We present a deterministic polynomial-time algorithm for estimating the volume of a hypercube intersected by a fixed number of constraints of the type $f(x) \leq b$, where $f$ is the sum of univariate functions that are each nonnegative, monotone, and convex. Such constraints include knapsack and norm-ball constraints. The case of the unit hypercube truncated by a single linear constraint (halfspace) is already #P-hard. Given $k$ such constraints in dimension $n$, with total input length of at most $L$ bits, total output length of at most $L_o$ bits, and an error parameter $\varepsilon > 0$, our algorithm computes a $(1 + \varepsilon)$-multiplicative approximation of the volume of their intersection with the unit hypercube $[0,1]^n$ in time poly$_k(n, 1/\varepsilon, L,L_o)$.

UiO-66 is the most widely studied metal-organic framework (MOF), on account of its structural tunability given by its capacity of sustaining high amounts of point defects in its structure. Its synthesis mechanism is largely unknown, with only a few works mostly focused on the formation of the Zr-oxide cluster. In this work, a partially reactive force field to model UiO-66, nb-UiO-FF, is introduced. This force field incorporates node--ligand reactivity via a Morse potential and the introduction of dummy atoms to reproduce the anisotropic charge distribution of the Zr atoms in the node. nb-UiO-FF reproduces structural features of both UiO-66 and its isoreticular analog UiO-67, mechanical properties and framework stability with or without defects, activated or filled with N,N-dimethylformamide or ethanol. The force field is further employed within a molecular dynamics scheme to study the early stages of solvothermal node--ligand binding. Transient structural motifs both thermodynamically and kinetically favored are identified. This force field enables studying the self-assembly of UiO-66, as well as the formation of its point defects.

Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple competing models, model uncertainty should be accounted for when performing inference based on available data. Bayesian model selection is a framework for testing mechanistic hypotheses and generating predictions under model uncertainty, which generally requires computation of the model evidence. In this work, we investigate the reliability of evidence computation methods when parameter non-identifiability -- the inability to distinguish between parameter values given available data -- is present, and find that deterministic evidence approximations can produce misleading model selection results because their underlying assumptions are violated. We propose a novel implementation of adaptive multiple importance sampling for evidence estimation, and demonstrate its robustness against non-identifiability. We use ecological case studies to demonstrate how simple model selection methods fail to produce accurate results, whereas our method yields model selection results that are comparable to those obtained by Markov chain Monte Carlo methods at substantially lower computational cost. Given the pervasiveness of parameter non-identifiability in mathematical biology, this work provides a practical approach to reliable model selection in the presence of poorly identified parameters.

We consider iterated preimages of curves by random products of birational transformations of the plane. Following a recent work of Diller and Roeder, we study the action of the Cremona group on the inverse limit of the spaces of currents in all models of the plane. We show equidistribution for generic finitely supported random walks.

Data-centric materials science is changing how materials are discovered, optimized, manufactured, and qualified, yet many deployment-limiting materials problems still depend on experimental, processing-rich, device-level, and field-relevant data that are difficult to capture in conventional materials databases. This perspective argues that the Great Plains and adjacent interior research corridor can make a distinctive national contribution by organizing distributed experimental assets into a trusted regional materials-data ecosystem. The proposed model emphasizes FAIR metadata, provenance, persistent sample identifiers, uncertainty-aware modeling, semi-closed-loop workflows, stackable workforce training, and tiered governance for academic, public, controlled-access, and industry-protected data. We identify five coupled barriers -- fragmented data, weak algorithm--laboratory translation, uneven access to cyberinfrastructure and technical staff, workforce gaps at the materials--data interface, and insufficient incentives for sharing and reuse -- and propose a staged roadmap for addressing them. A high-purity germanium pilot illustrates how regional strengths can be converted into reusable datasets, benchmark models, trained personnel, and decision-improving workflows. The broader message is that regional leadership in data-centric materials science will depend less on geographic concentration than on trustworthy data practices, interoperable infrastructure, cross-trained people, and application-driven materials challenges.

