Grid-scale batteries increasingly influence outcomes in wholesale electricity markets, but their observed bid patterns remain difficult to interpret. In particular, bids that appear to reflect strategic withholding may instead arise from rational operations under price uncertainty and risk management. We develop an asset-level model of a price-taking battery that submits stepwise buy and sell bid curves in the day-ahead market under a finite set of price scenarios. The battery chooses quantity--price pairs to maximize a mean--CVaR objective subject to physical and market constraints. A direct formulation is a mixed-integer linear program, but we show that its integer decisions can be removed, yielding an exact linear programming reformulation suitable for empirical analysis. Our empirical results deliver three insights. First, withholding behavior can arise even without market power, because scarce stored energy and uncertain future prices increase the value of holding energy. Second, the effect of uncertainty depends on the state of charge: when stored energy is scarce, greater uncertainty raises sell bid prices, whereas when stored energy is abundant it can lower them. Third, risk management reshapes bid curves into layered structures that secure profitable execution across a broad set of scenarios while preserving some exposure to rare but valuable price spikes.

Implicit feedback is the dominant data source for recommender systems, but behavioral logs are often contaminated by false-positive interactions caused by mis-clicks, biased exposure, and interface effects. Denoising recommendation methods improve robustness by down-weighting or filtering interactions suspected to be noisy, often relying on the small-loss heuristic. We revisit this heuristic through the lens of popularity bias. Tail-item positives can be harder to fit because they are sparsely observed, and thus may receive larger losses even when they reflect genuine user preference. Under such popularity-dependent loss patterns, monotone loss-based reweighting can suppress clean-but-hard tail signals and increase the head-tail imbalance in effective supervision. We formalize this interaction through the effective head-tail signal ratio induced by denoising weights and derive a conditional reallocation result: when the loss distribution of tail positives is right-shifted relative to that of head positives, small-loss reweighting increases the effective head-tail signal ratio compared with ERM. Motivated by this analysis, we propose Popularity-Aware Denoising (PAD), a lightweight plug-in framework that modulates denoising strength by item popularity. PAD applies stronger denoising to highly exposed items while being more conservative on tail items, preserving more clean-but-hard long-tail signals. Experiments on three datasets and three backbones show that PAD generally improves over representative denoising baselines and provides favorable accuracy-diversity tradeoffs, especially on MF-style recommenders.

Estimating the sensitivity of gravitational-wave searches is important for a wide variety of scientific applications spanning astrophysics and fundamental physics. In this work, we develop a fast semianalytic approximation for estimating matched-filter search sensitivity to physical effects not explicitly modeled in the template bank. This approximation utilizes fitting factors, i.e., the maximum overlap of a candidate signal over the search bank. As illustrations, we compare our estimates to the actual performance of searches against spinning binary neutron stars, and evaluate search sensitivity to compact binaries possessing orbital eccentricity or deviations from general relativity. Our work thus paves the way for fast sensitivity estimates for a variety of applications, including unmodeled effects in template banks such as deviations from general relativity, environmental effects, gravitational lensing, and waveform/calibration systematics.

Core-collapse supernovae are explosions of massive stars. While most massive stars end as iron-core-collapse supernovae, less massive stars are expected to explode as electron-capture supernovae (ECSNe), defining the low-mass boundary of core-collapse supernovae. ECSNe were proposed $\sim 40$ years ago, and first-principles simulations predict their successful explosions with low energies of $\sim 10^{50}$~erg. Nevertheless, only one convincing candidate, SN~2018zd, has been proposed other than SN~1054, the progenitor of the Crab Nebula. We search for ECSN candidates among Type~II SNe from the literature and a public Zwicky Transient Facility sample, using a color-based diagnostic, selecting ten candidates with blue colors at the middle of the plateau. We classify three as \textit{gold}, for which a spectrum around the middle of the plateau disfavors strong circumstellar-medium interaction that would make the SN bluer, and seven as \textit{silver} without such spectra. Comparing the observed multicolor light curves with radiation-hydrodynamical models, we infer the explosion energies, $(0.4-1.7)\times10^{50}$~erg for the \textit{gold candidates} and $(0.4-2.7)\times10^{50}$~erg including the \textit{silver candidates}, consistent with first-principles predictions and the mass-loss rates, $3\times10^{-3} - 3 \times 10^{-2}~M_{\odot}~{\rm yr}^{-1}$ for the \textit{gold candidates}, which remain similar when the \textit{silver candidates} are included, higher than those expected for the early super-asymptotic-giant-branch phase. The ECSN occurrence ratios among SNe~II are inferred as $3.0^{+10.6}_{-2.9}$ and $15.7^{+17.3}_{-12.7}~\%$ from the \textit{gold} and \textit{silver candidates}, respectively, which we interpret as lower and upper limits. To robustly identify ECSNe and refine this ratio, spectroscopic follow-ups of ECSN candidates around the middle of the plateau are essential.

