Conformal blocks in odd spacetime dimensions are not known in closed analytic form. To facilitate efficient computations in the conformal bootstrap, we introduce $\texttt{GoBlocks}$: a novel conformal-block generator implemented in the Go programming language, designed for rapid, on-the-fly, parallel evaluation using recursive relations. The package supports both multi-point and derivative-based bootstrap approaches and allows flexible control over accuracy and performance. We benchmark $\texttt{GoBlocks}$ against the $\texttt{scalar_blocks}$ package, finding significant speed improvements in applications where computational speed and moderate accuracy are critical, but ultra-high precision is not essential. As an illustration, we apply $\texttt{GoBlocks}$ to the mixed-correlator bootstrap of the three-dimensional Ising model, formulated as a non-convex optimisation problem in a suitable truncation scheme. We simultaneously optimise over external scaling dimensions and OPE CFT data. In addition, we discuss how the approach scales as we increase the number of mixed correlators in more general $O(N)$ vector models.

We develop spectral portfolio theory by establishing a direct identification: neural network weight matrices trained on stochastic processes are portfolio allocation matrices, and their spectral structure encodes factor decompositions and wealth concentration patterns. The three forces governing stochastic gradient descent (SGD) - gradient signal, dimensional regularisation, and eigenvalue repulsion - translate directly into portfolio dynamics: smart money, survival constraint, and endogenous diversification. The spectral properties of SGD weight matrices transition from Marchenko-Pastur statistics (additive regime, short horizon) to inverse-Wishart via the free log-normal (multiplicative regime, long horizon), mirroring the transition from daily returns to long-run wealth compounding. We unify the cross-sectional wealth dynamics of Bouchaud and Mezard (2000), the within-portfolio dynamics of Olsen et al. (2025), and the scalar Fokker-Planck framework via a common spectral foundation. A central result is the Spectral Invariance Theorem: any isotropic perturbation to the portfolio objective preserves the singular-value distribution up to scale and shift, while anisotropic perturbations produce spectral distortion proportional to their cross-asset variance. We develop applications to portfolio design, wealth inequality measurement, tax policy, and neural network diagnostics. In the tax context, the invariance result recovers and generalises the neutrality conditions of Froseth (2026).

We prove Rump's 100-euro conjecture by deriving a weighted affine escape theorem from Ball's plank theorem in [Invent. Math. \textbf{104} (1991)]. More precisely, let $\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}$ and let $A\in\mathbb{K}^{n\times n}$. For every $1\le p\le \infty$, we obtain an $\ell_p$-escape principle controlled by the row $\ell_q$-norms of $A$. Its cube case shows that $|A|e=ne$, where $e$ is the all-one vector, implies the existence of a nonzero vector $x$ satisfying $\|x\|_{\infty}\le 1$ and $|Ax|\ge e\ge |x|$, thereby settling the conjecture. As a consequence, we prove the global comparison $ρ_0(|A|)\le n\,ρ_{\mathbb{K}}(A)$,where $ρ_{\mathbb{K}}$ denotes the sign-real or complex spectral radius, respectively. This is the sharp form of Rump's Perron--Frobenius-type estimate, with the factor $3+2\sqrt{2}$ removed. Moreover, our $\ell_\infty$-escape principle sharpens Rump's result in [SIAM Rev. \textbf{41} (1999)] on the relation between the entrywise distance to singularity of a matrix and its entrywise Bauer--Skeel condition number. Finally, we also investigate the weaker Euclidean row condition, including sharp quantitative bounds and counterexamples to possible strengthenings. In particular, we use Gaussian probabilistic estimates to establish a complex analogue of a conjecture of Bünger.