Quantum computing is no longer a lab curiosity for academic research. Industrial processors exceeding 100 qubits are commercially accessible and, for the first time, can extract information from data in ways that classical algorithms struggle to match. The most direct way to monetize this capability for industrial production today is quantum feature extraction: turning raw business data (images, customer records, molecules, or sensor readings) into richer representations that outperform standard machine learning models. There is one obstacle, however, that stands between today's demonstrations and tomorrow's production systems: every sample of data costs a quantum computing execution. For a company with millions of customers, satellite images, or transactions per month, processing every sample on quantum hardware is simply not viable. This work introduces quantum feature surrogates, a framework developed by Kipu Quantum that breaks this bottleneck. The idea is intuitive though challenging: instead of asking the quantum computer to look at every single sample, we let it look at a small, carefully chosen subsample of the data, whose distribution faithfully represents the full set. A simple classical model, a surrogate, then learns the quantum-induced patterns and applies them to the rest of the dataset at near-zero cost. The quantum processor stops being a per-sample engine and becomes a teacher of representations, while production inference runs entirely on classical hardware.

We present a complete analysis of the glass transition in the self-overlap-corrected Sherrington-Kirkpatrick (SK) model in a transverse magnetic field, also referred to as the quantum SK model. In particular, we determine the phase boundary separating the glassy and paramagnetic phases. The proof is based on a simplified Parisi variational principle for the quantum pressure, which only involves classical Parisi order parameters. As part of the proof, we also analyze the pressure of the self-overlap-constrained quantum SK model and its Parisi description, as well as the pressure of generalized quantum Hopfield models.

This article extends a recently introduced kinetic closure of turbulence by developing its theoretical framework, operational realizations, and validation. In contrast with filtered Navier--Stokes formulations, filtering the Boltzmann equation retains subgrid advective transport under the linear streaming operator, so that unresolved physics is concentrated on the collision side. We show that in the dilute-gas LES and RANS regimes, the main limitation of Boltzmann and BGK-type collision models is not the breakdown of molecular chaos, but the retention of a Markovian collision process at a scale where filtering induces finite temporal correlations in the collision product. In a BGK-type framework, the closure problem is dual: one must infer the filtered fine-grained equilibrium, which is not computable from filtered moments alone, and model the non-Markovian collision dynamics generated by the collision-product covariance. The present framework makes this dual structure explicit and represents the resulting collision-covariance source term through a BGK-like closure built from the subgrid equilibrium residual, with the turbulent relaxation frequency given by a first phenomenological realization. The framework relies on a Chapman--Enskog analysis organized by the reference timescale ratio emerging directly from the nondimensionalization of the kinetic equation and performed in the classical sense, thereby avoiding artificial turbulent scale separations. We show that the Chapman--Enskog structure is not a pure one-parameter Knudsen scaling: the primary ordering is set by the kinetic-to-macroscopic timescale ratio, while higher moments retain an additional Mach dependence through the mixed scaling of particle velocity. The resulting kinetic closures are validated through lattice Boltzmann simulations and compared with the Smagorinsky model and regularization-based collision models.

Batteryless IoT systems have largely followed two paths: ambient-energy sensing, where energy arrival is decoupled from the event being monitored, and kinetic event telegrams, where a user actuation powers a short report of the actuation itself. Mechanically gated states expose a third case: the access motion is not only an event to report, but the moment at which a latent physical state may have changed and must be measured. We show that routine hinge motion can supply enough energy for one bounded wake-sense-transmit transaction, including ultrasonic sensing and a long-range LoRa uplink. We call this principle motion-coupled sensing and instantiate it with an open-source compact electromagnetic harvester that retrofits to bins, doors, and cabinets with no structural modification. We size the platform for the most demanding workload, waste-bin monitoring, where each actuation must power both an ultrasonic measurement and a long-range LoRa uplink. Across five campus locations and 5,945 lid actuations, the bin deployment achieves 99.3% per-event transmission reliability. Field deployments on room doors with 1,870 actuations and office cabinets with 1,636 actuations achieve 92% and 94% transmission success respectively, demonstrating that the same energy envelope transfers across hinge geometries without hardware redesign. These results show that mechanical access can be treated as a self-powered sensing transaction, removing periodic polling and scheduled battery maintenance for IoT deployments.

