reparameterization sensitivities inherent to the classical Kolmogorov--Arnold representation theorem, our algebraic quantum framework exhibits remarkable resilience. We prove that the representation remains stable against bounded physical perturbations acting on the inner measurement operators, and show via the Heisenberg picture that it is inherently immune to adversarial quantum channel attacks acting on the input states.

We characterize every almost abelian Lie algebra endowed with an integrable complex structure by a triple, called presentation, consisting of a real number, an element in some vector space and an endomorphism of that vector space. We then classify in terms of presentations the almost abelian Lie algebras admitting $p$-Kähler or $p$-pluriclosed structures, and in particular those carrying Kähler, balanced, pluriclosed and Gauduchon metrics.

The aim of this paper is to give a characterization of projective and weakly projective Boolean algebras using some modification of the Freese-Nation property.

X Persei is a classical Be/X-ray binary composed of an O9.5III-B0V Be-type star and a neutron star (NS). The NS exhibits coherent pulsations with a spin period of ~837 s, orbiting the Be star with a ~250 d period. X Persei is notable for its exceptionally hard X-ray emission extending beyond 100 keV. Due to the mild eccentricity of the orbit, ~0.11, the orbital separation varies between roughly 35 R_star at periastron and 44 R_star at apastron. In this work, we analyze five targeted observations obtained with the XMM-Newton and Chandra observatories taken over a 10-year time span, with the aim of investigating the structure and variability of the circumstellar disk surrounding the Be star, in particular the presence of over-dense areas known as clumps. We performed spectral and timing analyses, including average and NS spin-resolved spectroscopy for three of the observations, producing individual spectra at intervals as short as 210 s, corresponding to different epochs of the NS spin, resulting in approximately 1200 spectra. This detailed analysis aimed at resolving emission-line features otherwise diluted in averaged spectra and the evolution of continuum components along the NS spin. The observed spectra are accurately modeled by a two-component continuum comprising a high-temperature blackbody and a power-law component. Phase-resolved spectroscopy reveals transient Fe K alpha emission linked to clumps in the circumstellar disk during high-density epochs, with an 8-9% prevalence. Dips in the X-ray light curve are tied to clump passages. The disk-density modeling, based solely on X-ray data, suggests a compact and dense disk, with a radial density exponent alpha of 2.4-3.3, and a high inner disk density, rho_0 ~ (6-20) x 10^-10 g cm^-3, in agreement with previous studies conducted in the optical and infrared bands.

Stellar streams are thin, elongated collections of stars formed by gravitational disruption of orbiting star clusters or dwarf galaxies and are highly sensitive probes of the Milky Way's dark matter distribution and formation history. We present $\texttt{SCREAM}$ ($\textbf{S}$tream $\textbf{C}$ha$\textbf{R}$acterization with $\textbf{E}$rror $\textbf{A}$ware $\textbf{M}$achine Learning), a weakly-supervised framework to identify member stars of stellar streams. Building on the $\texttt{CATHODE}$ method originally developed for particle physics, $\texttt{SCREAM}$ identifies streams as localized feature-space over-densities, avoiding rigid physical priors like assumed gravitational potentials or strict isochrone filtering. Crucially, $\texttt{SCREAM}$ is the first machine learning (ML) framework in this domain to directly incorporate observational uncertainties into the neural network training objective. Using astrometric and photometric data from Gaia Data Release 3 and the Dark Energy Spectroscopic Instrument (DESI) Legacy imaging survey, we demonstrate our algorithm's performance on the prominent GD-1 stream. Validated against independent labels, $\texttt{SCREAM}$ achieves an F1 score of 0.745, substantially outperforming existing ML methods in both precision and recall. Furthermore, $\texttt{SCREAM}$ recovers the physically expected diffuse "cocoon" of GD-1 and faint main-sequence members that classical physics-based algorithms (e.g., $\texttt{STREAMFINDER}$) miss. Our results highlight the transformative potential of uncertainty-aware, weakly-supervised ML to uncover complex galactic structures.

