Estimating network formation models with degree heterogeneity raises two problems in empirical networks. First, agents that send no links, receive no links, or link to all remaining agents can make the fixed-effects MLE fail to exist. Trimming these agents changes the estimation sample and induces selection bias. Second, the incidental-parameter problem biases common parameters and average partial effects. We resolve both issues through a penalized likelihood approach. Our leading specification is a directed network model with reciprocity, nesting the standard undirected and non-reciprocal directed models. The penalty guarantees finite-sample existence and yields bias corrections for coefficients and partial effects. We establish asymptotic results without imposing compactness on the fixed-effects. Allowing the fixed effects to diverge at a logarithmic rate, our asymptotic framework accommodates the degree sparsity ubiquitous in large empirical networks. A global trade application demonstrates that our estimator avoids selection bias and recovers robust parameters where conventional methods fail.

In many-body quantum systems, unitary dynamics generically delocalize locally encoded information, causing single-site metrological sensitivity to vanish. We analytically demonstrate that a topological phase can prevent this dispersal. In the open Kitaev chain, a Majorana zero mode fixes the boundary quantum Fisher information (QFI) at a nonzero plateau that persists for times exponentially long in system size. We derive exact analytical expressions for the local QFI and identify the mechanism as the spatial separation of the two Majorana quadratures to opposite ends of the chain. This separation produces a boundary encoding-axis asymmetry that distinguishes topological boundary memory from a generic localized subgap signal. We show numerically that the asymmetry is robust to moderate quenched on-site disorder, while the boundary plateau remains visible under parity-preserving interactions in finite-size real-time simulations. The protocol requires only product-state initialization, Hamiltonian evolution, and single-site readout.

This paper provides a detailed investigation of voltage ride-through in large loads, such as Artificial Intelligence data centers. Voltage ride-through capability of large loads during transient disturbances in the power grid is important because of the potential impact on the stability and reliability of the Bulk Power System. A mathematical analysis is presented and it is shown how the traditional approach, based on reactive power compensation, may not be adequate for voltage ride-through in large loads. Ultimately, due to capacity limits of the load's power distribution infrastructure and grid's constraints, there is a limit to using reactive power as a corrective tool. A new dual active and reactive power (PQ) approach is proposed in which non-grid resources with dynamic P and Q capabilities are shown to be needed to help with voltage ride-through. Additionally, the analysis illustrates that at extreme voltage dips in the power grid maintaining an acceptable level of load voltage can become practically or theoretically unattainable, which may lead to the load's disconnection from the grid. Analytical results are provided with practical numerical examples.

Transition region (TR) loops are arcade-like features in the solar transition region, with temperatures roughly between $2\times10^4$ K and $6\times10^5$ K. They are a fundamental building block of TR, which are results of the coupling between the magnetic field and the TR plasma. Their dynamics is closely related to the transport of energy and mass through the TR. Studies on this class of loops since the launch of the Interface Region Imaging Spectrograph (IRIS) have revealed that they are distinct from coronal loops. Observations have revealed that they are associated with many small-scale dynamic phenomena in the TR, from which one can infer the physics behind the energy and mass transfer in a magnetically confined environment at TR temperature. This review summarises the observational results of TR loops, showing their morphology, dynamics, plasma parameters, their relationship with flux emergence, their heating properties, and their implication in the heating of the solar atmosphere. This class of magnetic loops is much less well understood than their coronal counterparts. This review also concludes with several critical questions that need to be answered in the coming era with more advanced observational techniques and more precise and realistic simulations.

Building on \cite{daworrpap,dawpap}, we prove two Zilber-Pink-type statements in $Y(1)^n$, assuming a weak form of the Lang-Trotter conjecture for pairs of elliptic curves.

We propose a computationally efficient inferential procedure for longitudinal function-on-function regression. The method follows a marginal three-step approach: (1) fit massive pointwise longitudinal scalar-on-function regression models, (2) smooth the resulting estimates along the bivariate functional domain, and (3) compute confidence bands using either an analytic approach for Gaussian data or a cluster bootstrap for Gaussian or non-Gaussian data. Simulation studies demonstrate that the proposed method achieves accurate estimation and valid inference, while substantially reducing computational burden compared to existing approaches. Methods are motivated by a physical activity intervention trial in older adults where high-dimensional wearable data were collected longitudinally across multiple visits. Our applications reveal significant increases in physical activity in the morning using interpersonal intervention strategies, but not intrapersonal strategies. The proposed methods are implemented in an R package.

