Papers

Self-supervised speech models encode rich phonetic information, but it remains unclear how to transform this information into interpretable metrics for second-language (L2) pronunciation assessment in spontaneous speech. We propose a native-reference coordinate geometry in which phone-class averages from native speech define a low-dimensional reference subspace, and L2 speech is evaluated by its distance to matching native phone-class coordinates. Unlike prior distance-based approaches, our method does not require parallel recordings with matched linguistic content or dedicated pronunciation labels. Across different self-supervised encoders and modeling choices, the resulting native-reference distances show negative Spearman correlations up to -0.5 with speaking proficiency, indicating that higher-proficiency speakers tend to have smaller distances to the corresponding native phone-class coordinates.

We study the Abelian maximal pattern complexity $p_{\alpha }^{\ast \mathrm{ab}}(k)$ of infinite words over finite alphabets. For recurrent aperiodic words using exactly $\ell\geq 2$ letters, we prove the sharp lower bound $p_{\alpha }^{\ast \mathrm{ab}}(k)\geq k+\ell-1$ and give a structural characterization of those words attaining equality for every $k\geq 1$. Without assuming recurrence, we prove that an infinite word $\alpha $ is aperiodic if and only if $\binom{p_{\alpha }^{\ast \mathrm{ab}}(k)}{2}\geq k$ for every positive integer $k$. For aperiodic words over $\ell\geq 2$ letters, each occurring infinitely often, we further prove that $p_{\alpha}^{\ast \mathrm{ab}}(k)\geq m$ whenever $\binom{m}{2}\leq(\ell-1)(k-\ell+2)$, for all positive integers $m,k$. Together with a matching construction, this shows that the minimum Abelian maximal pattern complexity in this class is $\sqrt{2(\ell-1)k}+O_{\ell}(1)$. We call a word an Abelian pattern Sturmian word if, for every positive integer $k$, its Abelian maximal pattern complexity is the least positive integer $m$ satisfying $\binom{m}{2}\geq k$. We show that a word is Abelian pattern Sturmian if and only if, after relabeling its alphabet, it is the characteristic word of an infinite set $E\subset\mathbb{N}_0$ whose bipartite incidence graph is a forest. This graph has two disjoint copies of $\mathbb{N}_0$ as its vertex classes, with a left vertex $r$ adjacent to a right vertex $s$ exactly when $r+s\in E$.

Prior work has explored quantum algorithms for topological data analysis (TDA), revealing the possibility of exponential quantum speedups in estimating the ratios of Betti numbers to the dimension of the combinatorial Laplacian. However, this quantity is only non-vanishing and efficient-to-quantumly-estimate when Betti numbers are exponentially large, a case for which concrete examples are rarely known. Furthermore, certain randomized classical algorithms are sometimes efficient in this regime. Thus, the prospect of achieving quantum advantage in conventional TDA appears fairly narrow. Here, we address these challenges to the quantum advantage in TDA by developing quantum algorithms for Mayer homology, which generalize simplicial homology to $N$-nilpotent boundary operators ($\partial^N =0$) and have recently been successfully applied to real-world TDA contexts. We introduce an efficient quantum algorithm for estimating Mayer Betti numbers and their persistent counterparts. We then prove that for high-order simplices, Mayer Betti numbers are often exponentially large in the dense regime, which ameliorates the normalization bottleneck of conventional quantum TDA. In the same regime, we argue that existing dequantization algorithms developed for conventional TDA, when applied to Mayer homology, generally lose theoretical guaranties, facing certain structural barriers that prevent their practical utilities. We also provide logical resource estimates revealing that a quantum computer with roughly a few hundred qubits and sixty million Toffoli gates could solve Mayer homology problems beyond the capabilities of known classical approaches. Finally, we discuss real-world applications of Mayer homology in genomics, supersymmetry, drug discovery, and neuroscience, revealing the potential of our quantum algorithm to deliver real-world impacts via Mayer homology.

