Contrary to the central claim (Hsu, 2026) published in Physics Letters B, the Tomonaga--Schwinger equation remains covariant despite the nonlinear modification of it. The proof of covariance becomes simple after the loopholes and mistakes in Hsu's arguments are identified.

Reconfigurable intelligent surface (RIS) is an emerging technology for application to wireless communications. In this paper, we consider the problem of anomalous reflection and model the RIS as a periodic surface impedance boundary. We utilize the mode matching method and Floquets expansion representation to compute the field reflected from a spatially periodic RIS, and evaluate the performance versus implementation complexity tradeoffs of RIS aided communications based on the global design criterion. This allows us to maximize the power reflected towards the intended direction of propagation, while minimizing the power reradiated towards undesired directions of propagation. In addition, we discuss the advantages of the proposed electromagnetically consistent approach to the design of RIS aided wireless systems.

We consider a nearest neighbor, Lagrangian particle discretization of the one dimensional porous medium equation. We prove that the particle model satisfies a discrete analog of the celebrated Aronson-Bénilan estimate, which we use to prove a growth estimate for the evolution of the support and an $L^\infty$ decay estimate which are both known to hold in the continuum. These estimates are uniform with respect to the number of particles. We also prove convergence of the scheme towards the solution to the porous medium equation in the full generality of $L^1$ initial data.

We introduce the concept of timelike entanglement entropy of Hawking radiation as a novel probe of the black hole information paradox. By analytically continuing black hole spacetimes to Euclidean signature, we define timelike correlations that reveal a sequence of timelike Page times at which the entanglement entropy equals the Bekenstein-Hawking entropy. Applying this framework to Schwarzschild, Reissner-Nordström, static higher-dimensional and braneworld solutions, four-dimensional Kerr, and higher-dimensional rotating Myers--Perry black holes, we demonstrate that timelike entanglement exhibits periodic or quasi-periodic behavior, with the recurrence times sensitive to surface gravity, charge, rotation, and spacetime dimensionality. Extremal and near-extremal black holes display effectively frozen thermal oscillations with persistent rotational modulation, reflecting their near-horizon geometries. Unlike conventional approaches based on islands or firewalls, our framework encodes information entirely in the Hawking radiation, preserving unitarity while avoiding violations of horizon smoothness. These results establish timelike entanglement as a robust and physically transparent mechanism for information recovery and provide a versatile tool for exploring quantum gravitational dynamics across a wide range of black hole spacetimes.

Ensuring software quality in embedded firmware is critical, especially in safety-critical domains where compliance with functional safety standards (ISO 26262) requires strong guarantees of software reliability. While machine learning-based fault prediction models have demonstrated high accuracy, their lack of interpretability limits their adoption in industrial settings. Developers need actionable insights that can be directly employed in software quality assurance processes and guide defect mitigation strategies. In this paper, we present a structured process for defining context-specific software metric thresholds suitable for integration into fault detection workflows in industrial settings. Our approach supports cross-project fault prediction by deriving thresholds from one set of projects and applying them to independently developed firmware, thereby enabling reuse across similar software systems without retraining or domain-specific tuning. We analyze three real-world C-embedded firmware projects provided by an industrial partner, using Coverity and Understand static analysis tools to extract software metrics. Through statistical analysis and hypothesis testing, we identify discriminative metrics and derived empirical threshold values capable of distinguishing faulty from non-faulty functions. The derived thresholds are validated through an experimental evaluation, demonstrating their effectiveness in identifying fault-prone functions with high precision. The results confirm that the derived thresholds can serve as an interpretable solution for fault prediction, aligning with industry standards and SQA practices. This approach provides a practical alternative to black-box AI models, allowing developers to systematically assess software quality, take preventive actions, and integrate metric-based fault prediction into industrial development workflows to mitigate software faults.

We construct an asymptotic prediction interval for the population-wise error rate (PWER), which is a multiple type I error criterion for clinical trials with overlapping patient populations. The PWER is the probability that a randomly selected patient will receive an ineffective treatment. It must usually be estimated due to unknown population strata sizes, such that only an estimate can be controlled at the given significance level. We apply the delta method to find a prediction interval for the resulting true PWER, we demonstrate by simulations that the interval has the required coverage probability, and illustrate the approach with real data examples.