Unifying the early-universe inflationary paradigm with late-time cosmic acceleration, while resolving the initial Big Bang singularity, remains one of the most profound challenges in modern cosmology. In this paper, we propose a non-singular quintessential inflation model embedded within the effective dynamics of Loop Quantum Cosmology (LQC) based on a Generalized Regularization Scheme. The quantum geometry effects naturally replace the initial singularity with a quantum bounce, followed by a phase of superinflation that sets robust initial conditions for the subsequent slow-roll inflation. To achieve a viable late-time dark energy epoch and address the coincidence problem, we introduce a coupling between the scalar field and massive neutrinos, known as Mass-Varying Neutrinos (MaVaNs). As neutrinos become non-relativistic in the post-inflationary evolution, their backreaction effectively freezes the scalar field, triggering the late-time accelerated expansion. We numerically trace the full background dynamics from the quantum bounce to the present day. Furthermore, we tightly constrain the model parameters utilizing the observational data, including the Type Ia supernovae sample, the Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillations (BAO) and Cosmic Microwave Background (CMB) distance priors. Our results demonstrate that this unified LQC-MaVaNs quintessential framework is highly consistent with current precision cosmological observations.

Beyond diagonal reconfigurable intelligent surface (BD-RIS) represents a promising architecture for advancing millimeter-wave (mmWave) communications. However, its intricate inter-element connections invalidate the conventional decoupled mathematical structure, thereby severely complicating cascaded channel estimation. In this paper, we formulate a novel block-Kronecker-structured cascaded channel model for a \textit{group-connected} BD-RIS-aided multi-user (MU) mmWave system equipped with uniform planar arrays (UPAs). By exploiting the cascaded channel sparsity, an efficient three-stage estimation protocol is proposed. Specifically, Stage I acquires the common angles of arrival (AoAs) at the base station (BS) via a discrete Fourier transform (DFT)-based approach. Stage II leverages the block-Kronecker structure alongside orthogonal matching pursuit (OMP) and correlation-based least squares (LS) to extract the complete cascaded channel for a designated typical user. Finally, Stage III utilizes a Hierarchical Block OMP (HBOMP) algorithm to estimate the other users' channels. This structurally reconstructs the common and user-specific components, which fundamentally reduces the computational complexity and substantially reduces the pilot overhead. Numerical simulations verify that the proposed protocol yields improved channel estimation accuracy while maintaining a relatively low pilot overhead.

Embryology has long played a foundational role in shaping our scientific understanding of animal evolution. In recent decades, growing evidence has also highlighted its role in cancer. Despite the indisputable similarities between embryonic development and cancer, there has been limited discussion on the profound embryological implications for the disease. This article explores the understanding of cancer as an embryological and evolutionary phenomenon, offering a fresh perspective on the disease and discussing immediate consequences in the search for therapeutic approaches

We prove the existence of a non-linear recursive relation for the volume of the moduli space of hyperbolic spheres with conical points or geodesic boundaries. This relation generalizes a result by Zograf, where the same was derived for cusps.

Infinite persistence marks the topological transition. For finite persistence, the canyon-finding rate Gamma(tau_p) on the p=2 spherical spin glass forms an inverted-U profile, peaking at an optimal tau_p^*. At low temperature (T=0.05), tau_p^* drops from 10 to 5 as N increases through 128, marking the discrete-to-quasi-continuous GOE crossover. For N=1024, the peak is flat between tau_p=5 and 6 within statistical uncertainties, preventing a more precise determination. For N>=128, the canyon width saturates at xi_eff=1, consistent with the measured tau_p^*=5 when beta=0.4. At higher temperatures (T>=0.15), tau_p^*=10 and beta(T) scales as 1/T, with temperature dependence entering only through v_th = sqrt(2T). For T=0.10 and N>=128, high-resolution scans give tau_p^*=8.0; for N<=64 at the same temperature, coarse scans place tau_p^* in the range 8-10. Thus, optimal persistence reveals the hidden topology of the landscape-a principle expected to be generic in disordered landscapes with entropic bottlenecks.