Supermassive black holes (SMBH, $M_{\rm{BH}} > 10^8 M_\odot$) powering luminous quasars already exist one billion years after the Big Bang, yet their connection to their star-forming host galaxies, their relation to the general galaxy population and their contribution to Reionisation remains deeply enigmatic. JWST is finding numerous Active Galactic Nuclei (AGN) in high-redshift galaxies with black hole masses that appear to be over-massive compared to their host's stellar mass, but rarely as massive as those found in luminous quasars. Here we report JWST/NIRSpec observations revealing overmassive SMBH in two ultra-luminous Lyman-$α$ emitters at $z\sim6.6$ that exhibit rare double-peaked Lyman-alpha profiles. The broad Balmer lines indicate black hole masses $M_{\rm{BH}}\simeq 2\times10^8 M_\odot$, matching that found in faint $z\sim 6-7$ quasars, and very high BH-to-stellar-mass ratio ($\sim 0.1-0.2$) that exceed the local relation by a factor $\sim$400-800. Stellar population modelling favours young ages ($<50$ Myr), inconsistent with the sustained average Eddington-rate accretion required to reach the observed BH masses by $z=6.6$. The double-peak Lyman-$α$ profiles require a large ionised bubble and high photoionisation rate that is consistent with the ionising output of quasars powered by black holes of similar mass, thus constraining the cessation of the last quasar episode to $<1$ Myr. We interpret both systems as post-quasar galaxies in which AGN feedback has delayed stellar mass assembly, and propose that episodic quasar activity partially explains the unexpected prevalence of large ionised bubbles deep into the Epoch of Reionisation.

Communications in highly dynamic channels relying on training-based channel estimation experience a trade-off between increasing channel measurement accuracy by sending more frequent training sequences and increasing data rate by sending fewer training sequences. Simultaneously, most communication systems use forward error correction to enable error detection and correction at the receiver. This paper presents decoder-provided pilots for time-varying channels by using decoded codewords as training sequences to update the channel estimate at the receiver. In contrast to approaches such as data-aided channel estimation, decision-feedback equalization, joint channel estimation and error correction, and turbo equalization, the decoder-provided pilots approach is non-iterative, which is ideal for low-latency requirements in highly dynamic scenarios. Furthermore, it is modulation-, code-, and decoder-agnostic, meaning it can be implemented on top of virtually any communication system that uses forward error correction. From an information-theoretic perspective, we derive the fundamental limits of decoder-provided pilots' ability to simultaneously sense the channel and transmit data. Simulation results demonstrate that decoder-provided pilots significantly improve performance, that when coding across frequency, soft-output can further enhance performance, and that when coding across time, short codes can outperform long codes of the same rate in fast-fading channels.

We show that the Lang-Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber-Pink conjecture for curves in $\mathcal{A}_3$. Unlike previous results for curves in $\mathcal{A}_g$, our result does not rely on any assumption on intersections with the boundary, and in particular applies to potentially compact curves. The argument is based on the $G$-functions method of Yves André.

Information sharing between individuals is crucial to improve performance in collective tasks. However, in a competitive world, individuals may be reluctant to share information with the others, and it is still unclear how the presence of strategic behaviors affects the collective performance of a group. In this study, we introduce an evolutionary game modeling the dynamics of individual behaviors in a collective estimation task. The individuals are organized in a network and have to guess the distribution of ball colors in a box. Each of them samples a given number of balls and can strategically decide whether to share or not this information with its neighbors. We develop a framework that allows to investigate analytically how the collective performance depends on the network structure. We find that the optimal network results from a trade-off between the sharing rate and the way the information is integrated in the network. We further reveal that there exists an intermediate average degree for each type of network maximizing the collective performance. In addition to the uniform case, we consider the case of non-homogeneous allocations of the number of individual samples, showing that the largest collective performance is obtained when the number of ball extracted by an individual is inversely proportional to its degree.