In this paper, we study the partial differential equation on the circle that was heuristically obtained by Steinerberg [32] on the real line and which represents the evolution of the density of the roots of polynomials under differentiation. After integrating the partial differential equation in question, we observe that it can be treated with the theory of viscosity solutions. This equation at hand is a non linear parabolic integro-differential equation which involves the elliptic operator called the half-Laplacian. Due to the singularity of the equation, we restrict our study to strictly positive initial condition. We obtain a comparison principle for solutions of the primitive equation which yields uniqueness, existence, continuity with respect to initial condition. We also present heuristics to justify that the system of particles indeed approximates the solution of the equation.

The pressureless Euler-Navier-Stokes system can be obtained formally from the Vlasov-Navier-Stokes system, under the assumption that the distribution function describing the density of particles is monokinetic. Its study has been the subject of several recent papers, which have established the global existence of solutions with high enough regularity, for small initial data. In this work, we demonstrate the global existence of strong solutions in the whole space case, without assuming the initial density to be small and regular: it suffices for it to be bounded and for the total mass to be finite. In passing, we obtain optimal decay estimates for the energy and dissipation functionals. As a corollary, we get a long-time description of the density. All these results are based on an elementary energy method, with no need of sophisticated Fourier analysis tools.

In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the degrees and heights of its elements. In addition to that, we propose two algorithms to effectively compute this parametrization.

In the context of civilian and military communications, anti-jamming techniques are essential to ensure information integrity in the presence of malicious interference. A conventional time-domain approach relies on computing the Wiener interpolation filter to estimate and suppress the jamming waveform from the received samples. It is widely acknowledged that this method is effective for protecting wideband systems against narrowband interference. In this work, this paradigm is questioned through the design of a $K$-tone jamming waveform that is intrinsically difficult to estimate assuming a $L$-tap Wiener interpolation filter. This design relies on an optimization procedure that maximizes the analytical Bayesian mean squared error associated with the jamming waveform estimate. Additionally, an analytical proof is provided showing that a multi-tone jamming waveform composed of $L/2+1$ tones is sufficient to render the Wiener-filter-based anti-jamming module completely ineffective. The analytical results are validated through Monte Carlo simulations assuming both perfect knowledge and practical estimates of the correlation functions of the received signal.

In this work, we present the first extension of the Many-Body Forces (MBF) Model to finite temperature. The MBF Model describes nuclear matter in a relativistic quantum hadrodynamics formalism that takes many-body forces into account through a field dependence of the nuclear interaction coupling constants. Assuming nuclear matter to be charge neutral, beta-equilibrated, and populated by the baryon octet, electrons, and muons, we explore the parameters of the model, three different hyperon coupling schemes (also introduced here for the first time in MBF), and temperature effects to describe basic properties of nuclear matter, including the speed of sound, compressibility, and adiabatic index. We also investigate the mass-radius relation of compact stars by solving the Tolman-Oppenheimer-Volkoff equations at zero and finite temperature, including scenarios with fixed entropy per baryon. Our original results at finite temperature open the path to a new description of proto-neutron stars.

We introduce a new family of invariants of oriented classical and virtual knots and links using fares, maps from paths in biquandle-colored diagrams to an abelian coefficient group. We consider the cases of 1-fares and 2-fares, provide examples to show that the enhancements are proper and end with some open questions about the cases of n-fares for n > 2.

We prove that the Bergman space of a Stein manifold separates points whenever its Bergman metric is well defined and has non-positive constant holomorphic sectional curvature. This, combined with earlier proved results, shows that a Stein manifold cannot admit a well-defined flat Bergman metric, and that it has a well-defined Bergman metric with negative constant holomorphic sectional curvature if and only if it is biholomorphic to the unit ball of the same dimension possibly with a pluripolar set removed. The proof is based on the Hormander L2-estimate for d-bar equations; and the curvature condition together with Calabi's rigidity and extension theorems is used to construct the required bounded strictly plurisubharmonic functions.