More than a century of physics is recorded in the American Physical Society (APS) archive, but the corpus cannot be analyzed as a single, time-resolved object because its subject metadata are fragmented across eras with no shared vocabulary. We close this gap by using a frontier large language model to retrospectively assign the modern Physics Subject Headings (PhySH) to the historical archive, yielding a unified subject map for every APS paper from 1893 to 2025. The resulting map not only reproduces century-scale disciplinary arcs but also resolves the fine-grained lifecycles of individual ideas, materials, techniques, and discoveries across a vocabulary of over 3,000 PhySH Concepts. The map turns a fragmented archive into a quantitative substrate for systematic search and for data-driven studies of how physics evolves.

In this paper, we consider a class of convex composite optimization problems arising from the joint estimation of clustered multiple Gaussian graphical models. The resulting model combines a log-determinant loss term with a nonsmooth sparse clustered regularizer, which encourages both similar sparsity patterns and consistent edge values across different graphs. We first establish a necessary and sufficient condition under which the solution is block diagonal, enabling a large-scale problem to be decomposed into smaller independent subproblems and substantially reducing computational complexity. To efficiently solve this problem, we develop a proximal augmented Lagrangian method in which each subproblem is handled by a superlinearly convergent semismooth Newton method. Unlike widely used first order methods, our approach fully exploits the underlying second order information through the semismooth Newton framework, thereby achieving faster convergence and improved robustness. The efficiency and robustness of the proposed algorithm are demonstrated through comparisons with state-of-the-art methods on both synthetic and real data sets.

Machine learning is beginning to influence rarefied-gas modeling at multiple levels, including equation-solving, operator learning, learned collision physics, moment closures, direct simulation Monte Carlo (DSMC) field surrogates, and gas--surface models. This Perspective argues that the central challenge is not demonstration-level success, but trustworthy use under realistic deployment conditions: multiregime Knudsen behavior, stochastic DSMC labels, sharp nonequilibrium structures, uncertain gas--surface interaction, and scarce direct experimental anchors. I classify the main method families by what is learned, distinguish soft physics penalties from structure-preserving designs, and propose evaluation standards based on extrapolation tests, noise-aware metrics, end-to-end cost accounting, and a three-level validation hierarchy. Most current evidence is solver-facing: it demonstrates surrogate fidelity to a teacher solver more often than direct physical fidelity to experiment. The aim is not to dismiss ML for rarefied and vacuum-related gas transport, but to separate what is already credible from what remains provisional, and to define a reporting standard that makes future claims auditable.