The Faddeev-Hopf model [1] supporting Hopfions was shown to emerge in the low-energy limit of four-dimensional scalar quantum electrodynamics (QED) with two charged scalar fields [2, 3]. Faddeev and Noemi conjectured that the Hopfions and Hopf-like solitons -- vortons -- can be based on a twisted toroidal structure inherent to QED [4-6]. This conjecture was discussed in detail in [2] in the approximation of negligibly small extrinsic curvature. Qualitative and semi-quantitative arguments were used to demonstrate the validity of the Faddeev-Noemi hypothesis. Here we further enhance the proof by applying a numerical analysis which confirms that large-size Hopf-like solitons exist as local energy minima in the full QED theory (in the Faddeev-Skyrme model they become topological solitons representing the global minima in the given topological sector).

We present a charged-current quasielastic neutrino-nucleus scattering model based on an unfactorized representation of the spectral function, employing relativistic momentum distributions for bound nucleons and the relativistic distorted-wave impulse approximation with an energy-dependent relativistic potential to describe the scattered nucleon. The model incorporates two-body meson-exchange currents contributing to one-particle-one-hole final states and tests several axial form factor parametrizations, including recent LQCD and MINERvA fits. It is implemented in the NEUT event generator and benchmarked against T2K and MINERvA $ν_μ$-$^{12}$C CC0$π$ measurements. We find that two-body meson-exchange currents lead to a sizeable increase of the total cross section, arising from an enhancement of the transverse response, which is the dominant component in charged-current neutrino scattering. On the other hand, recent fits of the axial form factor predict larger values than the standard dipole form, yielding a systematic enhancement of the cross section. The LQCD+MINERvA parametrization tends to overestimate the data, while the MINERvA-only fit provides a more moderate increase. Overall, no single configuration consistently provides the best agreement with the different datasets.

Infrastructure protocols like Congestion Control (CC) seek to provide reliable performance across a wide range of Internet environments. Currently, protocol designers assess performance through hand-designed test cases or data sets captured from real environments. However, such approaches may inadvertently overlook critical facets of the algorithm's behavior when they encounter an unanticipated environment or workload. We seek to understand the unanticipated with \sys, a system that automatically generates adversarial network environments that cause a target protocol implementation to perform poorly. AdvNet employs machine learning-based optimization to generate environments, and incorporates a robust noise-handling mechanism to mitigate the variability inherent in real-world protocol performance. Although our approach is more general, this paper focuses specifically on transport protocols and their CC implementations. We showcase AdvNet's capability to create adversarial scenarios for 27 kernel-space implementations of both single-path and multi-path CC protocols, for several use cases with different performance goals. AdvNet identifies problematic network conditions that expose previously unnoticed Linux kernel bugs and uncovers hidden limitations in CC implementations, and provides insights about robustness. These results suggest that automated adversarial testing can be a valuable tool in protocol development, and that robustness is a useful new dimension for benchmarking CC protocols.

We report and analyse the classification performance of an experimental hybrid spatio-temporal photonic reservoir computer based upon a free-space VCSEL array. We demonstrate experimentally the enhancement of spatial-only reservoir operation, featuring the diffractive coupling of lasers in an external cavity, by exploiting up to 88 virtual nodes with time multiplexing. We analyse the dependance of performance on the spatial and virtual node number, and achieve an improvement for both spatial- and temporal-only reservoirs with a reduced test error of 0.026 in a classification task. Further, given the high bandwidth of the non-linear laser transformation, we demonstrate the expansion of a 12 spatial node network to a 968 node network, operating at an input time of 17.6ns, maintaining high processing speed and improving network scalability and performance.

We introduce a functional inductive framework to verify discrete-time dynamical systems against hyperproperties specified as Hyperlinear temporal logic formulae via a notion of HyperCertificates. Unlike linear temporal logic (LTL) formulae which are concerned with individual traces of a system, hyperproperties are properties that are concerned with how the traces of a system relate to one another. HyperLTL is an extension of LTL for hyperproperties, and is useful to describe specifications such as opacity, privacy as well as notions of robustness. Our notion of HyperCertificates consists of a pair of functions, where the first models the lookahead, and the second relies on a combination of barrier and ranking functions. We use closure certificates, to act as a model for this lookahead and then rely on barrier and ranking function arguments modulo this lookahead to provide guarantees against HyperLTL formulae. We demonstrate how our approach is automatable via existing techniques such as sum-of-squares optimization (SOS) and satisfiability modulo theories (SMT) solvers. Finally, we demonstrate our approach on some case studies.