To reduce circuit depth when executing Quantum algorithms, it is necessary to maximize qubit connectivity on a near-term quantum processor. While addressing this, we also need to ensure high gate fidelity, suppression of unwanted ZZ cross-talk, a compact layout footprint, and minimal control hardware complexity to support scalability. In current superconducting quantum chips, fixed coupling is used as it is easier to scale, but it is limited by unwanted static ZZ interaction during single qubit operations, which degrades system performance. To overcome these challenges, we have introduced a first-of-its-kind hybrid tunable-coupling architecture that connects four fixed-frequency transmon qubits using a single coupler. This hybrid coupler uses off-resonant Stark drives to tune ZZ strength between qubit pairs. Experimentally backed simulation results indicate that our proposed hybrid design maximizes the qubit connectivity while reducing control overhead. This design achieves a near 20% reduction in circuit depth compared to IBM's Heavy-Hexagonal layout, showing its potential for scalability.

This paper is devoted to the long-term dynamics of solutions to the Gurtin-MacCamy population model with a bistable birth function. We consider a one-parameter monotone family of initial distributions for the population such that for small values of the parameter, the corresponding population density gets extinct as time passes, whereas for large values of them, the solutions exhibit a different behavior. We are interested in the intermediate set of values for the parameters, which are called threshold parameters. We prove the existence of a sharp transition between these two asymptotic dynamics; that is, there exists exactly one threshold value when the age-dependent birth rate of the population has compact support, utilizing the theory of monotone dynamical systems. The case when the birth rate is non-compactly supported is more intricate to deal with, as has been observed in several works, even if the nonlinear birth function is monostable. Nevertheless, the approach used in the present work turns out to be effective to handle a particular birth rate with noncompact support by translating the dynamics of the age-structured model into an integro-differential system.

A lower bound on the probability $P(0<X<δ)$ for all real $δ>0$ and all random variables $X$ with log-concave p.d.f.'s such that $EX=0$ and $EX^2=1$ is obtained.

The expansion of two circular rarefaction waves in vacuum or in a thin ambient plasma is examined with particle-in-cell simulations that resolve two spatial dimensions. In the simulation with no ambient plasma, the rarefaction waves interpenetrate near the symmetry line between both rarefaction wave centers. The exponential density decrease of rarefaction waves with distance implies that the sum of their density does not lead to a density maximum near the symmetry line. The absence of a density maximum, which would yield a repelling electric potential for the inflowing rarefaction wave ions near the symmetry line, and the high interpenetration speed of the ion beams lead to ion-ion instabilities rather than shocks in the overlap layer. The simulations with ambient plasma show that the rarefaction waves pile up the ions of the ambient plasma near the symmetry line. A localized piston of hot ambient ions forms. If its density is large enough, its thermoelectric field allows reverse shocks to grow in the rarefaction waves. These reverse shocks move slowly in the simulation frame and enclose a slab of downstream plasma. A decrease in the speed of the rarefaction wave ions upstream of the shocks with time leads to their collapse.

Dummett's argument for intuitionism is well known. There is a concern that the argument proves too much, specifically, that it supports the extreme and apparently incoherent position of strict finitism. The central question is how to explicate the notion that it is possible in practice to construct an arithmetical term or verify a statement. The strict finitist answer is plagued by the sorites paradox. We propose and develop feasibilism as a more plausible view, where computational feasibility, as captured by the class of polynomial-time problems, yields a robust and expedient explication of "possible in practice". In this approach, the complexity is bounded by a polynomial function of the input size, rather than bounded by a constant (as in strict finitism), thus resolving the sorites issues. We show that a system of strictly bounded arithmetic, introduced by Sam Buss, precisely formalizes the feasibilist view so as to satisfy Dummett's requirements.

Assuming that $ϕ(t)=o(t^2)$ as $t\to0$, we establish a lemma on simultaneous polynomial approximation in Orlicz-Beurling-Sobolev spaces $\ell_a^ϕ$. These spaces, endowed with the Luxemburg norm $\Vert \cdot \Vert_{\ell^ϕ}$, generalize the classical Beurling-Sobolev spaces $\ell_a^p$ for $p>2$. More precisely, we prove that for every $\varepsilon>0$, every $v\in\mathbb{N}$ and every function $φ$ continuous on $\partial\mathbb{D}$, there exist a polynomial $P(z)=\sum_{k=v}^d a_k z^k$ and a compact set $K\subset\partial\mathbb{D}$ with $m(K)>1-\varepsilon$ such that \[\|P\|_{\ell^ϕ}\le\varepsilon \quad \text{and}\quad \|P-φ\|_K\le\varepsilon.\] The proof relies on a result of independent interest describing the asymptotic behaviour of the Luxemburg norm $\|B^k\|_{\ell^ϕ}$ of powers of a finite Blaschke product $B$ which is not a monomial. This behaviour is governed by the comparison between $ϕ(t)$ and $t^2$ near $0$: the norms remain bounded when $ϕ\asymp t^2$, tend to $0$ when $ϕ=o(t^2)$, and diverge to $+\infty$ when $t^2=o(ϕ(t))$. A key ingredient in the proof is the qualitative limit $\sup_{j\ge0}|\widehat{B^k}(j)|\to0$ as $k\to\infty$. As an application of the simultaneous approximation lemma, we derive the existence of functions in $\ell_a^ϕ$ with universal properties, including Menshov universality of Taylor partial sums and universality with respect to radial boundary limits.