In this study, we present a method for selecting an arbitrary number of distinct configurations from a larger data set by applying k-means clustering to atomistic configuration fingerprints based on the CrystalNN model and radial distribution function (RDF). This approach improves the accuracy of fitting classical molecular dynamics interatomic potentials to density functional theory (DFT) data for both energies and forces while requiring fewer configurations than random selection. We demonstrate this improvement by fitting an embedded-atom method (EAM) potential for titanium, using various configurational sizes from an initial set of 1800 configurations. The k-means clustering consistently achieves better precision and lower standard deviations for a smaller number of configurations than random selection. The results also suggest that only about 30 configurations are sufficient to obtain an EAM model that describes well the full set of 1800 configurations in terms of energies and forces. Additionally, t-distributed stochastic neighbor embedding (t-SNE) method was used to reduce the configuration fingerprints into 2D space, and it revealed an overlap between two configuration subsets with and without Ti vacancy, indicating similar atomic environments. This similarity is captured by k-means clustering but not by random selection. Furthermore, when the overlapping configurations with vacancies were excluded from the k-means algorithm and used only as a test set, their energy and force predictions showed similar precision to those when they were included. This indicates that the overlapping configurations in the 2D t-SNE space indeed imply potential information redundancy among the atomistic configurations.

Thin-film strontium titanate (SrTiO$_3$, STO) layers grown on silicon require accurate stoichiometry and single-crystalline order to exploit their functional properties optimally. Oxide molecular beam epitaxy can provide an epitaxial interface, but suffers from source oxidation and resulting flux instabilities, yielding only a narrow growth process window for cationic stoichiometry control. Here, we investigate post-growth annealing in oxygen as a pathway to drive the STO layer toward stoichiometry in intentionally Sr-rich epitaxial STO films on silicon (001). Annealing over a broad temperature range revealed two distinct Sr-segregation mechanisms. Below 800 °C, excess Sr segregates toward the surface, forming SrO outgrowths that progressively sublimate at elevated temperatures. Above 800 °C, a second mechanism dominates: Sr accumulates within the interfacial SiO$_2$ layer formed by oxygen diffusion at the STO/Si interface. Together, these mechanisms effectively remove excess Sr from the STO lattice, yielding a more stoichiometric perovskite layer. Our results demonstrate that growing slightly Sr-rich STO templates followed by controlled annealing provides a practical route to improve crystalline quality, offering a scalable strategy for high-quality STO integration on silicon.

Target tracking is challenging when sensor detection thresholds cause state-dependent missed detections, particularly in multi-sensor scenarios with clutter and uncertain target existence. A recently developed missed detection framework models detection probability as a function of target state, sensor characteristics, and detection threshold, but it is limited to individual measurements and does not address the recursive tracking problem. This work extends the framework using a Bernoulli filter formulation to jointly handle recursive target tracking, clutter, and target existence uncertainty. A Bernoulli particle filter is evaluated in a simulated 2D multi-sensor tracking scenario with nonlinear measurements, clutter, and detection uncertainty. Incorporating accurate detection threshold knowledge reduces the generalized optimal subpattern assignment (GOSPA) metric by 62.4% compared to a conventional Bernoulli filter with fixed detection probability, while better balancing missed detections and false alarms.

Nuclear fission produces neutrinos, so the absence of a neutrino signal can be used to set a limit on the fission content of an explosion. This capability could be employed on former nuclear test sites to assure regulators, international monitors, or other observers that activities involving chemical explosions do not exceed a designated limit for nuclear fission. This paper quantifies the neutrino detector masses that would be required to set fission yield limits at source-to-detector distances up to 100 km, assuming detection by inverse beta decay with realistic background levels. The analysis indicates that detectors with active mass in the ton- to tens-of-kiloton range can set potentially useful limits on the fission yield of large chemical explosions at the Nevada National Security Site. In contrast, inverse beta decay detectors are not well suited to excluding fission yield at longer range or in the subcritical nuclear experiments that have occurred at some test sites following the cessation of explosive nuclear testing.

