Standard dynamical systems approaches to economic modeling, such as those deriving the Cobb-Douglas and CES production functions from exponential growth trajectories, typically rely on integer-order differential equations. While effective, these models assume that economic output depends solely on the instantaneous state of capital and labor, effectively ignoring the long-term ``memory effects'' inherent in policy, infrastructure, and technological adoption. This paper extends the exponential framework by introducing the Caputo fractional derivative into the underlying dynamical systems governing factor inputs. By replacing standard growth rates with fractional-order counterparts of order $0 < α\le 1$, we model economic trajectories where the rate of change is a non-local function of the system's entire history. We demonstrate that the Mittag-Leffler function emerges as the natural growth solution in this context, providing a nested generalization of the classical exponential model. Using this fractional approach, we derive a new class of time-independent invariants that serve as generalized production functions. We show that as the fractional order approaches unity, these forms converge exactly to the classical Cobb-Douglas function.

Brown dwarfs are compact objects that do not reach temperatures high enough to produce sustained hydrogen fusion. Consequently, they cool over time, gradually evolving through later spectral types. In fact, three new spectral types (L, T, and Y) were added to the Harvard sequence to accommodate the spectral features of brown dwarfs. During the cooling process, some brown dwarfs unexpectedly become bluer instead of redder (at optical and near-infrared wavelengths). This phenomenon, known as the bluing effect, is particularly noticeable at the L/T spectral transition. The aim of this work is to approximate the spectral type of brown dwarfs using only photometric data, in particular 2MASS and WISE magnitudes. We used two machine learning algorithms, Random Forest and Gaussian Processes, which were evaluated using a 70/30 train/test split. Both models were trained using 5-fold cross-validation and achieved F1-scores of 0.84 and 0.87, respectively, on the test set. After validating the reliability of the algorithms, we applied them to 21 isolated brown dwarfs without prior spectral type determinations. Our results indicate that 5 of these objects have a spectral type between L0 and L4, while the remaining 16 fall within the M6-M9 range. Machine learning algorithms, combined with multi-band photometry, are a powerful tool for estimating the spectral types of brown dwarfs.

This letter introduces attack-resilient Control Lyapunov Functions (AR-CLFs) and attack-resilient Control Barrier Functions (AR-CBFs) for nonlinear control-affine systems subject to control-input false data injection attacks (FDIA) satisfying an at-most-exponentially growing envelope. The proposed framework embeds a unified adaptive compensation term into both the CLF decrease and CBF safety constraints. In contrast to input-to-state stability/safety (ISS/ISSf)-based methods that certify disturbance-dependent enlarged safe sets, the proposed approach enables finite-time recovery to the nominal safe set without requiring a prior magnitude bound on the FDIA, relying instead on a growth-rate characterization used for analysis and an online gain tuning law that regulates the compensation term. A unified quadratic program (QP) is developed to enforce the AR-CLF and AR-CBF conditions simultaneously, guaranteeing uniformly ultimately bounded (UUB) stability and uniform ultimate safety (UUS) under unbounded FDIA. Numerical results demonstrate improved resilience compared to existing ISS-CLF, ISSf-CBF, and robust CLF-CBF-QP approaches.

Risk management is an important part of financial practice, essential for protecting assets and investments in modern-day volatile markets. This paper proposes a mixture of mirrored Weibull (MMW) distribution for modelling stock returns and estimating risk measures. Unlike common practices which are typically based on the normal distribution, the MMW model can flexibly accommodate non-normal features frequently exhibited in financial data. It also enjoys appealing properties such as having a simple density expression and fast parameter estimation. We demonstrate the effectiveness of our model by assessing its performance in Value-at-Risk (VaR) estimation of three S&P500 stocks. The MMW model compares favourably to Gaussian mixture model and t-mixture model, with significant improvements in VaR estimation and prediction.