We introduce an experimental technique for complete phase-sensitive characterization of arbitrary unitary spectral-temporal transformations of optical modes. Our method recovers the complex spectral transfer function, or Green's function, of a frequency converter by analyzing spectral interference in the response to a tunable bichromatic probe. We perform a proof-of-concept experiment on a frequency conversion module based on Bragg-scattering four-wave mixing in photonic crystal fiber. Our results validate our technique by recovering useful information in the phase of the Green's function, revealing the relative positions of regions of active frequency conversion and passive dispersive propagation within the module. Our work introduces a new approach to characterizing the performance of a variety of active devices with diverse applications in emerging quantum technologies.

We present a comprehensive framework for predicting the detection prospects of supermassive black hole binaries (SMBHBs) by future gravitational wave (GW) observatories, examining both space-borne detectors (LISA, Taiji, TianQin) and next-generation pulsar timing array (PTA) combined with the Square Kilometre Array (SKA-PTA). Leveraging dual active galactic nucleus (AGN) fractions and AGN X-ray luminosity functions, we systematically evaluate the detectable SMBHB populations with a detection threshold of signal-to-noise ratio $\geq 5$ for each GW observatory. Our analysis reveals that space-borne detectors are expected to identify approximately $\sim 1 \text{--} 2$ to $\sim 20$ events per year, depending on the SMBHB orbital evolution prescriptions. On the other hand, SKA-PTA demonstrates the potential to reach the first GW detection from individual SMBHBs within a few years of observation and achieve detectable GW source counts of $10^2 \text{--} 10^3$ after about 10 years, depending on PTA configurations. These facilities will significantly improve SMBHB detectability and enable characterization of their properties across different frequency bands.

We give an algebraic construction of shift operators for the non-symmetric Heckman-Opdam polynomials and the non-symmetric Macdonald-Koornwinder polynomials. To each linear character of the finite Weyl group, we associate forward and backward shift operators, which are differential-reflection and difference-reflection operators that satisfy certain transmutation relations with the (Dunkl-)Cherednik operators. In the Heckman-Opdam case, the construction recovers the non-symmetric shift operators of Opdam and Toledano Laredo for the sign character. Furthermore, in rank one, we recover the rank-one non-symmetric shift operators previously obtained by the authors and Schlösser.

Conformable derivatives involve a fractional parameter while preserving locality: on smooth functions they reduce to a classical derivative multiplied by an explicit weight. Exploiting this structural feature, we show that conformable time evolution does not give rise to a genuinely new semigroup theory. Rather, it can be fully interpreted as a classical $C_0$--semigroup observed through a nonlinear change of time. For $δ\in(0,1]$, we introduce the conformable clock \[ Ψ(t)=\frac{t^δ}δ, \] and prove that every $C_0$--$δ$--semigroup $\mathcal S_δ$ admits the representation \[ \mathcal S_δ(t)=\mathcal T(Ψ(t)), \] where $\mathcal T$ is a uniquely determined classical $C_0$--semigroup on the same state space. This correspondence is exact at the infinitesimal level: the $δ$--generator of $\mathcal S_δ$ coincides with the generator of $\mathcal T$ on a common domain, and conformable mild solutions are in one-to-one correspondence with classical mild solutions under the reparametrization $s=Ψ(t)$. In particular, orbit sets are unchanged by the conformable clock, so orbit-based linear dynamical properties are invariant; $δ$--hypercyclicity and $δ$--chaos coincide with their classical counterparts. As an application, we derive a conformable version of the Desch--Schappacher--Webb chaos criterion by transporting the classical result. The analysis is carried out in conformable Lebesgue spaces $L^{p,δ}$, which are shown to be isometrically equivalent to standard $L^p$ spaces, allowing a direct transfer of estimates and spectral arguments. Altogether, the results clarify which dynamical features of conformable models are intrinsic and which arise solely from a nonlinear change of time.