This paper presents a search for beyond the standard model physics using single-lepton events with a high multiplicity of jets, including those identified as bottom quark jets, without a requirement on missing transverse momentum. The analysis is based on proton-proton collision data collected with the CMS detector at the CERN LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. This search is sensitive to $R$-parity violating supersymmetry models, where supersymmetric particles can decay into standard-model particles through interactions that violate baryon number conservation. In particular, the signal model considered is gluino pair production, where each gluino decays into top, bottom, and strange quarks. The sum of large-radius jet masses is used to distinguish the signal from background, as it effectively captures the features of high jet multiplicity and high interaction energy. No significant excess of data over the background predictions is observed. Gluinos in this model have been excluded for masses below 1890 GeV at 95% confidence level.

Measured specific heats often exceed Debye's T^3-law, even in high-purity single crystals. Analogous excess energy fluctuations in molecular dynamics (MD) simulations of crystals with no defects come from fast energy modulations involving next-nearest-neighbor atoms. Here, a theory is developed for these modulations, based on time- and phase-averaging followed by thermal averaging. This order of averaging is guided by evidence from the simulations and various experimental techniques showing that localized excitations are decoupled from the heat bath. Emergent nonextensivity is interpreted by analogy with anomalous diffusion. The theory modifies the standard relation between energy fluctuations and specific heat, giving good agreement with the simulations and new insight into many measurements. The theory may also provide a basis for understanding excess specific heat in amorphous materials and anomalous noise in quantum devices.

Nonconcave games present a unique challenge, as neither pure Nash equilibria nor local Nash equilibria (LNE) are guaranteed to exist, even in zero-sum settings. Additionally, computing approximate LNE in smooth multiplayer games over bounded regions is PPAD-hard. These challenges, coupled with the inherent complexity, have driven recent research toward broader equilibrium concepts, such as min-max critical points, and first-order Nash equilibria (FONE), which correspond to solutions of specific non-monotone variational inequalities. This paper addresses general-sum multiplayer games with compact convex strategy sets and smooth, nonconcave utility functions. Daskalakis et al. introduced the STON'R algorithm for solving variational inequality problems and established convergence under smoothness assumptions. They further showed that the algorithm's limit points correspond to equilibria in specific classes of games, namely local minimax equilibria in two-player zero-sum games and Nash equilibria in smooth concave games. In this work, we extend the convergence result to multiplayer general-sum games and show that the variational inequality solutions targeted by STON'R correspond to first-order Nash equilibria (FONE), a general game-theoretic solution concept that unifies these previously studied cases. We demonstrate the effectiveness and robustness of the algorithm on various examples from recent literature.

We consider the role of a continuum operational time u and its mapping to calendar time t and how these relate to event time for option pricing problems. We derive option-pricing equations from an operational-time Markov lattice rather than from a calendar-time diffusion. The primitive model is a nearest-neighbour log-price lattice with state- and time-dependent transition probabilities. Its Chapman-Kolmogorov decomposition yields discrete forward and backward equations, which converge under local finite-variance scaling to the usual continuum adjoint pair. In price variables, the backward equation gives a generalized European pricing PDE and reduces to Black-Scholes-Merton under the risk-neutral drift restriction and constant volatility. Interpreted as a reaction-boundary model for limit-order-book mid-prices, the construction identifies local volatility with an activity-rescaled risk-neutral bid-ask reaction-boundary variance. The framework separates the operational kernel, calendar-time projection, and pricing-measure choice, to clarify how unspanned clock, jump, or renewal risks can lead to incomplete-market pricing.

Light bridges are commonly observed in active regions and are interpreted as signatures of magnetoconvective processes in sunspots. Several studies have attempted to classify them in the past based on their morphological characteristics. Recent observations have revealed new dynamical properties of light bridges, including their signatures in the upper solar atmosphere, particularly in the chromosphere, and their coupling with coronal features. In this study, we observed two cases of rare and unusual dynamics as light bridges evolve. Using data from the Solar Dynamics Observatory, the evolution of the light bridges is analysed, and the results are reported here. Based on our findings, we propose that the unique movements of the light bridges in the observed sunspot and earlier studies could be an apparent view of the umbral core dynamics. Investigation into these dynamics through signatures in the higher atmosphere reveals a clear coupling to coronal loops and their dynamics.