Networked systems operating under intermittent adverse conditions and long memory can remain stable on average while exhibiting rare but extreme trajectory-level excursions. We study linear regime-switching network dynamics with Volterra-type memory, formulated through a finite-dimensional lifted ordinary differential equation embedding. Despite finite-horizon annealed boundedness, we show that quenched amplification emerges generically from the interaction of regime persistence, memory accumulation, and non-normal lifted operator geometry. A lower bound on burst-size distributions reveals power-law tails whose exponent is determined by the ratio between unfavorable dwell-time rates and an operator-defined instantaneous growth parameter. This parameter is computable online via the Euclidean logarithmic norm of the lifted operator, yielding a practical early-warning indicator. Building on this structure, we introduce a dynamic data-driven intervention strategy that enforces contraction on demand along rare amplification channels, thereby shaping or truncating tail risk without altering exogenous regime statistics or typical system behavior. The results provide a geometrically grounded and operationally actionable framework for understanding and mitigating extreme events in memory-driven regime-switching systems.

Quantum-gravity-induced entanglement of masses (QGEM) provides a phase-sensitive probe of extra-dimensional corrections to the Newtonian potential at submillimeter separations. We compare three representative Kaluza-Klein spectral scenarios: the Randall-Sundrum II (RSII) and Arkani-Hamed-Dimopoulos-Dvali (ADD) models, and the case of a gapped continuum modeled by a Pöschl-Teller potential. We evaluate the entangling phase, concurrence, and normalized phase-response profiles over $d=40$-$80\,μ\mathrm{m}$ using representative benchmark parameters guided by current short-range gravity tests. In this range, the signal exhibits a stable hierarchy: ADD $>$ gapped $>$ RSII. For conservative experimental parameters, the ADD signal surpasses the nominal entanglement threshold at smaller separations, whereas the gapped benchmark is resolvable only at the lower end of the window, and RSII remains below resolution. In a more optimistic near-term scenario, all three spectral signatures comfortably exceed the threshold. We further show that normalized distance scans of the phase response clearly separate the RSII benchmark from the ADD and gapped cases, whereas ADD and the gapped continuum remain nearly indistinguishable in normalized profile. QGEM phase observables therefore provide a complementary discriminator of Kaluza-Klein spectral structure at submillimeter scales.

We present a comprehensive theoretical study of the masses of possible baryonic and mesonic configurations containing a single top quark. Our analysis includes the baryons $Λ_t$, $Ξ_t$, $Σ_t$, $Ξ'_t$, $Ω_t$, $Ω_{tcc}$, and $Ω_{tbb}$, together with the pseudoscalar and vector mesons $T_{t\bar n}^{\mathrm{Ps}}$, $T_{t\bar n}^{\mathrm{V}}$, $T_{t\bar s}^{\mathrm{Ps}}$, $T_{t\bar s}^{\mathrm{V}}$, $T_{t\bar c}^{\mathrm{Ps}}$, $T_{t\bar c}^{\mathrm{V}}$, $T_{t\bar b}^{\mathrm{Ps}}$, and $T_{t\bar b}^{\mathrm{V}}$. Motivated in part by recent experimental indications of a pseudoscalar enhancement near the $t\bar t$ threshold reported by the CMS and ATLAS collaborations, this study is carried out within the framework of two-point QCD sum rules to determine the corresponding ground-state masses by including perturbative contributions and nonperturbative condensates up to dimension eight. For several channels, including the $Λ_t$, $Ξ_t$, $Σ_t$, $T_{t\bar b}^{\mathrm{Ps}}$, and $T_{t\bar b}^{\mathrm{V}}$ states, the extracted central masses lie slightly below the corresponding sums of constituent quark masses, which may indicate nontrivial binding dynamics or near-threshold multiquark configurations within the uncertainties of the method. Moreover, when the full theoretical uncertainties are taken into account in a conservative manner, a larger subset of the investigated states exhibits a consistent tendency toward weak binding behavior, suggesting that the possibility of loosely bound configurations cannot be excluded for most of the considered baryonic and mesonic channels. These results provide useful first-principles theoretical benchmarks for possible top-containing hadronic systems, which may support future searches at the LHC, along with sensitivity analyses for next-generation facilities such as the FCC.