CuLa$_2$Ge$_2$O$_8$ forms a distorted triangular lattice of quantum spin-1/2 Cu$^{2+}$ ions. A crystal growth method was developed using the traveling-solvent floating zone technique resulting in the synthesis of a large single crystal (4 mm$\times$4 mm$\times$10 mm). The crystal was characterized with regard to phase purity and crystallinity using powder X-ray diffraction, energy dispersive X-ray analysis and Laue diffraction, and found to be of excellent quality. The magnetic properties were characterized using dc-susceptibility, magnetization, and heat capacity measurements which revealed weak magnetic frustration with long-range magnetic order occurring below $T_N=1.14(1)$~K. The magnetic structure determined using neutron powder diffraction is a commensurate, noncollinear antiferromagnetic, different from the 120$^{\circ}$ order of an equilateral triangular antiferromagnet. The ordered moments lie in the {\bf bc}-plane, with components $m_b=0.50(3)$~$μ_{B}$ and $m_c= 0.73(5)$~$μ_{B}$ along the {\bf b}- and {\bf c}-axes respectively, giving a total ordered moment of $M_{total}$= 0.89(6)$μ_{B}/$Cu$^{2+}$ at 20~mK.

We propose a heralded entanglement generation scheme based on Gaussian sources enhanced by photon addition and subtraction operations. By combining single-mode squeezing, linear interferometers, and conditional photon-number measurements on ancillary modes, our model can probabilistically generate dual-rail encoded Bell, GHZ, and W states. We systematically optimize the squeezing parameters and interferometer settings to maximize both the heralding success probability and the fidelity with the target states. Our results show that photon addition and subtraction significantly enhance the non-classicality of the output states and improve generation performance, while maintaining computational efficiency comparable to single-photon source models. We further analyze the robustness of the scheme under parameter perturbations and find that its performance remains stable under realistic experimental imperfections. This work provides a versatile and experimentally feasible framework for scalable heralded entanglement generation using Gaussian resources with non-Gaussian operations.

We establish Burgess-type bounds for short multiplicative character sums over finite fields $\mathbb{F}_{p^n}$ under a purely volumetric condition. We show that for a box $B \subset \mathbb{F}_{p^n}$, nontrivial cancellation occurs whenever $|B| \ge p^{n(1/4+\varepsilon)}$, without imposing lower bounds on the individual side lengths. This removes the coordinate-wise restrictions present in earlier results and extends work of Gabdullin for $n=2,3$ to arbitrary dimension. The proof combines methods from the geometry of numbers with multiplicative energy estimates and bounds for character sums due to Katz.

We investigate the electrochemical processes within an electrolyser cell, which are modelled by a coupled system of second-order quasi-linear elliptic PDEs. In this context, we study an inverse problem aiming to reconstruct both the non-linear diffusion coefficients and the phenomenological relation defining the electric potential. Our main results state that boundary measurements alone are not enough to reconstruct these non-linear quantities. However, we show that a combination of boundary and interior measurements allow for their unique reconstruction. To achieve this result we generalise a linearisation result in the context of the scalar quasi-linear Calderón problem, [Sun, Math. Z. 221 (1996)], to the setting of a system of PDEs with non-local nonlinearities. In contrast to the Calderón case, the generalised linearisation does not "freeze" the coefficients. We show that interior measurements are precisely what is required to achieve this freezing and thus enable the unique reconstruction.

Semicoherent precipitates govern strength, stability and transformation pathways in structural alloys, yet the kinetic defect process underlying their three-dimensional growth has remained unresolved. Here we show that lath growth is driven by diffusion-enabled, non-conservative reorganization of closed interfacial dislocation networks coupled to nanoscale growth ledges. Phase-field-crystal simulations of a model face-centred cubic/body-centred cubic transformation reveal strongly anisotropic kinetics: end faces advance continuously along the long axis, whereas broad facets thicken by discrete ledge sweeps accompanied by mixed glide-climb reactions. O-lattice analysis predicts the defect network, explains the anisotropy through misfit-localization geometry, and shows how the same dislocation motion accommodates transformation strain. In situ transmission electron microscopy of austenite precipitates in duplex stainless steel captures rapid ledge propagation on habit planes, consistent with the predicted mechanism. These results identify the missing kinetic unit of semicoherent precipitate growth and establish a transferable defect-kinetics framework for morphology selection.