Energetic particle induced geodesic acoustic modes (EGAMs) are axisymmetric perturbations of the radial electric field in tokamak plasmas. They are driven unstable by the phase space nonuniformity of a population of energetic particles (EP). In this paper, the nonlinear oscillation in the amplitude of the energetic-particle induced geodesic acoustic modes is studied by means of the gyrokinetic particle-in-cell code ORB5. Similarities are discussed with the beam-plasma instability (BPI), where a Langmuir wave is driven unstable by phase space nonuniformity of a population of energetic electrons. A similar scaling of the nonlinear oscillation frequency as a function of the mode amplitude is found for the EGAMs and for the BPI, confirming that their nonlinear dynamics is strongly determined by the same physical mechanisms. As a product of this study, a novel diagnostics is proposed for the evaluation of the EGAM intensity in tokamak plasmas.

A computational scheme, which utilizes neural networks, was developed to predict properties of molecular-based materials from chemical structures. The method uses a set of simple algorithms to encode the structure and composition of organic molecules directly into numerical vectors, which is used as input for neural networks. Backpropagation type neural networks are then used to correlate these numeric inputs with a set of desired properties. Calculated results for a series of hydrocarbons, hydrofluorocarbons, and crown ethers demonstrate average accuracies of 0.2-8.1% with maximum deviations of 16-20% for a broad range of thermodynamic, physical, and physical-chemical characteristics (heat capacity, enthalpy, heat of evaporation, boiling point, density, refractive index, stability constants, etc.). In addition, a number of physical and mechanical properties were estimated for polymeric materials and compared with regression analysis. Based on the neural network capabilities of formulating accurate quantitative structure property relationships, a technique called computational synthesis is suggested for performing materials design.

In this work, we analyze the ability of NCSN++ U-Net based audio dereverberation models to capture global room characteristics in their intermediate representations. Through an empirical study of both a state-of-the-art diffusion-based model and a discriminative counterpart, we show that deeper layers encode structured room impulse response (RIR)-dependent embeddings. Moreover, the discriminative ability of this implicit room representation correlates with dereverberation performance across objective metrics. Motivated by this observation, we propose a training strategy that explicitly conditions the network on pre-trained RIR embeddings, obtained via self-supervised contrastive learning. Incorporating RIR conditioning improves representation quality, accelerates convergence, and enhances dereverberation performance, while significantly reducing the number of reverse diffusion steps required by the diffusion-based model during inference.

We prove a sharp quantitative stability result for the affine \(L^p\)-Sobolev inequality, for \(p\ge2\), introduced by Lutwak--Yang--Zhang (\emph{J. Differential Geom.}, \textbf{62} (2002), 17--38). Moreover, the stability exponent is shown to be optimal, and equal to \(p\).

Optical trapping and micromanipulation rely on carefully shaped electromagnetic fields to exert precise forces and torques on microscopic particles. Despite their widespread application in biology and nanotechnology, the absolute physical limits of trapping performance, specifically the maximum achievable optical force and trap stiffness, have not yet been rigorously quantified. This work establishes a general theoretical framework to determine these fundamental bounds in the dipole approximation. By relating the optical force and stiffness to a local Taylor expansion of the electromagnetic field at the particle location, we formulate the performance limit as a solution to a quadratically constrained quadratic program. To evaluate these bounds, we employ two complementary approaches. First, we utilize a complete basis of vector spherical wave functions to determine the absolute theoretical limits of optical force and stiffness permitted by Maxwell's equations in free space, revealing Pareto-optimal trade-offs between stable confinement and directional force. Second, we introduce an aperture-based formulation that restricts the incident fields to those realizable by finite planar apertures. This yields device-consistent bounds directly applicable to experimental setups which rely mostly on electromagnetic beams. The finding that optimized aperture fields can outperform standard Gaussian beams by removing the severe axial bottleneck is particularly important. By comparing these two regimes, we identify the specific spatial modes that contribute to stable trapping and quantify the performance trade-offs inherent to physical beam shaping. This dual framework provides provably optimal bounds for power-normalized optical tweezers and serves as a rigorous benchmark for evaluating realistic beam designs.