Pure partition functions of multiple SLE are characterized by null-state partial differential equations, Möbius covariance, and boundary asymptotics. After quotienting by Möbius covariance, the case of three curves is the first genuinely multivariable one: the moduli space has three independent variables, naturally represented by the three unoriented cross-ratios of the three pairs of links. We solve this Möbius-normalized three-variable problem for the two basic link-pattern types of multiple \(3\)-SLE\(_\kappa\), namely the rainbow and neighbor patterns. Writing \(\beta=4/\kappa\), we construct explicit trivariate hypergeometric-series normal forms and identify them with the corresponding pure partition functions for all \(\beta>1/2\) in the rainbow case and all \(\beta\ge2/3\) in the neighbor case. Equivalently, these ranges are \(\kappa\in(0,8)\) and \(\kappa\in(0,6]\), respectively. The proof is analytic. The null-state PDEs and Möbius covariance yield recursion relations for the trivariate coefficient arrays. In the rainbow case, coefficient estimates give convergence and boundary regularity on the closed cube. In the neighbor case, Pfaff systems continue the local power series to a neighborhood of \([0,1)^3\), while side-face equations, regular normal estimates, and corner propagation give continuity on \([0,1]^3\) for \(\beta\ge2/3\). The endpoint \(\beta=2/3\), corresponding to \(\kappa=6\), requires a logarithmic normal term. The two-dimensional boundary degenerations are classical Appell \(F_1\) and Horn \(G_2\) functions. The probabilistic identification uses SLE martingale arguments and Itô calculus, together with positivity and boundary regularity. We also discuss boundary degenerations, including heuristic connections with boundary Green's functions.

The modern software supply chain, taking Node Package Manager (npm) dependency network for example, relies heavily on shared open-source dependencies. While this promotes rapid development, it introduces systemic vulnerabilities as well. Concerning this potential risk, we analyze the npm dependency network by modeling 53,481 packages and 78,520 dependency edges, and classify the network as a scale-free topology. Thus, we demonstrate its inherent vulnerability to targeted attacks on high-degree hubs. To mitigate this, we propose and evaluate a dual-pronged defense strategy consisting of Centrality-Based Node-Hardening and Dependency Weight Warning system. Moreover, by simulating the network under various attack scenarios, we prove that applying strict security protocols to just the top 1% of nodes, combined with pruning 30% of structurally trivial edges, prevents catastrophic network collapse and neutralizes cascading malware infections. The source code can be found at this https URL.

In this work, it is shown that many quantum error-manipulating techniques, such as distillation, error mitigation, and dynamical decoupling, are special cases of the most general framework for quantum error correction. This unifying perspective is achieved by extending quantum error correction to include state-adaptive and channel-adaptive settings, as well as multi-stage coding scenarios. Based on this insight, a model of self-correcting quantum memory is also proposed. This work clarifies the relationship among these techniques and illustrates, through explicit constructions, how the unified perspective can guide the design of reliable quantum information systems.

We prove that a monomial ideal has projective dimension one if and only if its minimal monomial generators can be ordered so that each successive colon ideal is principal, and show that this characterization is equivalent to the monomial version of the Hilbert-Burch Lemma. Furthermore, we prove that any squarefree monomial ideal of projective dimension one with a linear resolution has the property that all its powers \(I^s\) admit linear quotients, and we provide a partial classification of such ideals.

We present updated atmosphere models designed for calculating the post-formation evolution and cooling of giant planets with masses between $0.3$ and $10$ $M_J$. Our tables provide the entropy in the convective region at the base of the atmosphere, temperature ($T$)pressure ($P$) profiles, and emergent spectra for atmospheres calculated using the radiative transfer code \texttt{CoolTLusty} for $T_{\mathrm{eff}}$s over the range 100 to 1400 Kelvin and log$_{10}$($g$) from 2.8 to 4.4 ($cgs$) with the latest opacities and equations of state. Each spectrum and thermal profile is calculated using line-by-line opacity sampling. We construct tables at 3 different metallicities ($Z = 1, 3.16, 10 Z_\odot$) and 2 different helium fractions ($Y=0.15, 0.275$), with the improvement that we adopt a metal-inclusive EOS that treats heavy elements consistently with the opacity metallicity (rather than folding it into an effective $Y$). The result is tables that accommodate both changes in $Y$ due to helium rain and potential variations in $Z$ during envelope evolution. We present a comparison between TP profiles, modeled spectra, and evolutionary tracks, and find that on-the-fly interpolation of boundary conditions in atmospheric composition has a notable impact on the late stages of giant planet evolution, altering the timing of helium rain and therefore the subsequent cooling history and atmospheric helium depletion. We also provide an available toolkit that generates spectra and boundary conditions via efficient interpolation across the 4D parameter space $(T_{\rm eff}, \log_{10} g, Y, Z)$, which is useful for post processing evolutionary tracks to produce fully time-resolved spectral evolutions.