We study privacy filters, which enable privacy accounting for differentially private (DP) mechanisms with adaptively chosen privacy characteristics. We develop a general theory that characterizes the worst-case privacy loss of an interaction involving an analyst that respects some restrictions on what queries they may issue. We apply this theory to develop residue filters, which unifies existing privacy filters. We develop the Gaussian DP (GDP) residue filter, which strictly improves upon the naïve GDP filter. We also show that residue filters capture the natural filter, which promises greater utility by leveraging exact privacy accounting techniques. Earlier privacy filters consider only simple privacy parameters such as Rényi-DP or GDP parameters. Natural filters account for the entire privacy profile of every query, promising more efficient use of a given privacy budget. We show that, contrary to other forms of DP, natural privacy filters are not free in general. We present a characterization of when a family of private queries admits free natural filters for a given budget. In particular, only families of privacy mechanisms that are totally-ordered when composed admit free natural privacy filters with respect to an arbitrary privacy budget. Finally, we show that, while the natural approximate-DP filter can fail in the presence of adaptive adversary, it cannot fail too badly: the output remains approximate-DP with parameters at most poly-logarithmically worse than the intended privacy parameters.

Three-dimensional (3D) ultrasound promises various medical applications for abdominal, obstetrics, and breast imaging. However, ultrasound matrix arrays have extremely high element counts limiting their field of view (FOV). Current reduced element count architectures, such as row-column arrays, diverging lenses, or sparse arrays, suffer from limited resolution and high side- and grating-lobe levels. This work seeks to demonstrate an increased field-of-view using a reduced element count array design. The approach is to increase the element size and use advanced beamformers to maintain image quality. The delay and sum (DAS), Null Subtraction Imaging (NSI), directional coherence factor (DCF), and Minimum Variance (MV) beamformers were compared. K-wave simulations of the 3D point-spread functions (PSF) of NSI, DCF, and MV display reduced side lobes and narrowed main lobes compared to DAS. Experiments were conducted using a multiplexed 1024-element matrix array on a Verasonics 256 system. Elements were electronically coupled to imitate a larger pitch and element size. Then, a virtual large aperture was created by using a positioning system to collect data in sections with the matrix array. Resolution and contrast was also assessed on a rabbit liver in vivo. Resolution was maintained using coupling numbers up to four, doubling the FOV while reducing the element count. The NSI and DCF beamformers demonstrated the best resolution performance in simulations, in a phantom with the virtual aperture, and in vivo on a rabbit liver. Our results demonstrate how larger matrix arrays could be constructed with larger elements, with resolution maintained by advanced beamformers.

Several applications of medical ultrasound can benefit from a larger field of view (FOV). This study is aimed at increasing the FOV of linear array probes by increasing the element width. Coupled elements were used to imitate a larger element width. Through Fourier analysis, theoretical pressure amplitudes, and bandwidth estimates, coupled elements are shown to be close approximations of large elements. The effects of coupling on resolution, contrast, and speckle signal-to-noise ratio are investigated through phantom images and in-vivo images of a rabbit tumor reconstructed with plane-wave compounding. Furthermore, a positioning system was used to acquire data from a virtual large aperture with 120 mm FOV and 128 elements, collected in sections with a single probe. The Null Subtraction Imaging (NSI), Sign Coherence Factor (SCF), and Minimum Variance (MV) beamformers are compared for regaining resolution lost by an increased F-number. The NSI beamformer decreased Full-Width at Half-Max (FWHM) estimates of wire targets by 79% with coupling by 2 compared to uncoupled DAS. The MV beamformer was best for maintaining speckle statistics while improving resolution. Our results demonstrate how increased element width can increase FOV with no increase to element count.

