Time series analysis is a fundamental component of machine learning, especially in astrophysics and cosmology where temporal data abound. This chapter provides a pedagogical review of time series analysis techniques from a machine learning perspective. We cover the basic concepts of time series (stationarity, autocorrelation, seasonality), classical statistical models (autoregressive, moving average, ARIMA, exponential smoothing, state-space models), and modern machine learning approaches. In particular, we discuss how traditional statistical methods lay the groundwork, and then explore machine learning methods for time series, including feature-based regression, tree-based ensemble methods, hidden Markov models, Gaussian processes, and deep learning models (recurrent neural networks, convolutional networks, transformers). Throughout, we illustrate with examples drawn from multiple domains (e.g. astronomy, weather forecasting, finance) to emphasize common principles. The goal is to equip readers with both the theoretical understanding and practical context to apply machine learning techniques for time series analysis in their research.

The behavior of higher-order radiative corrections due to initial state radiation in processes of electron-positron annihilation is analyzed. Numerical results for energies of future colliders are presented. Uncertainties of the known results on these corrections are estimated. A modified scheme for simultaneous exponentiation of pure photonic and non-singlet pair corrections is presented. Matching of the exponentiated results with the existing analytic higher-order calculations is constructed. A new DIS-like subtraction scheme is discussed.

Imaging Atmospheric Cherenkov Telescopes (IACTs) are the leading instruments for very-high-energy (VHE) gamma-ray astronomy, covering the range from hundreds of GeV to hundreds of TeV. This chapter reviews the critical role of machine learning in reconstructing the physical properties of particles detected by IACTs. We introduce the IACT technique and its central challenge: distinguishing rare gamma-ray showers from the overwhelming cosmic-ray background. We detail the standard reconstruction pipeline, from image cleaning and Hillas parameterization to stereoscopic observation, and frame event reconstruction as a supervised learning problem encompassing particle classification and energy/direction regression. Two frontiers of innovation are then explored: the exploitation of the temporal dimension of shower images through novel timing-based features that enhance background rejection at low energies, and the application of advanced ensemble methods (gradient boosting, stacking) that surpass baseline Random Forests, notably in mitigating systematic energy bias. Finally, we discuss performance metrics and provide an outlook on next-generation approaches dominated by deep learning, including Convolutional and Graph Neural Networks.

State root computation dominates (78%) blockchain block processing time. Ethereum's canonical authenticated data structure, i.e., Merkle Patricia Trie (MPT), suffers from severe tree-height growth and is vulnerable to \textit{Nurgle attacks} (SP'24), where adversaries inflate path depth via hash collisions and degrade system performance at negligible cost. Existing defenses increase node fanout (span) to bound tree height, but higher span inflates proof size exponentially. Prior work mitigates this trade-off using vector commitments, at the cost of trusted setup or expensive verification. We present \textsc{Mhot}, a height-optimal authenticated data structure for blockchain state commitment that preserves standard hash-based verification without trusted setup. Unlike MPT's fixed-prefix indexing, which couples span and fanout exponentially, \textsc{Mhot} indexes by discriminative bits that actually distinguish keys, achieving adaptive span with linear fanout coupling and provably minimal height. To prevent high fanout from inflating proofs, we introduce hierarchical proofs, a two-layer Merkle construction that reduces per-node proof overhead from O(k) to O(log k). On Ethereum mainnet workloads, \textsc{Mhot} achieves up to 9X higher write throughput, 4X lower write amplification, and 2X smaller proofs than MPT. Under Nurgle attacks, even when the adversary consumes an entire block's gas budget, \textsc{Mhot} maintains a 0% attack success rate (v.s., 99.97% for MPT). Our results, somewhat surprisingly, show that height optimality (not new crypto primitives!) is the key abstraction for scalable and attack-resilient blockchain state commitment.

This paper proves normalisation theorems for intuitionist and classical positive free logic, without and with the iota operator for definite descriptions `the F'. Positive free logic also opens a number of options for rules for iota. In total, six different formalisations of theories of definite descriptions will be discussed, three proposed by Lambert, and three alternatives. The latter are motivated by considerations relating to proof-theoretic harmony between introduction and elimination rules. The philosophical importance of the various systems and results is indicated. The paper builds on Kürbis (2025), but is largely self-contained. The proofs for the present systems are easier than those for negative free logic.