In this paper, we establish some geometric and analytic foundations for free boundary Brakke flows. Specifically, we (i) introduce unit-regular and cyclic free boundary flows and show that they are preserved under reflections and weak limits, (ii) prove that the support of free boundary Brakke flows satisfies an avoidance principle, and (iii) introduce free boundary inner and outer flows and prove the existence of matching free boundary Brakke flows. These results serve as general tools to analyze free boundary flows through singularities, and in particular will be applied in forthcoming work with Haslhofer, where we address the mean-convex neighborhood conjecture and uniqueness conjecture for free boundary flows through (half) cylindrical singularities.

In this paper, we investigate congruences for meromorphic modular forms $F$ which have a pole at a single point $z$ in the fundamental domain of $\mathrm{SL}_2(\mathbb Z)$. For a prime $p$ with good supersingular reduction at the elliptic curve corresponding to $z$, we show that there exists a cusp form $f$ such that $F|U_p^m \equiv f|U_p^m \pmod{p^{\kappa_m}}$, where $\kappa_m=\alpha m -\beta$ with $\alpha$ only depending on the weight of $F$ and $\beta$ depending on $F$ and $p$ but is independent of $m$. In particular, if the space of cusp forms is trivial, then $F|U_p^m\equiv 0 \pmod{p^{\kappa_m}}$ vanishes $p$-adically to a high order. In order to prove these results, we use the fact that $p$ has supersingular reduction to realize $F$ as an overconvergent modular form and then utilize the theory of overconvergent forms to show the congruences.

This paper develops a unified framework for the study of real-order moments of arbitrary random variables. General integral representations are established in terms of cumulative distribution functions and survival functions, covering continuous, discrete, and mixed distributions supported on the whole real line. These formulas extend the classical tail-integral identities for nonnegative random variables and provide a common treatment of positive, fractional, and negative moments. For discrete distributions, explicit series representations are derived in terms of cumulative probabilities, yielding simple criteria for the existence of moments. Applications are presented for the zeta and Skellam distributions, illustrating how tail behavior determines moment finiteness and how moments can be represented geometrically through cumulative distribution functions. In addition, a representation for logarithmic moments is obtained, linking logarithmic means, Laplace transforms, and the classical Frullani identity. The results provide a unified perspective on moment representations and establish useful connections between tail probabilities, distribution functions, Laplace transforms, and moment existence.

Using a statistical model, we analyze published multiplicity distributions for identified hadrons produced in heavy ion collisions in the energy range from 2.7-200 \gev. Our analysis enables the prediction of the multiplicity distributions for multi-strangeness hadrons that have not yet been measured in lower-energy experiments. Furthermore, we obtain freeze-out parameters, including temperature, baryon chemical and strangeness potentials, the strangeness suppression factor, and the system radius, as functions of centrality and collision energy. Additionally, we computed and discussed the Skewness and its behavior at lower collision energies, highlighting the importance of the freeze-out parameters in determining the liquid-gas phase transition in nuclear matter.

In strong magnetic fields, charged quarks occupy the lowest Landau level, leading to an effective dimensional reduction of hadronic dynamics. This dimensional reduction naturally generates a hierarchy of scales, separating fast intra-meson quark dynamics from slow collective meson motion; this motivates a Born-Oppenheimer description of meson-meson systems. Our Born-Oppenheimer analysis shows that the infrared behavior is controlled by the interplay between dimensional reduction and the structure of the meson-meson interaction, leading to three distinct regimes: scattering-dominated, molecular, and compact multiquark states. Charged pseudoscalar mesons such as $\pi_+$ and $K_+$ provide a particularly interesting realization of this framework, as their lattice spectra at large magnetic fields suggest the emergence of loosely bound states near the boundary between scattering and molecular regimes. Our results suggest that strong magnetic fields provide a useful laboratory for exploring the emergence and classification of hadronic bound states.