In this paper we find analogues for $\varepsilon$-harmonic maps to the generalised energy identity and the existence of geodesic necks result discovered by Yuxiang Li and Youde Wang for $α$-harmonic maps. In particular there exist specific quantities depending only on $\varepsilon$ and the bubbling radius which entirely determine if the full energy identity holds and if a neck forms. In the case these fail we can calculate the energy lost and the length of the geodesic neck based on only these quantities and the biharmonic energy of the bubble.

In this paper we classify the low energy $\varepsilon$-harmonic maps from the surfaces of constant curvature with positive genus into the round sphere. We find that all such maps with degree $\pm1$ are all quantitively close to a bubble configuration with bubbles forming at special points on the domain with bubbling radius proportional to $\varepsilon^{1/4}$.

A fundamental challenge in data science is to match disparate point sets with each other. While optimal transport efficiently minimizes point displacements under a bijectivity constraint, it is inherently sensitive to rotations. Conversely, minimizing distortions via the Gromov-Wasserstein (GW) framework addresses this limitation but introduces a non-convex, computationally demanding optimization problem. In this work, we identify a broad class of distortion penalties that reduce to a simple alignment problem within a lifted feature space. Leveraging this insight, we introduce an iterative GW solver with a linear memory footprint and quadratic (rather than cubic) time complexity. Our method is differentiable, comes with strong theoretical guarantees, and scales to hundreds of thousands of points in minutes. This efficiency unlocks a wide range of geometric applications and enables the exploration of the GW energy landscape, whose local minima encode the symmetries of the matching problem.

The {\em Four-dimensional Light Orchestra} or {\em 4DLO} was an interactive sculpture at the National Museum of Mathematics (MoMath) from November 20, 2025 through January 2026, illustrating various sub-symmetries of the 24-cell with colored lights. This was part of a larger sequence of tubing sculptures aiming to bring to life a few lines of tables appearing in~\cite{conwayandsmith}, reprinted in~\cite{sot}, and further illuminated in~\cite{rastanawi}. Best of all museum patrons could manipulate {\em 4DLO}'s lighting by singing and making funny noises into a microphone, and they did so with gusto. Here we describe some of the technical aspects of this sculpture and its context.

50 years after Thompson's famous triangle inequality for the operator right modulus, we establish a triangle inequality for the quadratic symmetric modulus. We also discuss the corresponding equality cases as well as the infinite-dimensional setting. In addition, we obtain Clarkson--McCarthy type inequalities for the quadratic symmetric modulus. Moreover, we answer several questions raised by Bourin and Lee in [\emph{Bull. Lond. Math. Soc.} \textbf{44} (2012), no.~6, 1085--1102] and [\emph{Internat. J. Math.} \textbf{31} (2026), no.~6, 2650018].

Distributed energy storage devices can be aggregated to provide operational flexibility for power systems. This requires representing a massive device population as a single, tractable surrogate that is computationally efficient and accurate. However, surrogate identification is challenging due to heterogeneity, nonconvexity, and high dimensionality of storage devices. To address these challenges, this paper develops a mean-field learning framework for storage aggregation. We interpret aggregation as the average behavior of a large storage population and show that, as the population grows, aggregate performance converges to a unique, convex mean-field limit, enabling tractable population-level modeling. This convexity further yields a price-responsive characterization of aggregate storage behavior and allows us to bound the mean-field approximation error. We construct a convex surrogate model with physically interpretable parameters that approximates the aggregate behavior of large storage populations and can be embedded directly into power system operations. Surrogate parameter identification is formulated as an optimization problem using historical price-response data, and we adopt a gradient-based algorithm for efficient learning. Case studies validate the theoretical findings and demonstrate the effectiveness of the proposed framework in approximation accuracy and data efficiency.