Reliable control in motor imagery brain-computer interfaces (MI-BCIs) requires the precise decoding of user-specific neural rhythms, which vary significantly across individuals. The Common Spatial Pattern (CSP) algorithm is a cornerstone of MI-BCI decoding, yet its performance depends strongly on the spectral range of the input EEG data. Although Filter Bank CSP (FBCSP) extends this as a data-driven decoding framework, its frequency sub-bands are predefined rather than selected using subject-specific physiological criteria. This paper presents a proof-of-concept study of static functional connectivity (FC)-guided band selection for MI-BCI, demonstrated using a conventional FBCSP-based pipeline. The proposed method identifies the most discriminative spectral bands by calculating phase-based connectivity across four sensorimotor channels using wPLI, PLV, and PLI. Nine bands in a 4-40 Hz filter bank are ranked by the effect size of their hemispheric coupling differences and pruned to the top K bands for feature extraction and classification via FBCSP and a Support Vector Regressor. This framework was tested for K values ranging from 1 to 8 across the BCI Competition IV-2a (n = 9) and OpenBMI (n = 54) datasets. Performance was benchmarked against standard nine-band FBCSP and random ablation to determine the minimum number of bands (K*) required to maintain accuracy within a 2% baseline equivalence zone. Results show FC-guided selection can outperform random ablation and achieve near-baseline performance while reducing required CSP fits by 22.2% to 77.8%. PLV enables the most aggressive dimensionality reduction by prioritizing the μ and low-\b{eta} ranges, while wPLI demonstrates superior inter-session robustness by mitigating volume conduction. These findings establish FC-guided selection as a principled and interpretable alternative to heuristic filter bank designs.

Let $S$ be a set of $n$ points in $\mathbb{R}^2$. Our goal is to preprocess $S$ to efficiently compute the smallest enclosing disk of the points in $S$ that lie inside an axis-aligned query rectangle. Previous data structures for this problem achieve a query time of $O(\log^6 n)$ with $O(n \log^2 n)$ preprocessing time and space by lifting the points to 3D, dualizing them into polyhedra, and searching through their intersections. We present a significantly simpler approach, solely based on 2D geometric structures, specifically 2D farthest-point Voronoi diagrams. Our approach achieves a deterministic query time of $O(\log^4 n)$ and, via randomization, an expected query time of $O(\log^{5/2} n \log\log n)$ with the same preprocessing bounds.

The adoption of Internet of Things (IoT) systems at the network edge of smart architectures is increasing rapidly, intensifying the need for security mechanisms that are both adaptive and resource-efficient. In such environments, runtime defence mechanisms are no longer limited to detection alone but become a resource-constrained task of selecting mitigation actions. Security controls must be carefully selected, combined, and executed under latency, energy, and computational constraints, while preventing unsafe interactions between controls. Existing approaches predominantly rely on static rule sets and learned policies, which provide limited guarantees of feasibility, conflict safety, and execution correctness in resource-constrained edge settings. To address this limitation, we introduce ASPO, a self-adaptive multi-agent security pattern selection that integrates Large Language Model (LLM)-based reasoning with deterministic enforcement within a MAPE-K control loop. ASPO explicitly separates stochastic decision generation from execution: LLM agents propose candidate mitigation portfolios, while a deterministic optimisation core enforces closed-world action integrity, conflict-free composition, and resource feasibility at every decision epoch. We deploy ASPO on a distributed edge-gateway testbed and evaluate it across two workloads, each comprising 500 and 1000 runtime security decisions, using replayed IoT attack traffic. In addition, the results demonstrate invariant safety properties, including 100% conflict-free activation, consistent resource feasibility across workloads, and stable pattern dominance with perfect rank preservation. Importantly, deeper decision exploration reduces extreme-case execution costs, compressing tail latency and energy overheads by 21.9% and 23.1%, respectively, without increasing mean energy consumption.