This paper presents a novel class of high-order mass-, energy- and momentum-preserving exponential integrators for solving the derivative nonlinear Schrödinger equation. Firstly, we reformulate the original system into an exponential supplementary variable system based on the idea of the exponential supplementary variable approach, and then the reformulated system is discretized by using the standard Fourier pseudo-spectral method in space and the high-order prediction and correction Lawson Runge-Kutta method in time, respectively. The proposed method is highly efficient, temporally high-order accurate, and simultaneously preserves the mass, energy and momentum in the discrete setting. Finally, numerical experiments validate the accuracy and energy-preserving properties.

We analyze the geometry and kinematics of substructures within molecular clouds identified in an unbiased catalog from the MWISP survey. These substructures are defined as spatially connected regions enclosed by the 20% peak-integrated-intensity contour of each cloud. After applying selection criteria on voxel size and excluding structures truncated by map boundaries, we construct a sample and quantify their projected morphology using the projected scale ratio $R=Δb/(Δl\cdot\cos b)$. This ratio essentially measures $\tanθ$ where $θ$ is the plane-of-sky angle of an elongated filament relative to the Galactic plane. The resulting sample exhibits a median $R=0.96$, indicating a slight but systematic preference for elongation along Galactic longitude. This tendency becomes more pronounced at larger spatial scales. We further investigate the relative orientations among the structural major axes, velocity-gradient directions, and plane-of-sky magnetic-field orientations derived from Planck data for a subsample of well-defined structures. We find that, for cloud structures within our sample, with physical scale $\sim 0.3$ to $\sim 30$ pc, velocity gradients tend to be perpendicular to the major axes, while magnetic-field are generally aligned parallel to them. This scale range differs from those typically probed in studies of dense cores ($\sim 0.05$ pc) and GMC-scale structures ($\gtrsim$ 10 to 100 pc), which have reported scale-dependent variations in relative orientations. In addition, the alignment between velocity gradients and magnetic fields shows a gradual weakening with increasing physical scale. These results suggest that the observed anisotropy of molecular cloud substructures may arise from a combination of large-scale Galactic dynamics, anisotropic gas motions, and magnetic fields, with the relative importance of these effects varying with scale.

In this paper, we investigate energy extraction via the Comisso-Asenjo (CA) magnetic reconnection process near a coupled $\mathcal{N}=2,\,U(1)^2$ gauged supergravity Black Hole (BH). Our study focuses on the combined impact of the independent parameter set $p_i\in(N_g,g,v,e)$ with the spin parameter $a$ on the extracted energy ($ε_{\pm}$), efficiency ($η$), and extracted power ($\mathcal{P}_{CA}$), aiming to identify optimal combinations where energy can be extracted with higher efficiency in certain cases at lower spin $(a\sim0.39)$ than the Kerr extremal case $(a\sim1)$. Using the spacetime parameters, we explore various cases leading to distinct spacetimes and provide an extended comparison with the Kerr Black Hole (KBH). We also examine the influence of the orientation angle ($ξ$) and magnetization parameter ($σ_0$) on both efficiency and extracted power. Investigating low $[\,\forall p_i<0.2 \land N_g<0.08\,]$, mid $[\,\exists p_i\ge0.5 \land N_g\in(0.08,0.15)\,]$, high $[\,\exists p_i>0.7 \land N_g\in(0.16,0.23)\,]$, and mixed $[\,\forall p_i\in(0,1) \land N_g\in(0,0.23)\,]$ parameter combinations, we explore only extremal cases for all spacetime parameters and demonstrate that the extremal Kerr efficiency limit ($η>1.495$) can be exceeded. The statistical Kendall's Tau approach allows us to identify the key independent parameters acting as boosters or dampers in the energy extraction process and to visualize the relationship between $(N_g,g,v,e)$ and the physical outputs $(a_{\rm ext},r_E,r_{\rm ergo},ε_{\pm},η,\mathcal{P}_{CA},R_η,R_{\mathcal{P}})$. Furthermore, we show that the observable Lundquist number $S_{\rm obs}$ in rotating BH spacetimes acquires an observer-dependent angular dependence through the lapse function $(α)$. This leads to deviations from the standard Sweet-Parker scaling when expressed in terms of observable quantities.