We investigate the global optimization of the objective function arising in continuous sparse regression, specifically the Beurling LASSO (BLASSO), over the space of measures. While Conic Particle Gradient Descent (CPGD) methods are computationally efficient, they may become trapped in local minima due to the non-convexity of the parameterization. To overcome this limitation, we introduce Fast Spawn\&Prune (FS\&P), a stochastic algorithm that extends FastPart introduced in De Castro et al. (2025) and combines CPGD with a birth-death process. The birth mechanism ensures asymptotic global exploration by introducing particles in regions where first-order optimality conditions are violated, while the death process preserves computational efficiency by pruning non-informative particles. We provide the first theoretical guarantee of global convergence for this class of discrete-time stochastic algorithms, without requiring exponentially large initializations. Furthermore, we derive explicit convergence rates for the excess risk, which scale as $\mathcal{O}\big(\left(\log K / K\right)^{\frac{1}{2(2+d)}}\big)$, where $K$ denotes the number of iterations and d the dimension of the domain, thereby quantifying the trade-off between global exploration and local refinement. Moreover, the sample complexity is $\mathcal{O}\big(N^{-\frac{1}{4(2+d)}}\big)$ (up to logarithmic factors). We also propose a horizon-free variant that does not require prior knowledge of the iteration budget.

With an assumption on the codimension of the singular locus of a complex hypersurface $D$ in smooth variety $X$, we show that if $\underlineΩ^m_D \cong Ω^m_D$, then $\underlineΩ^i_D \cong Ω^i_D$ for all $0 \leq i \leq m$. We also discuss an analogue of this statement in positive characteristic.

Using 44.55 fb$^{-1}$ of $e^+e^-$ collision data collected by the BESIII detector at the BEPCII collider, we report the first measurement of the Born cross sections for the $e^+e^- \to K^+Ξ^0\barΣ^-$ reaction at fifty-six center-of-mass energies between 3.51 and 4.95~GeV. A fit to the dressed cross sections reveals the first observation of the $ψ(3770) \to K^+Ξ^0\barΣ^-$ process, with a statistical significance of 6.0$σ$ including systematic uncertainties. This result represents the first observation of charmless three-body baryonic decay of a vector charmonium state above the open-charm threshold. No significant signals for other charmonium(-like) states i.e., $ψ(4040)$, $ψ(4160)$, $Y(4230)$, $Y(4360)$, $ψ(4415)$, $Y(4500)$, $Y(4660)$ or $Y(4710)$ are observed, and the upper limits for the product of the branching fraction and the electronic partial width at the 90% confidence level for each assumed charmonium(-like) state are provided. Additionally, the ratios of Born cross sections between this work and the previous measurements of $e^+e^- \to K^{0}_{S}\barΞ^{-}Σ^-$ and $K^-\barΞ^+\barΣ^0$ are provided, which can be used to validate theoretical predictions related to isospin symmetry.

This paper addresses output reference tracking with prescribed transient performance for unknown nonlinear multi-input multi-output systems with arbitrary relative degree. We propose a novel derivative-free extension of funnel control based on a collection of filter variables that estimate the output derivatives. The resulting controller ensures that the tracking error evolves within prescribed performance bounds, while avoiding differentiation of the output signal and maintaining a simple structure with only a small number of tuning parameters. The effectiveness of the proposed approach is illustrated by a numerical example.