We study the cumulants of work in a slow isothermal process for gapped systems. Using the Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) formalism and the properties of connected correlation functions, we show that in this process, the $n$-th cumulant of work scales as $1/T^{n-1}$ , where $T$ is the time duration. This result holds generally for arbitrary smooth protocols. Furthermore, we derive the coefficients of the cumulants from equilibrium properties. These coefficients are found to be relevant to thermodynamic geometric tensors.

While LLM-based agents are increasingly used in scientific workflows, it remains unclear whether they are truly qualified for the dynamic and uncertain process of discovery. Existing static evaluations often conflate genuine reasoning with rote memorization. We introduce InquiTree, a diagnostic environment that formalizes scientific inquiry as interactive Research Trees: directed acyclic graphs capturing the logical dependencies among hypothesis formulation, study design, result interpretation, and belief updating. Evaluating agents on a 30-paper test pool and releasing the open-access InquidTree-18(IT-18) subset, we identify two key limitations. First, agents exhibit an "Erosion of Marginal Capabilities": during long-horizon interactions, they develop "cognitive tunneling," where critical judgment and anomaly detection degrade relative to their intrinsic baselines. Second, performance drops on papers published after model training cutoffs, revealing a boundary between interpolation and extrapolation and suggesting that apparent competence is partly driven by parametric memory. These findings indicate that scaling context alone is insufficient for reliable AI scientists; stronger architectures or human oversight may be required to preserve critical evaluation and generalization.

We study a Mach-Zehnder interferometer (MZI)-based optoelectronic magnonic parametric oscillator (OEMPO) incorporating a YIG-loaded magnonic branch and a tunable phase-shifter branch, enabling systematic investigation of adaptive interferometric oscillator dynamics under distributed phase perturbations. Through analysis of nondegenerate OEPO mode pairs and frequency-pulling behavior, the loop free spectral range (FSR) and effective delay time were quantitatively extracted. Despite the nominally frequency-pinned parametric operation, weak frequency pulling and OEPO mode softening were observed, revealing an additional adaptive interferometric degree of freedom introduced by the MZI architecture. By comparing local and global sampling configurations, we demonstrate that the YIG branch behaves predominantly as a local dispersive resonant subsystem governed by the complex magnonic susceptibility, whereas the phase-shifter branch primarily controls the global interferometric redistribution geometry. Nevertheless, coherent recombination and adaptive regeneration within the loop produce finite cross-coupling between the two branches, resulting in partially synchronized interferometric dynamics and branch-dependent adaptive redistribution. Quantitative complex-Lorentzian analysis further reveals substantial phase-to-amplitude conversion and distinct differences between the OEO and OEPO regimes: the phase-pinned OEPO favors strongly dispersive local YIG response, while the frequency-adaptive OEO exhibits more mixed absorptive--dispersive behavior due to spectral relaxation through frequency pulling. Broadly, the present platform establishes a versatile framework for exploring adaptive nonlinear interferometric physics, coherent phase redistribution, and branch-dependent synchronization phenomena in hybrid magnonic-photonic oscillator systems.

Recently, Starr used asymptotic methods to disprove a conjecture by Heim--Neuhauser and Abdesselam about the log-concavity of the D'Arcais polynomials, without giving an explicit counterexample. We refine the asymptotics, to give the necessary estimates on convolutions of $σ_{-1}$, and identify the first counterexample at $λ= 65\,214\,507\,758\,400$. We also consider the asymptotic density of such counterexamples.

We give a generating series expression for the sum of all multiple zeta values of a fixed weight, depth, and height, which end with a given string $\vec{\ell} = (\ell_1,\ldots,\ell_r)$; this builds upon the proof of the Ohno-Zagier Theorem. In particular, the sum of all multiple zeta values of fixed weight, depth and ending with $\vec{\ell}$ has bounded depth $\leq \ell_1 + \cdots + \ell_r$. We give some applications to evaluations of interpolated multiple zeta values, and to the generating series of double zeta values.