Under the ideal assumption of uniform propagation, cell-free massive MIMO (CF-mMIMO) provides uniformly high throughput over the network by effectively surrounding each user with its serving access point (AP) set. However, in realistic non-uniform urban propagation environments, it is difficult to consistently select good limited serving AP sets, resulting in significantly degraded throughput, reintroducing "edge-effect" for the worst-served users. To restore the uniformly good performance of scalable CF-mMIMO in realistic urban networks, we formulate a novel multi-objective optimization problem to jointly achieve high throughput by maximizing the sum data rate, uniform throughput by maximizing Jain's fairness index of the throughput per user, and scalability by minimizing the serving AP set size. We then propose the UnifSrv AP selection algorithms to solve this optimization problem, consisting of a deep reinforcement learning (DRL)-based algorithm UnifSrv-DRL and a heuristic algorithm UnifSrv-heu. We conduct a comprehensive performance evaluation of scalable CF-mMIMO under realistic urban network distributions, propagation, and mobility patterns, showing that the prior benchmark AP selection schemes fail to provide uniformly high throughput in practice. By contrast, UnifSrv at least doubles the throughput compared to prior benchmarks, or achieves comparable throughput but with half of the serving AP set size. Importantly, our heuristic algorithm achieves equivalent throughput to our DRL one, but with orders of magnitude lower complexity. We thus for the first time propose an AP selection algorithm that achieves uniformly good CF-mMIMO performance in realistic urban networks with low complexity.

Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis suggest that such models can support stationary patterns with sharp internal interfaces. In this work, we establish for a general class of bistable MCRD systems the existence of nonconstant radially symmetric stationary solutions with a single internal transition layer on an $N$-dimensional ball, for general spatial dimension $N$. Our approach incorporates the global mass constraint directly into a refined matched-asymptotic framework complemented by a uniform spectral/linear analysis. Beyond mere existence, our framework yields arbitrarily high-order asymptotic approximations of the constructed solutions together with quantitative uniform error estimates, which provides a quantitative higher-dimensional theory of transition-layer patterns in MCRD systems and a rigorous justification for their use in modeling phase separation and pattern formation in biological and ecological settings.

We study a combinatorial property of subsets in finite groups that is analogous to the notion of independence in graphs. Given a group $G$ and a non-empty subset $A\subset G$, we define a (right) $s$-factor as a subset $B\subset G$ satisfying the following conditions: (i) Every element of $AB$ can be written uniquely as $ab$ with $a\in A$ and $b\in B$. (ii) $B$ is maximal (with respect to inclusion) with this property. For a finite group $G$, the upper and lower indices of $A$ are the sizes of the largest and smallest $s$-factors associated with $A$. A subset is called stable if its upper and lower indices coincide. A group is called stable if all its subsets are stable. We then explore the connection between $s$-factors in groups and maximal independent sets in graphs. Specifically, we show that $s$-factors in $G$ associated with $A$ correspond to maximal independent sets in a Cayley graph Cay($G$, $S$), where $S=A^{-1}A\setminus\{e\}$. Consequently, the upper and lower indices of $A$ are equal to the independence number and the independent domination number of the associated Cayley graph. The concepts of $s$-factors, subset indices in groups, stable subsets, and stable groups (under different names) were introduced by Hooshmand in 2020. Later, Hooshmand and Yousefian-Arani classified stable groups using computer calculations. Using the connection with graphs, we compute the upper and lower indices for various groups and their subsets. Furthermore, we prove a classification theorem describing all stable groups without relying on computer calculations.