This paper deals with the extension of partial actions of topological groups on topological spaces. Within this framework, we introduce a class of topological embeddings defined via the inverse semigroup of homeomorphisms between open subsets of a topological space. We describe several embeddings of this type, referred to as $Γ$- embeddings, and we place particular emphasis on one of them. In particular, we prove that every topological space $Y$ admits a $Γ$-embedding into the space of continuous functions $C(X, Y )$, equipped with the compact-open topology, where $X$ is a compact space. Consequently, any partial action $θ$ of a topological group $G$ on $ Y$ naturally induces a partial action $\hatθ$ on $C(X, Y ).$ Throughout the paper, we investigate various relationships between these actions, as well as between their corresponding globalizations and enveloping spaces.

In this work, we have conducted a comprehensive and systematic theoretical investigation of the full cascade decays of charged pseudoscalar mesons, specifically $D_s$, $D$, $B$, and $B_c$, into $τν_τ$, followed by the subsequent decay of the $τ$ via its dominant experimentally reconstructible channels: $τ\to πν_τ$, $τ\to ρν_τ$, $τ\to e \barν_e ν_τ$, and $τ\to μ\barν_μν_τ$. Our study is framed within the model-independent low-energy effective field theory approach, which incorporates the most general set of four-fermion operators, including those coupling to right-handed neutrinos. We provide precise Standard Model predictions for differential decay rate as a function of the final-state charged particle energy, develop an innovative and robust methodology for extracting the magnitudes of the new physics couplings using energy moments, and identify and characterize fixed points in the normalized energy distributions. The fixed points are invariant under new physics contributions described by the considered effective Hamiltonian.

We study a one-shot joint source-channel coding setting where the source is encoded once and broadcast to $K$ decoders through independent channels. Success is predicated on at least one decoder recovering the source within a maximum distortion constraint. We find that in the one-shot regime, utilizing disjoint codebooks at each decoder yields a codebook diversity gain, distinct from the channel diversity gain that may be expected when several decoders observe independent realizations of the channel's output but share the same codebook. Coding schemes are introduced that leverage this phenomenon, where first- and second-order achievability bounds are derived via an adaptation of the Poisson matching lemma which allows for multiple decoders using disjoint codebooks. We further propose a hybrid coding scheme that partitions decoders into groups to optimally balance codebook and channel diversity. Numerical results on the binary symmetric channel demonstrate that the hybrid approach outperforms strategies where the decoders' codebooks are either fully shared or disjoint.

Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this task since their complexity is a function of the desired fraction of the spectrum. In addition, they generally rely on highly optimized and scalable kernels such as matrix-vector multiplications that leverage the massive parallelism and the computational power of modern exascale systems. The Chebyshev Accelerated Subspace iteration Eigensolver (ChASE) is able to compute several thousands of the most extreme eigenpairs of dense hermitian matrices with proven scalability over massive parallel accelerated clusters. This work presents an extension of ChASE to solve for a portion of the smallest positive eigenpairs of pseudo-hermitian Hamiltonians as they appear in the treatment of excitonic materials. By exploiting the numerical structure and spectral properties of the Hamiltonian matrix, we preserve the characteristic positive-negative symmetry in the treatment of the eigenvectors and propose an oblique variant of Rayleigh-Ritz projection that features quadratic convergence of the Ritz values with no explicit construction of the dual basis. Additionally, we introduce a parallel implementation of the recursive matrix-product operation appearing in the Chebyshev filter with limited amount of global communications. Our development is supported by a full numerical analysis and experimental tests.

The mass law is a cornerstone in predicting sound transmission loss, yet it neglects the constraints of causal dispersion. Current causality-based theories, such as the Rozanov limit, are applicable only to one-port reflective absorbers. Here, we derive a universal sum rule governing causal scattering in acoustic systems, establishing a rigorous analogy to the Baldin sum rule in quantum field theory. This relation reveals that the integral of the extinction cross-section is fundamentally locked by the scatterer's static effective mass and stiffness, which is validated numerically using seminal examples of underwater metamaterials. Furthermore, the proposed sum rule predicts an optimal condition for an anomalously broadened transmission loss bandwidth, as experimentally observed through the spectral shaping effect of an acoustic Fano resonator. Our findings open up an unexplored avenue for enhancing the scattering bandwidth of passive metamaterials.