The transition from standard generative AI to \emph{reasoning-centric architectures}, exemplified by models capable of extensive Chain-of-Thought~(CoT) processing, marks a fundamental paradigm shift in system requirements. Unlike traditional workloads dominated by compute-bound prefill, reasoning workloads generate long chains of reasoning tokens that shift inference into a \emph{Capacity-Bound regime}. This paper presents a comprehensive system characterization, evaluating models ranging from 8B to 671B parameters on GPUs clusters. By systematically exploring the interplay between Data, Tensor, and Pipeline parallelism, we identify critical bottlenecks that defy standard scaling heuristics. Our analysis reveals that data parallelism is throughput efficient for small models but hits a capacity trap on reasoning workloads as KV-cache fragmentation forces early throttling resulting in sub-optimal compute utilization. Tensor parallelism unlocks stranded memory and delivers sublinear gains near the 32B crossover. At frontier scale, dense models (e.g., Llama-405B) are interconnect and memory-bandwidth bound and favor high-degree TP, while sparse Mixture-of-Experts (MoE) models (e.g., DeepSeek-R1) are limited by routing and synchronization latency and benefit from hybrid strategies. These insights provide a rigorous decision framework for navigating the reasoning cliff, establishing new architectural imperatives for the next generation of inference infrastructure.

The breakup of thinning (stretching) liquid ligaments is strongly influenced by localized perturbations arising from impurities or suspended particles. Using numerical simulations and analytical modelling, we investigate the role of a solid particle on the breakup dynamics of a stretching liquid ligament. We show that particle-induced perturbations trigger a universal pinch-off dynamics in the viscous regime. Once the ligament surface approaches the particle, the subsequent breakup becomes self-similar and independent of the particle size. We derive an analytical expression for the pinch-off time based on the interplay between ligament stretching and Rayleigh-Plateau instability, which agrees quantitatively with simulations. Our results reveal a universal mechanism by which localized perturbations control the breakup of ligaments containing solid particles.

For the mixed CM point (a,b,c) = (1/6, 1/3, 1), define A_n^{mix} := 108^n [z^n] _2F_1(1/6, 1/3; 1; z)^3. For every split prime p >= 7, p == 1 mod 3, and every m >= 1, we prove unconditionally A_{mp}^{mix} == A_m^{mix} mod p^4. The exponent 4 exceeds the generic weight-3 Hodge-gap prediction of 3; the extra factor of p is a CM enhancement attached to j=0. We also establish the matching unconditional inert-prime obstruction (p == 2 mod 3), both as a formal-parameter congruence on the q-side and as a coefficient-level Cartier parity law modulo p. The proof uses the modular realization on Gamma_0(3) with parameter t = u/(1+27u)^2, a Lagrange-Burmann reduction to three Cartier identities Lambda_p(C_mix U_p^l) == 0 mod p^4 for l = 1,2,3, a saturated weak q-expansion lattice on the rigidified stack X_0(3) handling vertical integrality, and a length-three Witt-Cartier pole estimate at the elliptic point P_- driven by mu_3-equivariance of the canonical Frobenius lift.

Multimodal density estimation is a fundamental problem in scientific computing. Determining the number of modes in a distribution is a core numerical challenge with applications across ecology, economics, genomics, and astronomy. While the R ecosystem provides mature tools through the multimode package, the Python ecosystem has lacked an equivalent cohesive implementation. We present critband, a Python package for critical bandwidth bimodality detection based on Silverman's kernel density approach. The package implements critical bandwidth search with a robust bracketed mode-count solver and FFT-accelerated KDE, and provides additional features including k-mode detection, component decomposition, bimodality strength quantification, and excess mass estimation. Validation against twelve benchmark cases spanning separation regimes, unequal variances, unequal weights, and small sample sizes shows stable estimates for clearly separated cases and expected instability for boundary cases. Performance benchmarks show critband is typically 3-10 times faster per case than R's modetest() in the tested setup.