Young isolated neutron stars exhibit a wide range of magnetic field strengths. To understand the origin of this diversity, it is important to observationally constrain magnetic fields during the proto-neutron star (PNS) phase. We propose a novel diagnostic of PNS magnetic fields using neutrinos associated with supernova fallback. By performing one-dimensional general-relativistic magnetohydrodynamic simulations of the supernova fallback onto a magnetized PNS, we investigate how the energy spectra of the fallback neutrinos depend on the PNS magnetic field strength and the fallback accretion rate. We find that stronger magnetic fields and lower accretion rates produce softer spectra because the fallback neutrinos are emitted mainly near the magnetospheric radius, which becomes larger under these conditions. To quantify this spectral softening, we define a hardness ratio based on event rates above and below 30 MeV and introduce a hardness-event-rate diagram. Using this diagram, we identify the parameter region in which our diagnostic is applicable. Its applicability depends on the PNS magnetic field strength, fallback accretion rate, onset time of the fallback phase, and neutrino mass ordering. We also investigate the dependence on the PNS radius and find that a larger radius produces softer spectra, indicating a degeneracy between the magnetic field and PNS compactness. An independent constraint on the PNS compactness would therefore enable us to better constrain the magnetic field. These results suggest that future multimessenger observations of galactic supernovae can provide a new window into the NS diversity.

Ultrafast photoemission is a promising avenue for the development of petahertz electronics. For such devices, identifying the precise emission mechanism and quantifying the local field strength at the emission site are of utmost interest. While this information can be extracted from electron energy spectra or the scaling of the emission rate with peak intensity, such measurements are not always technically feasible and a clear interpretation of the results can be challenging. Here, we demonstrate channel closing as a precision gauge for the local enhanced optical nearfield strength. Channel closings originate from a field-induced upshift of the vacuum level, which leads to a small decrease of the emission yield with increasing intensity. We report the first experimental observation of such channel closings in the photoemission rate from an array of nanometer-sharp gold tips. Our data are well matched by simulated yields, enabling us to precisely measure the local, field-enhanced optical nearfield at the tip array in situ. We expect this method to be a versatile diagnostic tool for the characterization of lightwave optoelectronic devices, as it suffices to measure currents only.

We study the asymptotic behavior of the optimal stabilization prefactor for the free Schrödinger equation, optimized over all bounded stationary linear feedbacks. For a prescribed decay rate $\delta>0$, let $\widehat{C}_S(\delta)$ denote this optimal prefactor. Assuming that the uncontrolled region contains a nonempty open set and that the observability cost satisfies $C(T)\le C_0e^{C_0/T}$ for small $T>0$, we prove $$ e^{c\sqrt{\delta}}\le \widehat{C}_S(\delta)\le e^{C\sqrt{\delta}}, \qquad \delta\gg1. $$ The lower bound is based on the uncontrolled open hole and a quantitative cutoff construction adapted to the Laplacian, while the upper bound combines an exponentially weighted Gramian with the small-time observability cost $C(T)\lesssim e^{C/T}$. The results apply to controlled Schrödinger equations in three settings: flat tori, including a strip-control example beyond the geometric control condition; the whole space $\mathbb{R}^n$ with exterior-ball control; and bounded smooth domains satisfying the geometric control condition for generalized geodesics.

This paper refines the notion of cyclic Massey products to the bi-graded setting, just as quadruple ABC Massey products refine the notion of quadruple Massey products. The result, we call “cyclic ABC Massey products,” are in general non-trivial and contain information different from the quadruple ABC Massey products.

Mixture-of-Experts (MoE) training requires global load balance to prevent expert under-utilization and local balance for efficient expert-parallel execution. Existing distributed Quantile Balancing (QB) uses shard-dependent or approximate global quantiles, while token-independent expert biases cannot ensure microbatch-level balance. We introduce Exact Quantile Balancing (EQB), which computes exact global-batch BF16 quantiles with negligible communication, and Load-Error Injection (LEI), which injects local load errors directly into router-score gradients. On 7.5B-parameter MoEs trained for up to 500B tokens, EQB improves global balance and downstream performance over naive QB, while LEI improves local balance and outperforms the GShard loss at comparable quality.