We study the dynamics of quantum correlations in the hydrogen hyperfine spin system subject to Markovian phase noise. Treating the electron and proton spin degrees of freedom as an open two-qubit system governed by an isotropic hyperfine Hamiltonian and local dephasing, we obtain the exact time-dependent density matrix and derive analytical expressions for the full X-state family. We compute concurrence($C$), trace-distance measurement-induced nonlocality (Trace MIN--$\mathcal{N}_1$), and average steering coherence (ASC) in closed form and establish their strict ordering $ C(t)\leq \mathcal{N}_1(t)\leq \mathrm{ASC}(t) $ at all times. Entanglement is identified as the most fragile resource, undergoing sudden death at a finite time. Trace MIN exhibits dephasing-immune freezing for states with nonzero population imbalance, while ASC is the most robust quantity, persisting longest in every scenario studied.We additionally demonstrate that the dephased thermal hyperfine state serves as a resource for quantum teleportation, deriving a closed-form expression for the average fidelity and establishing that the teleportation advantage window coincides exactly with the entanglement survival interval, $\mathcal{F}_A > 2/3 \Longleftrightarrow \mathcal{C} > 0$, for the full X-state family with maximally mixed marginals. We identify four distinct dynamical regimes and map all three correlation measures onto directly measurable Pauli spin correlators, enabling experimental reconstruction of the full hierarchy without full state tomography.

How should one design efficient chemically open optical cavities for molecular strong coupling? Addressing this question is important for the development of soft-cavity platforms for dynamically tunable light--matter interactions, where direct access to confined electromagnetic modes is essential. Conventional cavity figures of merit such as $Q/\sqrt{V}$ and cooperativity successfully describe spectral confinement and dissipation but do not fully capture the role of linewidth asymmetry between cavity and molecular degrees of freedom. Here, we systematically investigate strong coupling between TDBC dye molecules and whispering gallery modes of polystyrene microspheres by varying the microsphere radius over a broad range. To quantify the robustness of strong coupling, we define the parameter $χ= \frac{g}{\max(κ,γ)}$, where $g$ is the coupling strength, while $κ$ and $γ$ denote the cavity and molecular linewidths, respectively. Although the coupling strength decreases monotonically with increasing cavity size due to mode-volume scaling, we find that $χ$ exhibits a pronounced maximum near the condition $κ\approx γ$. This observation suggests that linewidth matching is not merely a criterion for improved spectral visibility, but reflects a dissipation-matching condition that optimizes the robustness of coherent light--matter exchange in soft-cavities. Our results provide an alternative framework for designing morphology-dependent cavities for molecular strong coupling.

Industry has embraced Zero Trust (ZT) architectural tenets and implementations for cloud-native environments, following stricter security requirements to both internal and external tenants. Among others, these approaches combine fine-grained identity management and monitoring for both inventorying and better analysing the devices' security posture for overall protection, along with strict separation of concerns and isolation to enforce minimal privilege. Networking-wise, ZT approaches rely as well on isolation and least privilege; enacted by separate, secure tunnels per tenant connecting to a given infrastructure. Such implementations can also be applied to the connectivity within and towards experimental infrastructures. In this sense, this work contributes the design and evaluation of a cloud-native VPN-as-a-Service (VPNaaS) that can be (i) easily orchestrated to deploy on-the-fly, separate tunnels per each tenant remotely connecting to the infrastructure; (ii) integrated with common Identity and Access Management (IAM) tools, key to ZT deployments; and (iii) adapt to computing- or entropy- constrained environments. This solution is customisable and allows, among others, to select from RSA or Elliptic Curves (EC) as key generation algorithm and their parameters to achieve more secure keys and adapt to resource-constrained environments.