We investigate the diffusiophoresis of a non-polarizable droplet laden with soluble ionic surfactant, for which the surface charge arises from adsorption of surfactant at the fluid-fluid interface. Unlike previous studies that assume either a fixed surface charge or instantaneous equilibrium between the interface and the adjacent electrolyte, we formulate the interfacial transport based on the mass-balance framework incorporating Langmuir adsorption-desorption kinetics and finite surface diffusivity. The coupled electrokinetic problem is solved using a perturbation approach. Analytical expressions for the droplet mobility and interfacial velocity are derived for insoluble surfactants. We demonstrate that assuming uniform, immobile surface charge leads to unphysical predictions, including negative chemiphoresis and singular mobility, whereas allowing the surface charge to evolve through interfacial surfactant redistribution yields continuous and physically consistent droplet diffusiophoresis. Interfacial kinetic exchange is found to play a central role. Increasing the desorption rate enhances surfactant redistribution and Marangoni stress, weakens the negative mobility, reverses the direction of motion through competition between electrophoretic and chemiphoretic contributions, and subsequently leads to a strong enhancement of positive mobility before eventual saturation in the transport-limited regime. The dependence of mobility on viscosity ratio and electrolyte composition of different salts further reveals how mixed electrolytes provides a robust means of tuning droplet motion. This study highlights the critical role of finite-rate surfactant dynamics and interfacial transport in determining the diffusiophoresis of fluid particles, with implications for manipulating droplets in microfluidic and varying-salinity environments.

Near field mmWave sensing is poised to play a key role in future wireless systems, enabling environment-aware, embodied, and application adaptive operation under stringent form-factor and hardware constraints. However, achieving high spatial resolution in the near field typically requires large antenna arrays, multiple radio frequency (RF) chains, or mechanical scanning, creating a fundamental tension between spatial observability and system simplicity. This paper presents frequency as aperture clip on antenna fabric (FaACAF), a hardware efficient sensing by design architecture that synthesizes spatial aperture through the FaA paradigm using a single RF chain. FaACAF realizes a modular clip on aperture fabric, in which frequency selective clip on modules (CMs) are attached to a shared guided-wave substrate and implicitly coordinated by the instantaneous frequency modulated continuous wave (FMCW) excitation frequency. In this fabric, FMCW signaling simultaneously indexes the sensing aperture and orchestrates uplink/downlink signal distribution and echo multiplexing in a switch free, fully passive, and all analog manner, eliminating RF switching and multichannel front ends. An online self calibration mechanism stabilizes the frequency to aperture mapping under practical attachment variability without requiring full matrix calibration. Two case studies illustrate the robustness of the proposed approach and quantify the predictable sensing margin tradeoffs introduced by modular deployment. Overall, FaACAF demonstrates that near field spatial observability can be scaled through architectural coordination in the frequency domain rather than hardware expansion, providing a reconfigurable and hardware efficient pathway toward embodied sensing and integrated sensing and communication (ISAC) in future wireless systems.

ISAC enables pervasive monitoring, but modern sensing algorithms are often too complex for energy-constrained edge devices. This motivates the development of learning techniques that balance accuracy performance and energy efficiency. Spiking Neural Networks (SNNs) are a promising alternative, processing information as sparse binary spike trains and potentially reducing energy consumption by orders of magnitude. In this work, we propose a spiking convolutional autoencoder (SCAE) that learns tailored spike-encoded representations of channel impulse responses (CIR), jointly trained with an SNN for human activity recognition (HAR), thereby eliminating the need for Doppler domain preprocessing. The results show that our SCAE-SNN achieves F1 scores comparable to a hybrid approach (almost 96%), while producing substantially sparser spike encoding (81.1% sparsity). We also show that encoding CIR data prior to classification improves both HAR accuracy and efficiency. The code is available at https://github.com/ele-ciccia/SCAE-SNN-HAR.

We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if positions are recorded and speed is modelled by a diffusion. In finance, realized volatility or variations thereof can be used to construct observations of the latent integrated volatility process. Specifically, we assume that the integrated process is observed at equidistant, deterministic time points and consider the high-frequency/infinite horizon asymptotic scenario, where the number of observations, the sampling frequency and the time of the last observation all go to infinity. Subject to mild standard regularity conditions on the diffusion model, we prove the asymptotic existence and uniqueness of a consistent estimator for useful and tractable classes of prediction-based estimating functions. Asymptotic normality of the estimator is obtained under an additional assumption on the rates. The proofs are based on the useful Euler-Ito expansions of transformations of diffusions and integrated diffusions, which we study in some detail.