We study black hole thermodynamics using a two-dimensional effective theory obtained by dimensional reduction of four-dimensional Einstein--Maxwell theory. For spherically symmetric charged black holes, the resulting dilaton gravity has a nonlinear potential that reproduces the semiclassical phase structure of four-dimensional AdS black holes, including the Hawking--Page transition and the small/large Reissner--Nordström--AdS black hole transition. This shows that the two-dimensional theory before taking the near-horizon and near-extremal limits captures non-extremal thermodynamics beyond the Jackiw--Teitelboim gravity regime. We also include electromagnetic Kaluza--Klein modes on the internal sphere and integrate them out to derive the one-loop effective dilaton gravity. At leading order in the derivative expansion, these corrections appear as constant shifts in the black hole entropy and in the effective charge parameter of the dilaton potential. Therefore, the semiclassical phase structure is not qualitatively modified within this leading local approximation.

In the context of neutrino oscillation measurements from the T2K experiment, the off-axis near detector ND280 plays a crucial role in constraining the incoming neutrino flux and neutrino-nucleus interaction cross sections. The result is a robust control over systematic uncertainties in the fit of neutrino oscillation parameters to the data at the T2K far detector, Super-Kamiokande. This paper details the methodology and results of these constraints in the context of the latest neutrino oscillation analysis from T2K. It describes how a new neutrino cross-section model and refined flux prediction are parameterized and fit to data in new ND280 event selections. Additionally, this work reports the results of extensive robustness studies, including fits with alternative interaction models, consistency checks against publicly available cross-section measurements, and \textit{p}-value evaluations, to demonstrate the reliability and robustness of our methodology. Finally, we present a sensitivity study demonstrating that the upgraded ND280, with improved acceptance and a lower hadron threshold, may enhance future constraints and further reduce systematic uncertainties in oscillation measurements.

We investigate the viability of scalar-tensor (quintessence) models of dark energy with a quartic polynomial nonminimal coupling to gravity and a linear scalar potential. The polynomial nonminimal coupling is used to ensure that the field is well stabilized in the early universe. We perform a systematic exploration of the parameter space spanned by the quadratic and quartic nonminimal couplings, as well as the slope of the potential. We confront the predictions of the model with the latest Dark Energy Spectroscopic Instrument (DESI) constraints on the dark energy equation of state and also with complementary bounds from local tests of gravity, including solar system constraints and limits on the time variation of the effective Newton's constant. We identify bands in parameter space where all these constraints are satisfied, finding such bands to be very narrow.

We show that on linearly locally contractible (LLC) manifolds, the beta numbers (which describe unilateral flatness) are comparable to the theta numbers (which describe bilateral flatness), quantitatively. As an application, we show that if $M\subset\mathbb{R}^n$ is a compact LLC $m$-manifold with finite Menger $p$-energy for some $p>m(m+2)$, then $M$ is in fact a $C^{1,\alpha}$ manifold. We also show that the bound $m(m+2)$ is critical by constructing, for each $n\geq 3$, an LLC $n$-sphere in $\mathbb{R}^{n+1}$ that has finite Menger $p$-energy for every $p<m(m+2)$ but is not even quasisymmetrically equivalent to the standard $n$-sphere.

The paper presents the science operation framework for Prime Focus Spectrograph (PFS or 'Onohi'ula in its Hawaiian name) installed at the 8.2m Subaru Telescope on the summit of Maunakea. PFS is a massively multiplexed, wide-field, fiber-fed spectrograph covering 1.25 square degrees with 2386 science fibers. The instrument has been offered to the Subaru scientific community since March 2025. In order to fully exploit the unique capabilities of PFS, the Subaru Telescope has introduced a new, dedicated science operation framework for PFS. The default observing mode is queue observing, and multiple observing programs (in the same field) can be executed in the same exposure to achieve high observing efficiency. The quality of an exposure is based on the delivered signal-to-noise ratio and is quantified in terms of 'effective exposure time', and exposures are taken until the allocated 'fiber hours' for each program or target are achieved. The fiber hour is a new unit for observing time at Subaru; if we expose a fiber for 1 hour under the fiducial conditions, it is 1 fiber hour. Each observing program is granted the total fiber hours by the Time Allocation Committee. In addition to normal observing programs, which are selected through the standard peer-review process, there are two filler categories; community filler and observatory filler. As the names imply, the former is proposed by the community and the latter is prepared by the observatory. These filler targets are used whenever unassigned fibers are available. After an observing run, the data are fully reduced by the observatory and delivered to the users through the PFS Science Platform, a cloud-based data analysis environment. The paper gives a summary of all of this new framework and the actual implementation of it.