Gravitational waves from extreme-mass-ratio inspirals (EMRI) provide a direct probe of the strong-field geometry of black holes. Motivated by this, we study the motion of test particles and the resulting gravitational wave emission in the spacetime of a charged black hole inspired by loop quantum gravity (LQG), where the classical singularity is replaced by a smooth transition surface arising from the LQG polymerization, in which its radius is set by the LQG area gap condition. As a result, the polymerization parameter $δ_b$ is uniquely determined by the mass $M$ and charge parameter $Q$, so that all cases examined in this work contain LQG correction. By constructing the effective potential, the innermost stable circular orbit (ISCO) and the marginally bound orbit (MBO) are determined. Periodic orbits are classified using the Levin-Perez-Giz zoom-whirl taxonomy, showing how the orbit topology shapes the waveform, so that each closed trajectory is labeled by the triple integer $(z, w, v)$ and located through the rational frequency ratio $q = ω_ϕ/ω_r - 1$. Within the quadrupole approximation, the gravitational waveforms for an EMRIs are estimated, and the resulting polarizations are obtained in the time-domain and frequency-domain. The resulting polarizations in the time-domain exhibit a zoom-whirl morphology, with the waveform amplitude and phase dependent on the LQG parameter. The characteristic strain peaks in the millihertz band for all values of the charge parameter $Q$, and they exceed the projected sensitivities of LISA, Taiji, and TianQin, suggesting that future observations could place meaningful constraints on the LQG polymerization parameter in the strong-field regime.

Let $X$ be the Segre product of three projective lines. For a fixed effective divisor $D$ on $X$, we introduce the notions of $D$-'t Hooft, $(D_i,D_j)$-special and $D$-sectional special bundle. The varieties parameterizing these bundles yield a natural stratification of the moduli space of stable instanton bundles with fixed Chern classes. After characterizing the curves associated with these bundles via Serre correspondence, we describe the corresponding Hilbert schemes. Using this description, we analyze the moduli spaces of $h_i$-'t Hooft bundles and the smaller strata of $(h_i,h_j)$-special and $(h_i)$-sectional special bundles. Finally, we provide a detailed study of the low-charge cases.

This document is a pdf generated from old plain-TeX files of 1986, of Nils Lid Hjort's `Notes on the Theory of Statistical Symbol Recogntion', a limited circulation 207-pages monograph published at the Norwegian Computing Centre, as Report no. 778/1986. It gives the basics of the statistical pattern recognition theory developed to suit the needs of several industrial projects, related to contracts with the Norwegian-German firm SysScan, the Royal Norwegian Research Council, and yet others, involving symbol recognition and classification analysis from noisy images, related to maps, documents, satellite imaging, etc. The methods and algorithms developed also needed to fit the technology of that time, anno c. 1986, with machines scanning documents, converting these to vector representation, within computational and machine system boundaries. There is an accompanying and also limited circulation booklet, `Statistical Symbol Recognition: Development of a System', by Knut Bråten, Erik Holbæk-Hanssen, and Torfinn Taxt (Report No.777/1986, Norwegian Computing Centre, Oslo), detailing the system developments. Thus developments took form and shape on two frontiers, in close collaboration, Hjort's statistical methods and getting the technology to work, with its multiple components, hardware and software.

We perform a Bayesian inference analysis of an inflationary model based on an inverse-tangent potential, incorporating reheating dynamics in both constant and dynamical equation-of-state (DEOS) frameworks. Using Planck and ACT constraints on the scalar spectral index, we find preferred values $κ\simeq0.5-0.6$ and $N_k\simeq40-60$, leading to reheating temperatures $T_{RH}\sim10^{10}-10^{14}$ GeV and reheating durations $N_{RH}\sim3-36$ e-folds. Reheating weighted $H_0$ posteriors shift the Planck inference towards the ACT preferred region through the intrinsic $n_s-H_0$ degeneracy of the CMB likelihood. In the DEOS framework, reheating with a constant decay rate yields $N_{RH}\simeq4-8$ e-folds and $T_{RH}\simeq10^{13}$ GeV, while a dynamical decay rate produces a strong dependence on the Yukawa coupling $y$, with $N_{RH}$ varying from $\mathcal{O}(30)$ to $\mathcal{O}(1)$ e-folds and the reheating temperature spanning $\sim10^{-2}-10^{14}$ GeV. Imposing inflation-reheating consistency significantly restricts the viable parameter space to a narrow region around $n_s\simeq0.9720-0.9725$ and $r\simeq0.026-0.060$, demonstrating that reheating dynamics provide a nontrivial bridge between early-universe inflation and late-time cosmological parameter inference.