We show that the non-relativistic theory of mutual coherence and localization in Coulomb-disordered media can be extended to relativistic electron beams used in transmission electron microscopy (TEM). Starting from the Dirac equation, we derive a paraxial Schrödinger-like equation for the envelope spinor and obtain an effective coupling constant $A_{\rm rel}=(γ+1)/(2γ\hbar v)$ that governs the disorder-induced phase fluctuations. In the non-relativistic limit $γ\to1$ this reduces to $1/(\hbar v)$, while for ultra-relativistic electrons it saturates at $1/(2\hbar c)$. The universal relation between the transverse coherence length $ρ_c$ and the single-particle localization length $\ell$, namely $ρ_c\simλ_D\sqrt{\ell/L}$, remains unchanged. We compare the asymptotic behaviour of the phase structure function $D_ϕ(ρ)$ and the localization length in the non-relativistic and relativistic regimes, and show that the emergent algebraic decay of mutual coherence at large separations, analogous to the wave-structure-function asymptotics in turbulent media, persists in both cases. The results imply that standard TEM energies (100--300~keV) are already close to the optimal regime for minimizing Coulomb decoherence, and that further increasing the beam energy yields diminishing returns. While the asymptotic coherence decay is algebraic rather than exponential, the corresponding exponent can still be large for realistic experimental parameters, so the effect is primarily of conceptual and asymptotic significance.

Online, comprehensive molecular profiling of exhaled breath provides a non-invasive window into human metabolism, yet current optical platforms are restricted by narrow instantaneous spectral coverage. Here, we present a novel ultra-broadband mid-infrared spectroscopic platform that enables simultaneous, high-sensitivity detection of a comprehensive profile of breath biomarkers. By integrating an intrapulse difference-frequency generation (IDFG) supercontinuum source spanning 2.9-11.5 $μ$m (2580 cm$^{-1}$) with a custom-built Fourier transform spectrometer, we achieve a spectral resolution of 0.1 cm$^{-1}$ - surpassing current laser-based approaches. Combined with a standardized online sampling system, the platform achieves sensitivities in the tens of parts per billion over three minutes, resolving dynamic metabolic changes of ammonia, methane, isoprene, acetone, carbon monoxide, and nitrous oxide. We demonstrate the system's utility through proof-of-concept case studies tracking responses to fasting, protein intake, and smoking. This calibration-free platform establishes a powerful and versatile tool for online breath analysis, with broad potential in clinical diagnostics and exposure monitoring.

Advanced Traffic Signal Control (TSC) algorithms require real-time phase control, yet existing Hardware-in-the-Loop Simulation (HILS) testbeds only support pre-programmed timing plans. In this paper, we present the first HILS testbed for real-time phase control. We develop a novel middleware architecture that translates dynamic phase actions (selection, switch, and duration) into commands for NTCIP-compliant commercial hardware controllers. This middleware manages phase transitions, synchronizes signal states, and handles errors without interrupting the hardware's internal operations. Experimental validation demonstrates that the system executes real-time phase commands, handles system conflicts, and achieves a low system internal latency at sub-millisecond on average.

In clinical studies, persistence, which measures the duration of time a patient continues to take a prescribed medication without discontinuation, is increasingly recognized as a critical indicator of adherence to medication. Adherence encompasses not only whether a patient takes their medication as prescribed but also the consistency and duration with which they do so. Among the various metrics used to evaluate adherence, persistence stands out as a particularly robust measure because it provides a temporal dimension, reflecting the sustained commitment of patients to their therapeutic regimens. This focus on persistence offers unique insights into adherence-related quality and performance, shedding light on the challenges and opportunities to optimize long-term medication use. The comparison of upper-tail clinical performance, which measures the extent to which very large responses persist among top responders, is often more decisive in therapy evaluation than conventional summaries. In this paper, we introduce the quantile-based effectiveness persistence function defined as the ratio between the tail mean and the quantile function. The notion parallels expected shortfall in risk theory and is tailored to detect clinically meaningful deviations in the upper tail. We establish key properties and show that the function is equivalent to the first L-moment of the scaled tail, yielding robust inference tools. We derive a simple nonparametric estimator of the function and develop a bootstrap-calibrated two-sample (upper-tail) equivalence test. Simulation studies and real-data analysis illustrate that the proposed measures captures clinically relevant tail persistence that complements median and mean-based summaries.