Backscatter communication has proven to be a key enabler for energy-neutral sensor nodes in the IoT. It allows ultra-low-power nodes to transmit sensor data by reflecting incident RF signals. Practical large-scale deployment requires hardware solutions that are both cost-efficient and widely available. This paper investigates the practical limits of implementing backscatter transmitters exclusively using COTS components. We compare a two-load and multi-load architecture in terms of hardware requirements, complexity and spectral efficiency highlighting the most important trade-offs. A multi-load backscatter architecture is developed using a resource constrained low-power microcontroller, levering DMA to achieve high switching speeds while minimizing processing overhead. Furthermore, we present a layout agnostic load design methodology based on scattering parameters, allowing precise control of the reflection coefficients. A prototype implementation demonstrates a successful backscatter transmission of a single-sideband chirp with reduced harmonic distortion. Measurement results show suppression of the backscattered carrier and the second sideband by 10 dBm. This demonstrates that low-cost sensor nodes can be built using COTS components enabling remote monitoring at extended lifetimes.

We study degenerations of orbits in varieties of chain complexes of projective modules. We show that degenerations are characterized in terms of certain admissible short exact sequences in the exact category of complexes of projectives, analogously to work from Riedtmann and Zwara. We then extend our study to the homotopy category. In this context, complexes of projectives with a given $g$-vector form an ind-variety, and we prove that degenerations of orbits are characterized by the existence of certain distinguished triangles in the category. This links to the algebraic definition of degeneration for triangulated categories introduced by Jensen, Su and Zimmermann.

A new wavefront sensing framework based on the interference of counter-accelerating Airy beams is presented. An engineered cubic phase function transforms a single Gaussian beam into two coherent Airy beams with opposite transverse accelerations, which self-recombine during free-space propagation to form an interference pattern encoding the aberrated incident wavefront. Numerical simulations demonstrate accurate recovery of the aberrated exit-pupil phase across the aberration sets considered, with a root-mean-square phase reconstruction error below $10^{-6} \mathrm{\;rad}$ for the aberration set shown and consistently low errors for the other sets, while maintaining accurate recovery in the presence of measurement noise. The approach eliminates collection optics and enables a compact wavefront-sensing architecture for applications where conventional interferometric systems are difficult to implement, including electron-optical systems, augmented and virtual reality systems.

Video understanding is usually benchmarked on curated, single-actor, or professionally filmed clips, and a strong score there is routinely read as evidence a model is robust enough for deployment. Amateur team sport is a useful, largely untested place to check that assumption: over eight million students played a school sport in the United States in 2024-25 alone, almost none of it filmed by more than a single fixed camera, with several candidate actors crowded into frame and no operator or second angle to fall back on. Using volleyball as a test case, we ask whether strong performance on general video and world-model benchmarks translates into reliable, per-player attribution once footage is this chaotic, turning footage into statistics through a chain of tasks from finding play boundaries to naming who did what. We evaluate four approaches (prompting and agentic reasoning over frontier vision-language models, classical computer vision with small trained specialists, self-supervised video world models, and manual annotation) at every stage, on 66 amateur matches with 46,648 human-labelled contacts, filmed under conditions no published benchmark uses. No single paradigm wins every stage, and static, single-frame computer vision is not competitive at any stage involving motion or identity. A prompted model segments matches well, yet a far smaller trained model beats it at spotting contacts for a fraction of the cost, and the sport's own rules recover rally outcomes the pixels cannot. Identity is where every automated approach struggles: a jersey number is a static fact temporal reasoning cannot recover if never visible, unlike sporting action, a repeated motor pattern a temporal model can exploit, which is why holistic reasoning improves event detection while identity stays unchanged. We close with where each approach earns its cost, and what transfers beyond volleyball to amateur sport.