The rapid adoption of Web3 infrastructures has led to a growing number of security incidents affecting cryptocurrency exchanges, custody services and blockchain-based platforms. While existing research predominantly focuses on vulnerabilities in smart contracts and blockchain protocols, a substantial portion of real-world losses originates from off-chain systems, organizational processes and human-centered operational workflows. This paper presents a qualitative, incident-based analysis of publicly documented, high-impact security breaches in the Web3 ecosystem, including the Bybit exchange incident (2025), the Ronin Network bridge compromise (2022), and the DMM Bitcoin exchange breach (2024). The selected cases are systematically analysed and mapped to established Web2 security reference frameworks, including OWASP-based vulnerability categories and organizational security control domains. The results indicate that dominant failure patterns in Web3 environments are insufficiently addressed by generic security control catalogues, particularly with respect to cryptographic key management, transaction approval governance, signer and validator infrastructure, third-party tooling dependencies, and human-in-the-loop processes. Based on these findings, this paper argues for the adoption of established information security management systems (ISMS) in Web3 organizations and derives a structured set of blockchain-specific cybersecurity control categories to operationalize existing ISMS frameworks for blockchain-based systems. The proposed categories aim to bridge the gap between generic security governance frameworks and domain-specific risks inherent to Web3 infrastructures.

Contextual biasing is essential to improving the recognition of rare and domain-specific words in an automatic speech recognition (ASR) system. While numerous methods have been proposed in recent years, most of them focus on offline settings and do not explicitly address the challenges of streaming ASR. For example, CTC-based word spotting (CTC-WS) have demonstrated strong performance by directly detecting keywords from CTC log-probabilities, but they are limited to offline processing and require access to the full utterance. In This work, we present a streaming extension of CTC-WS for real-time contextual biasing. Our method maintains active keyword paths across audio chunks using a stateful token passing algorithm, enabling the detection of keywords that span multiple chunks. To ensure low latency and stable output, we introduce an incremental commitment mechanism that only emits segments guaranteed not to be affected by future audio, while deferring uncertain regions. This method naturally integrates with streaming ASR pipelines and does not require modifications to the underlying acoustic model or additional training, making it practical for real-world deployment. Experimental results show that our method reduces overall WER and effectively improves keyword F-score, demonstrating its effectiveness for real-time ASR applications.

Recent progress in gravitational wave observations has positioned Pulsar Timing Arrays as a key tool for detecting the stochastic gravitational wave background in the nanohertz band. It is widely believed that this background is primarily attributed to the cosmic ensemble of inspiraling supermassive black hole binaries. While traditional analyses have predominantly focused on the spectral amplitude and frequency dependence of the gravitational wave background, higher-order statistics such as variance, skewness, and kurtosis could potentially be useful for extracting further physical information. However, these statistical moments are known to diverge when the redshift integration is extended down to z=0. In this study, we propose a strategy to resolve this issue by introducing a physically motivated lower integration limit, z_min, defined by the sensitivity for detecting individual sources. Since higher-order statistics are primarily determined by local sources, we may adopt the lowest-order approximation with respect to redshift in their computations. Under this approximation, we demonstrate that all higher-order statistics beyond the expectation value depend on the mass function only through a weighted average of the chirp mass, <\mathcal{M}^{10/3}>, irrespective of the redshift evolution model. We show that the ratio of the variance to the expectation value provides information on <\mathcal{M}^{10/3}>/<\mathcal{M}^{5/3}> independently of the total number of mergers. We also find a consistency relation between the kurtosis and the squared skewness, paving the way for testing the binary-origin hypothesis of the gravitational wave background. Our findings demonstrate that higher-order statistics provide a new window for interpreting the gravitational wave background, offering a methodology to break existing degeneracies and refine our understanding of the mass function.

We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical. The model captures realistic features observed in many economic observables, which can be explained as market-driven firm entries/exits, worker inflow/outflow, and income growth/loss. This model is not conservative and, despite the asymmetry in the entry and exit rates, we find that the system eventually relaxes to a stationary distribution. Moreover, our analysis reveals three distinct dynamical regimes in the moments of the distribution, arising from the interplay between volatility, drift, entry, and exit rates. We further derive the survival probability and the mean first-passage time associated with the observed variable reaching certain threshold under the competing entry-exit processes. Interestingly, we identify an optimal exit rate that minimizes the mean first-passage time, providing insights into how entry and exit policies can influence the outcome of the system. These results should be useful for understanding the long-run behavior of economic systems in which growth, volatility, entry, and exit jointly shape the evolution of heterogeneous units.