Discrete Gaussian Sampling on lattices is a fundamental problem in lattice-based cryptography. It appears both in basic cryptographic primitives such as digital signatures and as an important cryptanalysis building block for solving hard lattice problems. In this paper, we show a quantum algorithm based on the quantum rejection sampling technique whose complexity is asymptotically quadratically faster than its classical counterpart in [Wang & Ling, IEEE Trans. Inf. Theory 2019]. Our sampler outputs a quantum state which can either be measured to get the desired distribution or be used directly as such in other quantum algorithms. By doing so, we derive two versions of quantum dual attacks that improve upon the previous ones in [Pouly & Shen, EUROCRYPT 2024]. The two versions are incomparable, each having distinct advantages (speed vs memory requirement). The second version is particularly interesting as it requires only polynomial classical and quantum memory, excluding the classical memory used in the preprocessing step of the Discrete Gaussian sampler. Our quantum Discrete Gaussian sampler can also be used to speed up the algorithm for solving the Short Integer Solution problem, in any norm, of [Bollauf, Pouly & Shen, ePrint 2026/225].

For any connected complex reductive group $G$ and element $z$ of its Weyl group $W$, we use work of Lusztig and Abreu-Nigro to compute the graded $W$-character of the intersection cohomology of any closed Lusztig variety for $z$ over the regular semisimple locus of $G$. We relate the resulting formula to unipotent Lusztig varieties, giving a new geometric model for unicellular LLT polynomials. We then consider Laurent polynomials $α_{ψ, G}^z$ indexed by irreducible characters $ψ$, encoding how our formula decomposes into ungraded characters arising from the Springer theory of $G$. From evidence in low rank, we conjecture that if $ψ$ is inflated from type $A$ in a particular way, then the nonzero coefficients of $α_{ψ, G}^z$ are positive and unimodal. This offers an answer to a 1993 question of Haiman about generalizing a conjecture he posed for symmetric groups. We also prove that the matrix formed by the $α_{ψ, G}^z$ is partially triangular, and that their positivity and unimodality properties are stable under inclusions of Levi subgroups.

We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the line and general interface conditions prescribed at the origin. Cahn-Hilliard-type models emerge in applied mathematics in connection to a spectacular variety of phenomena of mathematical physics, continuum mechanics, chemistry and biology. A novel implementation of Fokas' unified transform method is in force herein for a fourth-order operator for the first time, with particular challenges arising due to the nature and the generality of the problems under consideration. Our explicit formulae directly lend themselves to exploration of the solution's qualitative properties such as regularity and asymptotic behavior. This work is also useful in the investigation of well-posedness for nonlinear counterparts as well as in the study of free-boundary and diffuse-interface problems.

This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with information-theoretically grounded flipping rules. In particular, we reinterpret stochastic Chase decoding as a random-coding construction for error-pattern covering codes. Our approach builds on the framework of Nguyen et al., who introduced a rate-distortion formulation of multiple-attempt decoding for Reed-Solomon codes over nonbinary channels. In their formulation, erasure patterns are generated so as to align with, and thereby mask, hard-decision errors. We adapt this framework to the design of bit-flip probabilities for Chase decoding over BMS channels. This yields an explicit characterization of the asymptotically optimal bit-flipping rule, together with the expected list size required to ensure that the transmitted codeword appears in the decoding list with high probability. Moreover, for binary and quaternary symmetric channels, we demonstrate that the optimal bit-flipping rule, determined by exhaustive search, closely matches the information-theoretic rule even at short block lengths.

We investigate quantum periods and toric Landau-Ginzburg models under divisorial contractions of terminal Fano threefolds. Let $g:Y \rightarrow X$ be a divisorial contraction between $\mathbb{Q}$-factorial Fano threefolds with ordinary terminal singularities and $E$ be the exceptional divisor. Assuming that the center of the contraction is either a smooth point, a terminal quotient point, a point of type cA/n, or a smooth curve with singularities of type cA or cA/n, we prove the regularized period identity $$ \lim_{r\to+\infty}\hat{G}_{Y,rE}(t)=\hat{G}_X(t) $$ where $\hat{G}_{Y,rE}(t)$ and $\hat{G}_X(t)$ are the regularized quantum periods of $(Y,rE)$ and $X$ respectively. This gives a mirror approach to the computation of the Sarkisov links and higher syzygies of central models of dimension 3.

Privacy constraints have driven the rise of federated learning (FL), which enables multi-site analyses without sharing individual participant data. We develop a framework for FL with missing data, identifying conditions under which the complete case (CC) estimator is preferred over the inverse probability weighting (IPW) estimator. For settings where the CC estimator fails, we introduce a calibrated weight estimation approach that combines candidate weighting models across sites and remains consistent if at least one is correctly specified. Consistency conditions are stated at the site level, ensuring that the federated estimator inherits validity from local properties. We derive a sandwich variance estimator that accounts for uncertainty in weight estimation, and illustrate the framework by evaluating risk factors for 90-day mortality among patients with pleural infections treated with intrapleural enzyme therapy.