Modern information retrieval (IR) systems rarely represent time, yet many information needs depend on it: in clinical, journalistic, and legal search, when an event occurred can decide whether a document is relevant. Dense retrievers and Retrieval-Augmented Generation (RAG) pipelines match queries to documents well on topic but poorly on time, so they surface content that is on-topic yet temporally wrong. We introduce Temporal Textual Similarity (TTS), a task that measures how well two anchored texts align in time, independent of their topical similarity. We then present TEMPS (Temporal Embedding Model for Precise Search), a modular temporal branch that attaches to a frozen semantic retriever and trains on that signal. It resolves anchored temporal expressions to intervals and moment-matches each one to a Gaussian; the resulting ordering supervises an anchor-date-conditioned encoder, whose score we fuse with the semantic score at inference. Grounding supplies the supervision, so training uses no hand-labeled temporal data. The temporal score itself is the Gaussian-KL inclusion measure from distributional embeddings; what TEMPS adds is the grounding and the moment-matched supervision. On three temporal benchmarks, TEMPS improves MRR for every semantic backbone tested and, on TS- Retriever, lifts R@1 from 19.92 to 25.39 over the prior temporal state of the art.

We prove that the Dirichlet-to-Neumann map associated to the Schrödinger operator $-\Delta+q$ on a planar bounded Lipschitz domain uniquely determines an arbitrary complex-valued potential $q\in L^p$, $p>1$, whenever zero is not a Dirichlet eigenvalue. Our argument uses Nachman's d-bar equation only at sufficiently large complex frequencies, where exceptional points are absent. A new annular frequency estimate converts the first asymptotic coefficient of the complex geometric optics solutions into a pointwise bound for a primitive of the potential difference, reducing the inverse problem to a unique-continuation argument.

Let $\Omega\subset\mathbb R^2$ be a bounded smooth domain. We prove that the weak Dirichlet-to-Neumann map for $-\Delta+V$ uniquely determines every complex-valued potential $V\in L^p(\Omega)$, $p>1$, provided that zero is not a Dirichlet eigenvalue. This extends the previously known range $p>4/3$ to all $p>1$. The proof uses Bukhgeim's quadratic-phase solutions and an average of Alessandrini's identity over the phase center. After separating the Neumann-series tails, we show that each remaining Born term tends to zero. The fixed-order estimates combine bounds for the absolute kernels with oscillatory cancellation and a duality argument for the product of the two Cauchy transforms.

Large language model (LLM)-empowered photonic agents connect natural-language intents to executable solvers, showing significant advantages over conventional optical design approaches. However, current multi-agent frameworks operate within a collaborative paradigm without extrinsic selective pressure, which could inherit shared blind spots, converge prematurely, and fail to accumulate transferable experience for intricate tasks. Here, we introduce a group photonics collaboration-compete evolution (GCCE) framework and its LLM instantiation, termed Photonics-GCCE. Two independent agent groups pursue the same design target and undergo structured competitive evaluation across refractive-index fidelity, fabrication sensitivity, algorithmic adequacy, and physical consistency. Each group comprises a leader and three specialist agents dedicated to materials, optimization, and code validation. Agents refine their skills through competitive evaluation across design rounds. Benchmarking across six device categories against single-agent and multi-agent baselines shows that Photonics-GCCE elevates composite scores into the high 90s, improves fabrication robustness by 15 to 17 points, and reduces solver iterations to roughly 40 rounds. A representative quasi?BIC demonstration achieves a practically fabricable design with a quality factor of 13120. Our results demonstrate Photonics-GCCE as a general-purpose and closed-loop framework for autonomous optical design, capable of producing high-performance, fabrication-ready devices across diverse nanophotonic tasks.

The High-Luminosity Large Hadron Collider (HL-LHC) will substantially increase the charged-particle multiplicity and detector occupancy in the ATLAS and CMS experiments, posing new challenges for the reconstruction of charged-particle tracks. Both experiments are upgrading their tracking detectors, with fully silicon-based systems providing a finer granularity, extended acceptance and updated geometry with respect to the current ones, with the goal to reduce the combinatorial complexity of pattern recognition tasks. At the same time, the more demanding reconstruction environment at the HL-LHC requires algorithms capable of retaining high tracking efficiency while reducing the associated computational cost. To this purpose, both the ATLAS and CMS Collaborations are developing tracking algorithms for offline and online reconstruction, exploiting parallelized, vectorized and heterogeneous architectures. The ATLAS experiment is moving toward an ACTS reconstruction chain, based on the Combinatorial Kalman Filter algorithm. In the CMS experiment, the new High-Level Trigger tracking baseline combines the Patatrack and the Line Segment Tracking algorithms for seed reconstruction, using the mkFit algorithm for track building. These developments yield tracking efficiencies above 85% across the full phase space at high pileup, extending the acceptance to forward and displaced tracks with transverse displacements of up to tens of centimetres, while significantly reducing the reconstruction time. Machine-learning techniques are also being explored at several stages of the reconstruction, including track building. The state-of-the-art performances of the tracking strategies developed by the ATLAS and CMS Collaborations for the HL-LHC are presented, together with prospects of further improvements.