The Traveling Salesman Problem (TSP) is a prototypical combinatorial optimization problem, but its quantum implementation is limited by the O(n^2)-qubit overhead of standard one-hot encodings. Here, we propose a resource-efficient variational quantum framework based on compact binary-register encoding, a permutation-preserving problem-inspired ansatz, and a complementary divide-and-conquer execution strategy. The compact encoding reduces the data-qubit requirement to O(n log n), while the divide-and-conquer formulation lowers the number of qubits required in each local hardware execution to the size of the largest subsystem. Numerical simulations on TSP instances with 4, 5, and 6 cities achieve best average success rates of 100%, 100%, and 95.5%, respectively. A local two-qubit implementation of the divide-and-conquer approximation is further evaluated for a 5-city TSP instance on SpinQ Gemini Pro and SpinQ Triangulum II NMR quantum computers. Taken together, the results indicate how compact encoding and divide-and-conquer execution with classical post-processing can be used to study small combinatorial optimization instances on resource-constrained quantum hardware.

Team project-based learning (TPBL) combines two learning techniques: project-based learning (PBL) and teamwork. This combination leverages the learning outcomes of both methods and places students in a real work situation where they must develop and solve a real project while working as a team. TPBL has been used in two advanced database subjects in Jaume I University (UJI)'s Computer Science degree program. This learning method was used for four years (academic years from 2018/19 to 2021/2022) with positive outcomes. This study presents the project development, which includes teamwork formation, activities, timetable, and exercised learning competencies (both soft and specific). Further, the project's results were evaluated from three different perspectives: a) teamwork evaluation by teammates, b) Students' opinions on the subject and project, and c) subject final grades.

Quintessential inflation models provide a framework that simultaneously describes inflation and dynamical dark energy, the latter of which has recently received growing support from DESI observations. A distinctive feature of these models is the kination phase after inflation, which enhances primordial gravitational waves at high frequencies. In this work, we study a class of alpha-attractor quintessential inflation models using a fully numerical approach that follows the scalar-field evolution from inflation to the dark-energy-dominated era, allowing us to compute with high precision both the dynamics of dark energy and the primordial gravitational wave spectrum. Using the latest observational data, including DESI and ACT, we constrain the model parameters and show that the model becomes disfavored once constraints from the gravitational-wave contribution to the effective number of relativistic degrees of freedom, Δ Neff, are included. This is because the model predicts a scalar spectral index ns that becomes too small to remain consistent with observations when the gravitational-wave abundance is constrained to stay below the Δ Neff bound. Finally, we present the resulting primordial gravitational wave power spectrum computed using our constrained parameter values, which highlights prospects for detection by future CMB B-mode experiments at low frequencies and by gravitational-wave interferometer experiments at high frequencies.

Flexible AC Transmission Systems (FACTS), particularly Static Synchronous Series Compensators (SSSC), can improve network transfer capability and complement restricted transmission expansion. Evaluations of FACTS within large-scale, real-world power system planning are currently lacking. This paper develops a capacity expansion model for the contiguous U.S. power system toward 2050, incorporating SSSC-modified linear power flow equations and accounting for impedance feedback in transmission expansion. Cost-optimal system expansion leverages widespread nationwide SSSC deployment on small-to-medium capacity lines and reduces the number of corridors to be reinforced. Overall, SSSCs reduce annualized system costs by $1.9 billion or decrease transmission expansion requirements by 20%. The most advantageous deployments achieving benefit-cost ratios of 59 concentrated in the Midwest, facilitating the delivery of central U.S. wind power to eastern load centers. The value proposition of SSSCs is robust to cost sensitivities and potential competition from HVDC network expansion, and increases under higher demand growth and more stringent decarbonization policies. These findings provide a blueprint for leveraging SSSC deployment in the U.S. power system.

In this chapter we provide a pedagogical introduction to the main theoretical aspects related to topology and $θ$-dependence in Quantum Chromo-Dynamics (QCD), and to their phenomenological relevance in the Standard Model ($η^\prime$ physics, neutron electric dipole moment) and beyond (strong CP problem and the axion solution). We then provide an overview of the main analytic predictions for $θ$-dependence obtained using several different approaches (chiral effective theories, large-$N$ arguments, semiclassical methods) and their regimes of validity, as well as a selection of the most recent numerical results about QCD topology obtained via Monte Carlo simulations of the lattice-discretized theory.