This paper constructs solutions to linear and nonlinear Schrödinger-type equations in two and three spatial dimensions that exhibit prescribed, extraordinary gradient amplification and localization. For any finite time interval $[0,T]$, any prescribed collection of $n\in\mathbb{N}$ distinct points on $\partial D$, where $D$ is the compact support of the anisotropic coefficients, lower-order terms, or nonlinearities, and any amplitude threshold $\mathcal{M}>0$, we show that one can design smooth initial and/or boundary data such that the spatial gradients of the resulting solutions exceed $\mathcal{M}$ in neighborhoods of these points outside $D$ for almost every $t\in[0,T]$. Moreover, the ratio between the local $C^{1,\frac12}$-norm of the solution near each prescribed point outside $D$ and the $C^{1,\frac12}$-norm inside $D$ is bounded from below by $\mathcal{M}/2$ for almost every $t\in[0,T]$. We further prove that the spatial measure of the regions where the gradient magnitude exceeds $\mathcal{M}$ tends to zero as $\mathcal{M}\to\infty$, demonstrating that the amplification phenomenon is highly localized. This effect arises from the structure of the Schrödinger-type equation combined with carefully designed input profiles. From a physical perspective, the results provide a deterministic analogue of localization phenomena observed in quantum scattering and Anderson localization. In addition, the observed trade-off between extreme spatial localization and large gradient amplification is fully consistent with the spirit of the Heisenberg uncertainty principle: while the latter is traditionally formulated in a global $L^2$ space--frequency framework, our results offer a complementary deterministic manifestation at the level of localized spatial gradients in Schrödinger dynamics.

The MAGIC detection of near-TeV gamma rays from the 2021 RS Oph ($2.45$ kpc) outburst has established recurrent novae as TeV particle accelerators. However, the origin of this emission (hadronic vs leptonic) remains unclear due to the lack of coincident neutrinos detected by IceCube. The upcoming outburst of the much closer T Coronae Borealis (T CrB, $\sim0.887$ kpc) offers a unique opportunity to detect these rare nova neutrinos. Here we present the first comparative analysis of the hadronic secondary fluxes expected from the upcoming T CrB outburst and evaluate their detectability across major observatories, considering two proton-acceleration mechanisms: (i) an external shock (ES) at $\sim10^{13}$ cm, and (ii) magnetic reconnection (MR), near the white dwarf surface at $\sim10^{9}$ cm. While the benchmark ES model predicts a gamma-ray flux detectable by current facilities, its corresponding neutrino flux largely remains undetectable. In contrast, the MR scenario generates a robust neutrino flux within the reach of IceCube and KM3NeT. Importantly, as the MR-produced gamma-rays are absorbed, the escaping MR neutrinos will arrive hours before any ES-origin signals. This distinct temporal separation can create a powerful phenomenological signature to disentangle the nova acceleration physics.

We show that the set of points where the blow-up, in the sense of Preiss, of a signed Radon measure on $\mathbb{R}^n$ is unique and its invariant subspace has dimension $k$ is $k$-rectifiable. As simple applications, we obtain a rectifiability criterion for signed Radon measures and the extension of a result, due to Mattila, on measures having unique blow-up almost everywhere.

Audio-Visual Speaker Detection (AVSD) hinges on modeling both individual temporal continuity and inter-personal social context. Existing coupled architectures struggle to reconcile these tasks in shared representation spaces due to conflicting inductive biases: temporal modeling favors low-frequency smoothness, while inter-personal interaction requires high-frequency discriminability. We propose D$^2$Stream, a decoupled dual-stream framework that explicitly isolates these functionalities into parallel, task-specific branches. Specifically, the Intra-speaker Temporal Continuity (ITC) stream captures longitudinal stability, whereas the Inter-personal Social Relation (ISR) stream models transversal social cues. Quantitative gradient analysis reveals an evolutionary divergence in update directions, stabilizing at 86.1°, which confirms the inherent task conflict and the effectiveness of our structural decoupling. D$^2$Stream breaks the long-standing performance plateau, achieving a state-of-the-art 95.6% mAP on AVA-ActiveSpeaker and superior generalization on Columbia ASD, all within a lightweight and efficient design.