We present the theory of exciton optical alignment and optical orientation effects in a single semiconductor nanoplatelet (NPL) and in an ensemble of NPLs. The theoretical model is developed to take into account the emission from both bright and dark exciton states in the case of strong electron-hole exchange interaction and an isotropic distribution of in-plane orientations of the NPLs' edges with respect to the linear polarization axis. The conditions for the linear optical response regime on the polarized resonant excitation of the bright exciton are considered, and the steady-state and time-dependent expressions for polarized photoluminescence are presented for the low temperature case in the Faraday magnetic field at normal incidence. The symmetry of the obtained optical response corresponds to the $C_{2}$ point group for the single NPL and the $C_{\infty}$ point group for the NPL ensemble. The bright-to-dark exciton coupling mechanism allowing one to observe the optical alignment of the dark exciton is considered. The example calculations of the effects are presented for the parameters close to those of CdSe/CdS core/shell NPLs. The effect of the fluctuations in the exciton parameters in the ensemble on the polarization dephasing in the transverse effective magnetic field is demonstrated.

Conference policies distinguish using Large Language Models (LLMs) to polish one's own review from delegating the critique, but current Artificial Text Detection (ATD) methods largely measure surface form rather than the origin of its content. We instead measure the external information carried by a review: information not explained by the reviewed paper and a generic reviewing instruction. We propose Self-Conditioning, an unsupervised information-theoretic estimator that compares the likelihood of a review under its production context with its likelihood when that context is augmented with hints extracted from the review itself. On the IntelLabs peer-review benchmark, Self-Conditioning separates fully-delegated from machine-polished reviews with AUC up to $1.0$ while remaining largely insensitive to surface rewriting. Moreover, as generators receive increasing amounts of externally-provided information, their scores move monotonically towards the human regime, unlike standard ATD baselines. High-temperature sampling can evade the estimator, but at the cost of output quality.

This paper characterises substantive agency and identifies the additional bridges under which it has a standard complexity-theoretic consequence: conditionally, P __ = N P . The constitutive core separates coherent plurality, causal openness, anticipatory non-pointing, act-level singularisation, and endogenous sourcehood. Its temporal claim yields a two-sided modal result: exact passive pre-act selection is incompatible with jointly retaining singularising priority and invariance under causally inert informational extension. If every standard polynomial procedure is deployable in that passive form, the actualisation map $\alpha$ has no polynomial-time selector. On an effective presentation, $\alpha$ is therefore either computable outside FP or noncomputable. A separate certifiedactualisation protocol supplies polynomially bounded, polynomially verifiable traces with extensional unique projection. This is the constructive interface that turns historical actualisation into a total standard search relation; combined with the modal result, it places that relation in TFNP search \ FP search , from which a self-contained search argument yields P __ = N P . The result is a domain-relative conditional transfer theorem: it neither assumes polynomial non-anticipability in the definition of agency nor proves that human decision-making satisfies the bridge and certification premises.

General expressions are derived for the amplitude equation valid at a Turing bifurcation of a system of reaction-diffusion equations in one spatial dimension, with an arbitrary number of components. The normal form is computed up to fifth order, which enables the detection and analysis of codimension-two points where the criticality of the bifurcation changes. The expressions are implemented within a Python package, in which the user needs to specify only expressions for the reaction kinetics and the values of diffusion constants. The code is augmented with a Mathematica routine to compute curves of Turing bifurcations in a parameter plane and automatically detect codimension-two points. The software is illustrated with examples that show the versatility of the method including a case with cross-diffusion, a higher-order scalar equation, and a four-component system.