We demonstrate direct single-shot retrieval of the full in-plane vector field of broadband terahertz waves using electro-optic sampling. Implemented with a circularly polarized optical probe and polarization-sensitive camera, the method overcomes the projection constraints of conventional electro-optic sampling and enables direct time-domain reconstruction of transverse vector fields without Fourier-domain inversion or sequential polarization analysis. We experimentally validate the approach through spatiotemporal imaging of linear, circular, azimuthal and radial terahertz fields generated by polarization-engineered silicon metamaterials. The measurements reveal ultrafast time-resolved vector-field dynamics inaccessible to conventional scalar detection, including helicoidal field rotation within a single optical cycle and the spatiotemporal evolution of structured polarization topologies. Beyond structured-field imaging, we demonstrate single-scan vector-field spectroscopy through measurements of quartz birefringence and broadband terahertz waveplate performance. More broadly, this work transforms electro-optic sampling from a projection-based measurement into a vector-resolved imaging and spectroscopy platform for structured electromagnetic fields.

Political scientists often interpret coefficient shrinkage under fixed effects as evidence that pooled associations are confounded. This paper shows why that inference is unreliable for slow-moving, mismeasured regressors. Fixed effects can remove much of the signal and identify coefficients from within-unit variation that is disproportionately measurement error, attenuating estimates toward zero. A lone fixed effects coefficient may therefore be unable to distinguish confounding from measurement error. I show that the attenuation depends on a regressor's empirical intraclass correlation and measurement reliability. I then propose a default workflow for panel regression. Researchers estimate reliability when possible, report pooled and fixed effects estimates with corrected within reliability, use partial identification bounds when the estimates share a sign, and report fixed effects as a within-unit estimate when they do not. For variables with no reliability estimate, I introduce an autocorrelation frontier that bounds the attenuation factor directly. I conclude by applying this workflow to several published results to show that the data often cannot distinguish attenuation from confounding, and the workflow makes clear which case the researcher faces.

In recent years, the Institute of Electrical and Electronics Engineers (IEEE) and the European Telecommunications Standards Institute (ETSI) have developed a series of security communication standards for vehicular communications. These standards include mechanisms such as the Security Credential Management System (SCMS) and Butterfly Key Expansion (BKE) to protect vehicle privacy. However, these standards are mainly based on the Elliptic-Curve Cryptography (ECC), which may be vulnerable to attacks from quantum computing in the future. In response to this potential risk, this study proposes a hybrid certificate that combines the ECC with Post-Quantum Cryptography (PQC). This approach enables infrastructure systems to be built on cryptographic foundations that are more resilient to quantum-based attacks. Furthermore, this study presents a generalized pseudonym scheme that is compatible with various cryptographic algorithms for generating pseudonym certificates. This design aims to eliminate the possibility of inferring any correlation between the public key in a pseudonym certificate and that in an enrollment certificate. This study also conducts a comprehensive performance evaluation of the RSA, ECC, and PQC algorithms, particularly those standardized by the National Institute of Standards and Technology (NIST). The comparison considers factors such as message length and computation time. Based on the findings, this study recommends suitable pseudonym schemes that adopt hybrid certificates for secure and efficient use in vehicular communications.