A diassociative algebra (or dialgebra), a generalization of associative algebras with two associative products, is a fundamental algebraic structure of great importance and wide-ranging applications. In this paper, we establish a bialgebra theory for dialgebras completely and systematically. Explicitly, we introduce the notion of diassociative bialgebras (bi-dialgebras) which are equivalent to double constructions of Frobenius dialgebras as well as matched pairs of dialgebras. Moreover, we show that a bi-dialgebra gives rise to a Leibniz bialgebra, thereby lifting the classical relation between dialgebras and Leibniz algebras to the bialgebra level. In the coboundary cases, we introduce the diassociative Yang-Baxter equation (DAYBE) in a dialgebra, and solutions whose skew-symmetric part is invariant give rise to the so-called quasi-triangular bi-dialgebras. Moreover, weighted $\mathcal{O}$-operators on dialgebras are defined, which afford an operator interpretation for such solutions of the DAYBE. Finally, we also develop the triangular and factorizable theories for bi-dialgebras, and introduce skew-symmetric Rota-Baxter Frobenius dialgebras of arbitrary weight. We show that skew-symmetric Rota-Baxter Frobenius dialgebras of weight zero give rise to triangular bi-dialgebras, whereas those of nonzero weight induce factorizable bi-dialgebras. As an application, we provide concrete examples of factorizable bi-dialgebras from associative algebras and dialgebras, respectively.

We construct KMS states for the Nelson model, the spinless Pauli--Fierz model, and the Pauli--Fierz model with spin by functional integral representations, and study point-source models after removal of the infrared and ultraviolet cutoffs. If the physical test-function space can distinguish the zero mode, the absence of off-diagonal long-range order, the vanishing of the zero-mode form, the vanishing of the condensate density, the order-parameter criterion, and the triviality of the BEC directions and the BEC ideal are equivalent. We also describe the infrared quotient and the BEC ideal in the resolvent algebra uniformly for the three models, and formulate an operator-algebraic sufficient condition for separately given spatially translation-invariant KMS states.

This paper presents a method for controlling traffic via the use of connected and automated vehicles (CAVs) acting as moving bottlenecks. Current methods for moving bottleneck control use a couple PDE-ODE model, based on the Lighthill-Whitham-Richard (LWR) model, to represent the influence of the CAV. Control of the CAV is normally achieved by designing the control on the ODE which models the speed of the moving bottleneck. The proposed method in this paper instead looks to reduce the computational burden of controlling multiple CAVs by designing the moving bottleneck controller first on the PDE. The original control designed on the PDE is a linear quadratic regulator (LQR) that determines the optimal variable speed limit (VSL) for the entire length of freeway in order to regulate density to a desired setpoint. Then, a continuification approach is utilized to determine the input speed for each CAV. Results show that multiple CAVs can be controlled via this method, with minimal computational burden, and that as the number of CAVs increases the solution approaches the global optimal solution determined by the LQR.

Distributed Fiber Sensing (DFS) leverages optical backscattering signals to predict failure events and enable just-in-time restoration in metropolitan optical networks, i.e., without optical amplifiers. In this paper, we study the effectiveness of proactive restoration based on DFS information in all-optical networks, while considering different sensing devices' capabilities. We evaluate whether restoration can be provisioned just-in-time before a failure happens, and its impact on key performance metrics, including the number of affected and suspended optical circuits, bandwidth blocking rate, and service downtime. Simulation results demonstrate that just-in-time restoration enabled by DFS with a prediction time capability of 15~ms can reduce circuit disruptions by more than 90\% compared to restoration without sensing and ensure optical service continuity in optical networks comparable to resource-intensive protection schemes, at a fraction of the spectral resources.

We generalize the convergence results of an explosive autoregression, pioneered in Anderson (1959), in three ways: First, we demonstrate that the centered least-squares estimator converges geometrically to a ratio of limits, even in settings where the innovations are correlated and not centered around zero. Secondly, we demonstrate that the requirement of independent innovations in Anderson (1959), Theorem 2.3, can be relaxed to $α$-mixing. Third, we provide an autocorrelation-robust feasible test statistic for the explosive parameter under Gaussian ARMA innovations.