We show functional inequalities with logarithmic weights as a critical case of Caffarelli-Kohn-Nirenberg inequalities. Original CKN inequalities have polynomial weights and are shown via scaling argument. In this paper, we develop this argument into it for nonlinear scaling. Our inequalities are generalizations of critical Hardy type inequalities.

A wave bifurcation is the counterpart to a Turing instability in reaction-diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a zero temporal eigenvalue. Such bifurcations require at least three components and give rise to patterns that are periodic in both space and time. Depending on boundary conditions, these patterns can comprise either rotating or standing waves. Restricting to systems in one spatial dimension, complete formulae are derived for the evaluation of the coefficients of the weakly nonlinear normal form of the bifurcation up to order five, including those that determine the criticality of both rotating and standing waves. The formulae apply to arbitrary $n$-component systems ($n\geq 3$) and their evaluation is implemented in software which is made available as supplementary material. The theory is illustrated on two different versions of three-component reaction-diffusion models of excitable media that were previously shown to feature super- and subcritical wave instabilities and on a five-component model of two-layer chemical reaction. In each case, two-parameter bifurcation diagrams are produced to illustrate the connection between complex dispersion relations and different types of Hopf, Turing, and wave bifurcations, including the existence of several codimension-two bifurcations.

Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with $n$ components and a diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on a study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to $\infty$, gives a constructive method for choosing diffusion constants. The results are illustrated on a model for the dispersion of malaria, a 3-component FitzHugh-Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4 components

Large-scale and high-dimensional discrete optimal transport often involves a tension between scalability and exact assignment feasibility: many scalable approaches optimize relaxed, factorized, or sparse transport plans rather than maintaining a one-to-one assignment throughout optimization. We introduce SWAP, an iterative solver that operates directly in permutation space for equally weighted point clouds. Starting from any feasible assignment, SWAP uses geometry-aware proposals to identify cost-decreasing local rearrangements. Consequently, every iterate is a valid permutation, so the one-to-one constraints are satisfied exactly throughout the optimization without rounding or feasibility correction. SWAP avoids constructing an $N\times N$ cost or coupling matrix and requires only $O(Nd)$ memory. We establish monotone descent, introduce a family of cycle-stability conditions, prove that SWAP reaches pairwise stability almost surely under generic nonparallel conditions, and derive sufficient conditions under which pairwise stability implies global optimality. Experiments on an ImageNet assignment with 640,500 points in 2,048 dimensions, synthetic benchmarks, and MERFISH spatial alignment demonstrate that SWAP achieves lower transport costs on challenging large-scale and high-dimensional problems, with substantially reduced runtime and memory compared with

In this paper, we investigate energy conservation for weak solutions to the two-component Camassa-Holm system. We derive a local energy balance equation in the sense of distributions with an explicit defect term. As an application, we determine that the Onsager exponent is 1, and as a consequence, we also obtain the uniqueness of weak solutions.

Outer-hair-cell (OHC) loss is a primary deficit of sensorineural hearing loss (SNHL), impairing cochlear amplification and frequency selectivity and thereby elevating hearing thresholds. Biophysically-inspired DNN-based hearing-aid (HA) algorithms have been proposed to compensate for OHC deficits and have shown clear benefits in objective speech intelligibility and quality metrics (e.g. HASPI, HASQI). However, comprehensive subjective validation of these benefits in human listeners is still missing. In this work, we present a subjective evaluation of a biophysically-inspired HA model targeting OHC deficits. The cochlear module of an auditory model was individualized based on each listener's pure-tone audiogram and integrated into a trainable system, which includes the personalized model and a normal-hearing reference model, and the resulting trained HA was evaluated using a Matrix test comparing intelligibility scores for unprocessed and HA-processed noisy speech. The results revealed a significant benefit of the HA model over the unprocessed condition in the range of +1 to +27%, providing behavioral confirmation of the efficacy of the HA model. This study closes the gap between objective and perceptual evidence for this new generation of DNN-based HA algorithms, paving the way for their integration into next-generation DNN-accelerated chips for hearables and hearing aids.