We study membership of rational inner functions on the bidisk $\mathbb{D}^2$ in a scale of Dirichlet spaces considered by Bera, Chavan, and Ghara, and in higher-order variants of these spaces. We give a characterization for membership in terms of the geometric concept of contact order of a rational inner function at its singular points, and we further record some consequences and variants of our main result.

Electromagnetic navigation systems (eMNS) are increasingly used in minimally invasive procedures such as endovascular interventions and targeted drug delivery due to their ability to generate fast and precise magnetic fields. In this paper, we utilize the OctoMag and a custom 13-coil eMNS to achieve remote levitation and control of multiple rigid bodies across large air gaps, showcasing the dynamic capabilities of such systems. A compact parametric analytical model maps coil currents to the forces and torques acting on the levitating object, eliminating the need for computationally expensive simulations or lookup tables and establishing a levitator- and platform-agnostic control framework. Translational motion is stabilized using linear quadratic regulators. A nonlinear time-invariant controller is used to regulate the reduced attitude accounting for the inherent uncontrollability of rotations about the dipole axis and stabilizing the full five degrees of freedom controllable pose subspace. We analyze key design limitations and evaluate the approach through trajectory tracking experiments across different objects and actuation platforms. Notably, our proposed controller demonstrates superiority over an equivalent baseline PID formulation, reliably tracking large spatial angles up to 65$^\circ$. This work demonstrates the dynamic capabilities and potential of feedback control in electromagnetic navigation, which is likely to open up new medical applications.

We perform searches for gravitational wave memory in the data of two major Pulsar Timing Array (PTA) experiments located in Europe and Australia. Supermassive black hole binaries (SMBHBs) are the primary sources of gravitational waves in PTA experiments. We develop and carry out the first search for late inspirals and mergers of these sources based on full numerical relativity waveforms with null (nonlinear) gravitational wave memory. Additionally, we search for generic bursts of null gravitational wave memory, exploring possibilities of reducing the computational cost of these searches through kernel density and normalizing flow approximation of the posteriors. We rule out the mergers of SMBHBs with a chirp mass of 10^10 Solar Mass up to 700 Mpc over 18 years of observation at 95% credibility. We rule out the observation of generic displacement memory bursts with strain amplitudes > 10^-14 in brief periods of the observation time but across the sky, or over the whole observation time but for certain preferred sky positions, at 95%$credibility.

In a performance based earthquake engineering (PBEE) framework, nonlinear time-history response analysis (NLTHA) for numerous ground motions are required to assess the seismic risk of buildings or civil engineering structures. However, such numerical simulations are computationally expensive, limiting the real-world practical application of the framework. To address this issue, previous studies have used machine learning to predict the structural responses to ground motions with low computational costs. These studies typically conduct NLTHAs for a few hundreds ground motions and use the results to train and validate surrogate models. However, most of the previous studies focused on computationally-inexpensive response analysis models such as single degree of freedom. Surrogate models of high-fidelity response analysis are required to enrich the quantity and diversity of information used for damage assessment in PBEE. Notably, the computational cost of creating training and validation datasets increases if the fidelity of response analysis model becomes higher. Therefore, methods that enable surrogate modeling of high-fidelity response analysis without a large number of training samples are needed. This study proposes a framework that uses transfer learning to construct the surrogate model of a high-fidelity response analysis model. This framework uses a surrogate model of low-fidelity response analysis as the pretrained model and transfers its knowledge to construct surrogate models for high-fidelity response analysis with substantially reduced computational cost. As a case study, surrogate models that predict responses of a 20-story steel moment frame were constructed with only 20 samples as the training dataset. The responses to the ground motions predicted by constructed surrogate model were consistent with a site-specific time-based hazard.