We present a combined theory-experiment study to quantify spin diffusion in the square lattice quantum spin-1/2 XY model at finite temperature. On the theory side, we leverage a recently developed dynamical high-temperature expansion method to faithfully capture the long spatiotemporal scales of the hydrodynamic regime. Experimental results are obtained from an optical lattice hard-core boson quantum simulator. The excellent agreement of spin diffusion constants marks a breakthrough in spin-transport beyond one dimension and for the quantitative validation of state-of-the-art quantum simulation platforms. We also provide theory predictions for future experiments on dynamic spin conductivity or anisotropy-induced integrability breaking.

The growing adoption of Retrieval-Augmented Generation (RAG) has led to a rise in adversarial attacks. Existing defenses, relying on semantic analysis or voting, face a trade-off between high computational cost and limited robustness under strong poisoning attacks. Their fundamental limitation is the exclusive focus on semantic content relevance, while neglecting the retrieval context that is critically defined by ranking structures. To this end, we investigate the bidirectional ranking behavior of poisoned and benign documents, and discover a key discriminative pattern: poisoned documents exhibit significantly stronger alignment between their backward rankings and the query's forward ranking. Capitalizing on this, we propose BiRD, a bidirectional ranking defense mechanism built upon a dual-signal framework that leverages forward ranking to assess semantic content relevance and backward ranking to quantify ranking context consistency. This design directly addresses the fundamental limitation of prior approaches, enabling simultaneous efficiency and robustness. Extensive evaluation across 3 datasets with 3 retrievers and 3 LLMs under 2 attack scenarios validates BiRD's effectiveness. Notably, BiRD reduces the attack success rate of PoisonedRAG by up to 54% while simultaneously improving task accuracy by up to 56%, with average additional latency under 1 second.

Recent observations from the James Webb Space Telescope (JWST) have revealed proximate damped Lyman-$α$ systems (PDLAs) in the foreground of high redshift galaxies ($z \gt 5$), which have been interpreted as neutral circumgalactic media (CGM). The ionization state of the CGM, potentially inferred from DLA strength, may serve as a probe to trace the progress of reionization, similarly to the ionization state of the intergalactic medium (IGM). To determine if this method has merit, we use the cosmological hydrodynamical simulation TECHNICOLOR DAWN to study simulated gas halos at redshifts $z = 10, 8, 6,$ and $5.5$. We investigate the reionization topology to determine whether the CGM and IGM have similar ionization histories, and we study the relation between column density of neutral hydrogen (observationally measured by DLA strength), neutral fraction, and gas mass fraction of the foreground gas to determine whether PDLAs can be used to trace the progress of reionization. We find an inside-out-middle reionization topology, where the CGM reionizes after the IGM and remains partially neutral at $ z= 5.5$. The foreground column density of neutral hydrogen depends mostly on halo mass, with a weak dependence on neutral fraction or redshift. Therefore, provided precise estimates of halo or stellar mass, PDLAs may be used to trace the progress of reionization particularly at high redshifts.

High-energy (mJ) and high-peak-power (MW) multicycle terahertz (THz) pulses are essential for nonlinear THz spectroscopy and compact accelerator technologies, yet their generation by nonlinear optical frequency conversion remains inefficient and imposes severe demands on femtosecond driving lasers. Amplifying existing THz pulses offers an appealing alternative, but no power-scalable amplifier has been realized in the sub-THz regime. Here, we demonstrate an all-optical THz amplifier operating at 0.35 THz based on the modulation of nanosecond laser pulses by a weak THz field in periodically poled lithium niobate (PPLN). The THz-induced phase modulation is converted into an amplitude modulation using controlled group delay dispersion, forming a tailored pulse train that can efficiently drive high-energy THz generation in a second crystal, thereby amplifying the THz seed. By analogy to electronic klystrons, we term this device the Phlystron, in which the electron beam carrying the power is replaced by a photon beam. In this proof-of-concept experiment, a 3.3-fold increase in THz energy is achieved with commercial crystals. Scaling analysis indicates the potential for higher gain when using large-aperture PPLN devices and multi-stage amplification. The Phlystron thus provides a scalable route to powerful multicycle THz sources driven by readily available narrowband lasers.