In a recent paper arxiv.org/abs/2609.21031, we have introduced the concept of a relational background field as a new approach to the renormalization group (RG) for discrete quantum gravity models, focusing on random matrix models. The proposed method offers the dual advantage of preserving the model's gauge symmetry (typically $U(N)$ or $O(N)$), whose breaking in conventional approaches has remained an open problem, and providing a more satisfactory treatment of the continuum or infrared (IR) limit. In this limit, the theory is described by a non-local field theory in dimension $D = 2k + 3$, where $k$ denotes the number of cuts in the effective spectrum as dictated by random matrix theory. This pedagogical paper reviews this construction for real random vector models in zero dimensions, with $O(N)$ as the symmetry group. Following the general strategy of background-field-type formulations, we show, using the BBP (Baik-Ben Arrous-P'ech'e) phase transition, that a partial Hubbard–Stratonovich decomposition of the quartic interaction, involving a matrix-valued intermediate field, allows a preferred notion of scale to emerge. This scale, in turn, defines an RG flow, whose perturbative structure is analyzed. Our calculation demonstrates the existence of an asymptotic Wilson–Fisher-type fixed point, whose sole relevant critical exponent is in qualitative agreement with the double-scaling critical exponent of these models.

The detection of gravitational waves (GWs) from compact binary coalescences (CBCs) using matched filtering is computationally demanding because detector data must be correlated with many template waveforms spanning a high-dimensional intrinsic parameter space. In our previous work, we showed that a convolutional neural network (CNN) can classify noisy signals against pure noise and constrain the intrinsic parameter space of a true non-spinning binary black hole (BBH) signal, enabling a narrower matched-filter search region and reducing computational cost. Here, we extend this framework to aligned-spin BBH systems and investigate how different parameter-space representations affect CNN-based patch identification. Using IMRPhenomD waveforms over the aligned-spin BBH parameter space and Advanced LIGO design sensitivity, we show that a CNN trained solely on the aligned-spin template bank achieves more than 99.8% signal-noise classification accuracy on independently generated uniformly sampled BBH signals, indicating that additional uniformly sampled training data are unnecessary. We partition the template bank into four approximately balanced patches using a Principal Component Analysis (PCA)-based quantile scheme and evaluate five parameter-space representations for patch identification. The chirp mass-duration representation achieves the highest average accuracy (93.2%), followed by chirp mass (91.6%) and component masses (90.5%). The post-Newtonian coordinates tau_0-tau_3 and theta_0-theta_3-theta_3s yield substantially lower accuracies. These results show that the existing template bank is sufficient for training and high-accuracy signal detection, while the choice of parameter-space representation is critical for constraining the parameters of the true signal.

Lenticular (S0) galaxies that remain actively star-forming (SFS0s) are a unique transition population among galaxies. We investigated the HI (21cm) neutral hydrogen content of a sample of lenticular galaxies identified from within the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey and which have been classified as star-forming or quiescent (qS0s). We compared these populations to each other and to a sample of star-forming spiral (SFSp) galaxies in MaNGA. We found that the HI mass fraction and HI deficiency of the SFS0s were intermediate between the qS0s and the SFSps, but more similar to the spirals. The HI depletion time of the qS0s is very much longer than that of the SFS0s and spirals, which have roughly similar times. We also compared the molecular gas fractions of the three groups which shows that the lowest fraction of the three populations is found in the qS0s, followed by the SFS0s and then the SFSps. A comparison of total baryonic mass indicates that the SFS0s have significantly lower masses than the qS0s in the sample. This suggests that the SFS0s must form from lower mass progenitors (unobserved by MaNGA) which either accrete external gas or lose spiral arms. The more massive qS0s are a completely separate population, most likely to be formed either from fading SFSps or from medium- to high-mass spirals undergoing mergers. The SFS0s in this sample cannot form from the qS0s in this sample that receive in-falling gas, nor can they fade to create these qS0s.