A test of uniformity on [0,1] is developed for the setting of a single observation recorded with sufficient precision. Although consistency against general alternatives is not attainable with only one draw in the classical large-sample sense, a multiscale harmonic digit expansion provides a framework for structured inference. By aggregating trigonometric components across digit scales at Hadamard-gap frequencies, a quadratic test statistic is constructed whose null distribution converges to a chi-square law via a lacunary central limit theorem. Under departures from uniformity, the statistic is driven by Fourier components induced by digit-scale transformations of the observation, with detectability depending on their coherent accumulation as precision increases. The resulting procedure detects multiscale harmonic structure that remains invisible to classical digit-frequency methods.

The blazar 3C 279 is well known for its rapid and large-amplitude variability. On 20 December 2013, the source exhibited an orphan γ-ray flare characterized by a flux-doubling timescale of a few hours, a very hard spectrum, a time-asymmetric light curve with a slow decay, and no significant optical variability. We propose a new interpretation of this event based on a two-zone scenario in which a stationary emission region produces the quiescent emission, while a second zone accelerates within the broad-line region(BLR). We compute the time-dependent radiative output of both zones with the EMBLEM code, including synchrotron, synchrotron self-Compton, and external inverse-Compton processes, as well as bulk acceleration, adiabatic expansion, and a Fokker-Planck treatment of the electron distribution. This is the first attempt to precisely model the asymmetric γ-ray flux evolution during this flare. A model with a stationary region outside the dusty torus and an accelerating plasma blob reproduces the main features of the event: a short and intense γ-ray flare with a hard spectrum and no optical counterpart. The flare results from the variation of the external photon field in the blob frame as the blob crosses the BLR and reaches its terminal Lorentz factor not far from the inner radius of the BLR. Bulk acceleration and the propagation of a plasma blob within the jet provide a natural mechanism for producing high-energy flares and asymmetric light curves without requiring an ad hoc time-dependent particle injection. The model predictsa delayed EUV/X-ray enhancement once the blob exits the BLR. No very-high-energy data are available for this event, but if γ-rays were emitted in this band, a delay would be expected with respect to the Fermi-LAT flare.

We compare four polynomial-resource measurement strategies, (I) $Z$-basis-only, (II) nearest-neighbor $ZZ$ (NN), (III) multi-basis ($Z$, $X$, $Y$), and (IV) classical shadows, for classifying three quantum circuit families: IQP, Clifford, and Clifford$+T$. We find $Z$-only measurements outperform multi-basis and classical shadows across all qubit counts and all four classifiers evaluated, and the $O(\nqubits)$-feature NN strategy matches $Z$-only to within $0.02$ in Random Forest accuracy. The best result is a Random Forest accuracy of $0.91$ at 4--5 qubits under $Z$-only ($0.89$ for NN, $0.85$ for multi-basis, $0.67$ for shadows). All four strategies collapse to near-chance accuracy ($\approx 0.33$) above approximately 12 qubits under the quadratic shot budget $\shots = 16\nqubits^2$. These findings indicate that the discriminative signal between these circuit families is concentrated in local, nearest-neighbor $Z$-basis correlations, consistent with the diagonal gate structure of IQP circuits, and that additional Pauli correlator types or long-range correlations carry no compensating discriminative power for this task. We provide a formal theoretical framework showing that circuits with high diagonal fraction in a given basis concentrate their correlator structure in that basis, and that any deviation from the dominant basis incurs a provably higher estimator variance. These results establish that a quadratic shot budget is insufficient for reliable classification above approximately 12 qubits, but do not rule out the existence of a subquadratic or otherwise more efficient polynomial-resource strategy; whether any polynomial measurement protocol can classify these families at large qubit counts remains an open question.

Recent years have seen growing application potential for Lattice-skin Plate Structures in advanced manufacturing fields such as aerospace and automotive engineering. For multiscale performance evaluation of such structures, conventional homogenization methods for lattice-filled volume structures are often used for equivalent analysis. However, in finite-thickness Lattice-skin Plate Structures, periodic boundary conditions imposed along the three orthogonal directions of the representative cell cannot adequately capture the boundary effect of the free surfaces in the thickness direction, which introduces bias into the prediction of effective properties. To reduce this bias, this study develops and open-sources a homogenization method for Lattice-skin Plate Structures, forming an open-source computational framework for this class of structures. Representative numerical examples show that the framework can stably extract effective plate/shell stiffness matrices and can be extended to predict multiphase material properties and analyze steady-state heat conduction. The tool provides an open and reusable analysis foundation for the high-fidelity design of multifunctional lightweight structures.