We use the latest ANTARES Galactic Ridge neutrino measurements to investigate their implications for indirect dark matter (DM) searches. We consider both annihilating and decaying DM scenarios, spanning a wide range of masses and final states, and systematically compare the resulting neutrino fluxes with the expected astrophysical Galactic diffuse emission. Furthermore, we compare the results for different DM density profiles allowed by the observations, from spike and cuspy to cored profiles. We do so for the WIMP model-independent scenario and explore two more specific models: branons and very heavy sterile neutrinos, where a cold DM candidate arises naturally from the theory. We show the potential neutrino measurements in the Galactic Ridge for DM and make predictions for future neutrino observatories.

We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim t^{-α}$ and show that the system undergoes a transition at $α=1$, separating a super-diffusive regime for $α<1$ from ballistic regime for $α\geq 1$. Using the results for velocity correlations and persistence statistics, together with finite time scaling of the Binder cumulant and displacement fluctuations, we characterize the transition and its properties in detail. We further argue that the transition is not limited to the power law form, but can also arise for several other time dependent reversal probabilities satisfying the same criterion. The transition persists in arbitrary spatial dimensions provided isotropy of the velocity space is preserved.

We study the random conductance model on the lattice $\Z^d$, i.e. we consider a linear, finite-difference, divergence-form operator with random conductances $a$. We allow the conductances $a$ to be unbounded and degenerate. Assuming the conductances satisfy a spectral-gap inequality, we establish sharp bounds on the spatial growth of correctors, together with a quantitative relation between the stochastic integrability of the correctors and that of $a$.

We introduce and study the axiom of null player neutrality in the context of cooperative games with transferable utility (TU-games). This axiom weakens the classical coalitional strategic equivalence: rather than requiring that augmenting a game by a null-player game leaves that player's payoff unchanged, it only requires that any change in payoff be independent of the specific augmenting game, provided both the null-player condition and the grand-coalition value are preserved. We show that efficiency, linearity, symmetry, and null player neutrality together characterize the family of all real linear combinations of the Shapley value and the equal division solution, a family that strictly extends the well-known class of $α$-egalitarian Shapley values (convex combinations, $α\in [0,1]$) to arbitrary $α\in \mathbb{R}$. Replacing null player neutrality by its natural analogue for nullifying players uniquely pins down the equal division solution.

Spectral-siren cosmology constrains the Hubble constant $H_0$ using gravitational-wave observations of compact-binary coalescences. The method combines luminosity distances inferred from the waveform with redshift information statistically encoded in population features of the source-frame mass spectrum. Because the detector measures redshifted masses, structure in the intrinsic mass distribution acts as an internal ``ruler'', making the inference sensitive to assumptions about the population model. In particular, redshift evolution of the mass spectrum is widely discussed as a potential systematic for $H_0$ measurements. We revisit spectral-siren constraints with the GWTC-4.0 binary black hole catalog, explicitly allowing the main mass scales of a standard parametric mass model to evolve with redshift. We find no compelling evidence for evolution at current sensitivity. Allowing evolution produces a modest, non--statistically--significant shift of the $H_0$ posterior toward lower values, which we interpret with targeted posterior and event-level diagnostics. Importantly, the associated systematic uncertainty is subdominant to that induced by alternative redshift-independent descriptions of the mass spectrum, such as the number of spectral features and the functional form used to model them. Our results indicate that, at current sensitivity, spectral-siren constraints on $H_0$ are robust to redshift evolution of the mass spectrum within the flexibility explored here. Using injection studies, we show that this mild $H_0$ shift is reproduced when a non-evolving underlying population is analyzed with an evolving model, consistent with an over-flexible population description at the present signal-to-noise. The sign and magnitude of the shift can, however, depend on detector sensitivity and redshift reach as the population features become increasingly constrained directly by the data.

The specific advance of this work is to propose a mechanism by which superpositions collapse during measurement of the separated subsystems of entangled quantum states. It is shown how the phase that locks together entangled states plays a special role in the measurement of isolated subsystems. This `contextual' phase is installed randomly into the entangled state, and decides the measurement outcomes for the subsystems by directing the collapse of each superposition to a particular classical outcome when a subsystem is measured. The measuring apparatus thus obtains a classical read-out of the quantum correlations embedded in an entangled state. More broadly, these results solidify the theory of measurement of quantum superpositions.