Reasoning about array data structures is a key requirement for many applications in hardware and software verification, especially in combination with machine integers. The Satisfiability Modulo Theories (SMT) theory of extensional arrays provides array read and write operators and allows extensionality over arrays. This is sufficient to express many aspects of computer-aided verification, but lacks succinctness to efficiently deal with arrays that are initialized with a default value. Existing procedures for extending the SMT-LIB theory of arrays with support for constant arrays are limited to arrays with infinite index domains, and existing implementations in SMT solvers only support a fragment of the theory for finite index domains. In this paper, we present a novel decision procedure for the theory of arrays with constant arrays that supports arbitrary index domains and is not limited to the infinite case. We present our procedure as an abstract calculus and show its refutational and satisfiability soundness. We implement a decision procedure based on our calculus in the state-of-the-art SMT solver Bitwuzla and evaluate its performance on a diverse collection of benchmarks and use cases.

We define a group of lower-triangular matrices whose columns are defined by power series. This group can be seen as a generalization of the (ordinary) Riordan group and the double Riordan group. Elements of this group are defined by three power series. Sequence bisections and vertically stretched Riordan arrays play an important role in the formulation of this group. We give a production matrix characterization of this new group. We also indicate how higher order groups can be defined, based on $n$-tuples of power series. We have chosen to name this group in memory of Renzo Sprugnoli, who was a pioneer in the application of the Riordan group to combinatorial problems as well as contributing to an understanding of the rich structure of Riordan arrays.

We give three explicit quantum Latin squares of order $6$, with cardinalities $13$, $15$, and $17$. Throughout, vectors differing only by a global phase are counted as identical. The cardinality-$13$ construction is based on an orthogonal direct-sum decomposition $\C^6=\C^4\oplus\C^2$. The cardinality-$15$ and cardinality-$17$ constructions are based on two-dimensional Hadamard pairs supported on coordinate planes.

For any $α\in (0,1/3)$, we construct exact $C^α$ self-similar blowup profiles for the vorticity of the 3D incompressible Euler equation without swirl, and build on them to prove asymptotically self-similar blowup from $C_c^α$ initial vorticity and $C^{1,α}\cap L^2$ initial velocity. Moreover, we provide a complete characterization of the limiting behavior of the $C^α$ vorticity profiles and the associated blowup solutions as $α\to(1/3)^-$. Specifically, as $α\to(1/3)^-$, the spatial blowup rate $\mathsf{c}_{\mathsf{x},α}$ diverges to $\infty$, while the $C^α$ vorticity profile $Ω_{*,α}^θ$ asymptotically factorizes and converges strongly in a weighted $L^\infty$ norm to a nonzero constant multiple of $r^{1/3}\bar W_{1/3}(z)$, where $\bar W_{1/3}$ is a $C^\infty$ 1D blowup profile. Our construction is inspired by the Hou--Zhang blowup scenario. Using a fixed-point argument, we lift the $C^\infty$ blowup profiles for a 1D model constructed in the companion work [11] to exact 3D blowup profiles. To overcome the lack of $r$-directional decay in the approximate profile and capture the anisotropic structure, we develop a family of anisotropic weighted estimates and introduce a crucial integration-by-parts method along trajectories that exploits the equation twice. We then develop a finite codimension stability argument in a low-regularity setting to prove stability of the 3D profiles and establish asymptotically self-similar blowup. This blowup result is sharp in view of the global regularity theory for axisymmetric Euler without swirl with $ C_c^α$ initial vorticity for all $α\geq 1/3$. To the best of our knowledge, our results provide the first example in which a singularity from a 1D nonlocal fluid model is lifted to construct blowup for incompressible fluid equations in $\mathbb{R}^2$ or $\mathbb{R}^3$.