Blockchain consensus mechanisms based on Proof-of-Work consume significant energy, with Bitcoin alone estimated at approximately 150 TWh per year. Proof-of-Space reduces this cost by replacing repeated computation with storage, but plot generation remains bottlenecked by CPU hashing throughput. Prior work on VaultX demonstrated a high-performance CPU-based Proof-of-Space plotter using multi-threaded Blake3 hashing, achieving plotting speeds 4 to 50x faster than Chia depending on hardware configuration. In this paper, we present VaultxGPU, a GPU-accelerated extension of the VaultX plotter that offloads the Blake3 hashing pipeline to the GPU using custom kernels. We implement the plotter in both CUDA for NVIDIA hardware and SYCL for AMD and Intel GPUs, keeping Table 1 entirely in GPU VRAM and fusing the sort and match stages into a single kernel to minimize data movement. We evaluate VaultxGPU across K-values 27 through 31 against CPU baselines. Our SYCL GPU implementation achieves a 59.2x speedup over a single-threaded CPU baseline, completing a K=31 plot in 45.4 seconds compared to 2688 seconds, and outperforms even the best 384-thread CPU configuration. These results confirm that GPU acceleration is the correct direction for scaling Proof-of-Space plotting beyond what CPU parallelism can achieve.

Prosody is central to oral communication, conveying information like the emotional state of the speaker and cues needed for meaning disambiguation. Many self-supervised models of speech produce embeddings that encode prosodic as well as linguistic, and speaker information. This entanglement of information is problematic in scenarios where prosody is the main distinguishing factor while other factors may vary between training and deployment; in such cases, a purely prosodic representation would be more robust. Such representation could also be used for analyzing the role of prosody in a given task or as input to speech synthesis systems. In this work, we propose a variety of approaches for producing global prosodic embeddings based on auto-encoder models of pitch and energy. We develop a benchmark for assessing the performance of these representations, showing that our embeddings provide competitive or superior performance under challenging conditions, compared to various alternatives.

Frames provide redundant representations that enable stable signal reconstruction under coefficient losses. In this paper, we study optimal dual frames for probabilistic erasures using the Hilbert--Schmidt norm of the associated error operators. We characterize dual frames that are optimal for $1-$erasures and establish conditions under which the canonical dual is not only optimal but also unique. We further derive lower bounds for the probabilistic reconstruction error for any $m-$ erasure and identify classes of frames for which the canonical dual remains optimal. In addition, we analyze the geometric structure of the set of optimal dual frames, showing that it is a nonempty compact convex set. These results provide new insights into robustness and optimal reconstruction in probabilistic erasure models.

Wave optics is essential for analyzing lensed gravitational waves (GWs), yet evaluating the diffraction integral $F(\omega, y)$ is computationally expensive. We present a Sinusoidal Representation Networks (SIRENs) framework for the dimensionless amplification factor, demonstrating its efficacy and generalization through Point Mass Lens (PML) and Singular Isothermal Sphere (SIS) test cases. Unlike standard architectures that suffer from spectral bias, the network's periodic activation functions structurally align with the integral's oscillatory kernel, effectively resolving high-frequency spectral features. The resulting estimator achieves $\mathcal{O}(10^{-3})$ relative accuracy and a $\sim 100\times$ speedup compared to direct numerical integration. By shifting the computational burden to offline training, our framework yields a stable $\mathcal{O}(1)$ inference complexity. This guarantees constant, sub-millisecond evaluation times even in the weak-lensing diffraction tail where traditional methods stagnate. Additionally, the dimensionless formulation ensures intrinsic scale invariance, enabling direct application across astrophysical regimes from stellar-mass lenses in the ground-based LVK band to supermassive black holes in the space-based LISA band.

In this paper, we introduce pre-vertex algebras and pre-Poisson vertex algebras as preLie-algebras in the chiral and classical pseudo-tensor categories, respectively. We show that a pre-vertex algebra gives rise to a vertex algebra, that every Rota-Baxter operator on a vertex algebra induces a pre-vertex algebra, and that every pre-vertex algebra can be embedded into a vertex algebra equipped with a Rota-Baxter operator. Moreover, we prove that pre-vertex algebras are equivalent to dendriform vertex algebras. In the Poisson setting, we demonstrate that pre-Poisson vertex algebras are obtained from Rota-Baxter operators on Poisson vertex algebras, from filtrations of pre-vertex algebras, and as classical limits of pre-vertex formal deformations of differential Zinbiel algebras. This extends the classical relationships among Rota-Baxter operators, pre-Lie algebras, and Poisson algebras to the framework of vertex algebras.