We study the Hermitian hull-variation problem for vector rank-metric codes. Except for one parameter pair, we show that the Hermitian hull dimension of such a code can be reduced to any smaller value within its equivalence class, and in particular every such code is equivalent to a Hermitian LCD code. We then address the existence of maximum rank distance (MRD) codes with prescribed Hermitian hull dimension. To this end, we introduce the notion of a \emph{scaled trace-self-dual basis} of a finite field extension, which exists in all cases, and use it to construct Hermitian self-orthogonal generalized Gabidulin codes for every prime power. Combined with the hull-variation theorem, this yields MRD codes attaining every admissible Hermitian hull dimension.

We develop a motivic framework for Feynman integrals of one-loop graphs in momentum space. Its advantage compared to the already existing framework in Feynman representation is that it naturally includes graphs with cuts. To each such graph, we associate a motivic local system over the space of generic kinematics. Our construction is functorial with respect to the natural operations on graphs: edge contraction and cutting. We compute the weight-graded pieces of the motivic local systems. They are Tate twists of quadratic Artin motives associated with maximally cut quotient graphs. We also derive a formula for the (co)action of the de Rham motivic Galois group, expressed in terms of cut quotient graphs.

Background: Face morphometry has been shown to work as a diagnosis tool in a set of syndromes. Face similarities are usually indications of more complete genetic similarities. Purpose: To show preliminary results on the face morphometry profile of the Cuban population and to argue that it could be used to define early markers for diseases, like Alzheimer. Methods: A dataset composed of photos of 200000 men is processed. Facial landmarks are extracted by means of the DLIB library and distances between them are computed. By clustering samples with similar facial traits, groups are formed and their densities inside the population are computed. Results: The face morphometry profiles for two age cohorts are obtained, showing the population dynamics. Genes involved in facial development are shown to be related to Alzheimer's disease. Conclusions: Late multifactorial diseases develop against the genetic background of each individual, which is expressed by its face morphometry. The latter can be thus considered a risk marker.

We investigate a non-relativistic realization of the boostless cosmological collider in a scenario where inflationary interactions are mediated by a massive tilted-ghost spectator field. Unlike standard boostless collider constructions, in which the characteristic non-Gaussian signatures are mainly generated by boost-breaking interaction vertices, the dominant effect in the present framework arises directly from the propagation of the spectator modes. Non-relativistic corrections deform the bulk mode functions, inducing a tilt that modifies the in-in correlators and generates a distinctive collider signal. The resulting squeezed-limit non-Gaussianity reproduces the qualitative structure of boostless cosmological-collider signals while originating from a fundamentally different dynamical mechanism. A central feature of the construction is the emergence of an effective chemical-potential-like parameter that controls the relative weight of the two late-time oscillatory branches. However, the tilted-ghost mode exhibits distinctive dynamical features and does not correspond to a conventional chemical-potential deformation. Depending on the sign of the tilt, the corresponding non-Gaussian signal can be either enhanced or suppressed. We show that the tilted-ghost scenario provides a simple effective framework in which boostless-collider phenomenology and chemical-potential-like branch asymmetries arise naturally from non-relativistic propagation effects.

The Fourier extension conjecture of E. Stein was proved in the plane in 1970 by C. Fefferman, see also Zygmund and Carleson and Sjölin, with simplifications given by other authors later on, in particular by L. Hörmander and T. Tao. We discuss yet two more proofs of this classical theorem on the parabola. The first proof uses C. Fefferman's decoupling together with a decomposition into Haar wavelets. This sets the stage for the second proof in Rios and Sawyer, that uses smooth Alpert wavelets and a new decoupling method, which exploits averaging smooth Alpert projections over grids, the extraction of Dirichlet kernels, and periodic stationary phase, all of which was extended to higher dimensions in arXiv:2512.24990v7.

Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit tests for assessing their compatibility with data. We develop the first goodness-of-fit test for IC models that is supported by a theoretical validity guarantee when the data dimension and sample size diverge proportionally. This is made possible by the fact that the test does not rely on a pre-whitening step, which often limits the applicability of other goodness-of-fit tests in high dimensions. Our theoretical analysis is complemented with numerical experiments that demonstrate the test's size control and power under a range of conditions. In addition, we provide examples involving gene-expression data to illustrate that the test has potential for effective diagnostic use in practice.