We show that if $M$ is a metric space of Nagata dimension at most $d$, then there exists an atlas on $M$ modeled on $\mathbb R^d$ such that every Lipschitz map $f:M\to Y$ (with values in an arbitrary Banach space $Y$) can be uniformly approximated by maps that are affine, and thus $\mathcal{C}^1$-smooth, with respect to this atlas. The construction relies on random metric partitions and stochastic retractions inside Lipschitz-free spaces. As an application, we introduce approximate continuous upper gradient $X$-structures (ACUG $X$-structures) on metric spaces and prove that every space of finite Nagata dimension carries an ACUG structure modeled on a superreflexive Banach space. Finally, adapting a proof due to Bourgain, we show that if $M$ has an ACUG superreflexive-structure, then the Lipschitz-free space $\mathcal{F}(M)$ has Pelczyński's property (V*). In particular, at least in the compact case, our result recovers all previously known examples of metric spaces $M$ for which $\mathcal{F}(M)$ has property (V*).

Molecular hydrides have attracted relatively less attention in the search for high Tc superconductors because their hydrogen quasi-molecular units tend to be electronically inactive for superconductivity. In contrast, hydrogen rich compounds under high pressure have been widely considered strong candidates for achieving room-temperature superconductivity. However, their dependence on extreme pressure conditions significantly constrains their practical applicability. This work investigates hydrogen-rich superconducting materials that may be stable under ambient pressure conditions. Motivated by recent studies on the MgZrH2n family, a LiMgZr2H12 structure with Pmmm symmetry was designed. The mechanical, thermodynamic, and dynamical stability of the compound, together with its electronic and optical properties, were systematically investigated using first-principles calculations. Li doping in LiMgZr2H12 significantly increases the hydrogen derived contribution near the Fermi level (EF) and strengthens the electron-phonon coupling constant (λ) compared with MgZrH6. LiMgZr2H12 exhibits a critical temperature of 72.76 K at ambient pressure, which is further enhanced by applying pressure. At 10 GPa the critical temperature increases to 77.3 K. Elastic property analysis shows that the material remains mechanically stable over the pressure range studied (0-10 GPa). It also behaves like a ductile material suitable for current carrying applications. The material has a high machinability index, which is much higher than that of stainless steels. In addition, LiMgZr2H12 exhibits a gravimetric hydrogen storage capacity of 5.36 wt%, indicating its potential as a promising candidate for hybrid hydrogen storage technologies. This work offers a new direction for designing high-Tc hydrides at ambient conditions.

We formulate and prove a conditional finite-scale reduction theorem for the local one-component regularity problem for suitable weak solutions of the three-dimensional Navier--Stokes equations. Starting from a scale-invariant bound Phi(1) <= M and smallness of the critical vertical component C_3(1) = delta, the argument compares the solution with a strict two-and-a-half-dimensional shadow class. The comparison is made in the harmonic-pressure quotient, which is the natural local topology for pressure compactness. The Reynolds commutator produced by coarse graining is treated as a positive covariance stress and is absorbed by an unresolved-variance buffer; consequently this stress contributes additively, while the genuinely vertical residuals carry a positive power of delta and may pass through finite-stage exponential constants. The theorem is deliberately stated as a reduction theorem. Under the explicitly listed structural inputs--prepared pressure-covariance closure, weak horizontal-defect admissibility, sharp admissible-time trace tightness, singular-stratum tangent-cone inputs, strict limiting smoothing and decay, finite-window trace-cost/Newton solvability, and the vertical-duality active-residual estimate--we derive r_reg(0,0) >= c_{M,theta} |log C_3(1)|^{-sigma/3}. The paper does not constitute an unconditional resolution of the logarithmic one-component regularity problem. Its contribution is a theorem-driven reduction: strict-shadow selection failure is reduced to a finite-mode flat trace obstruction, and that obstruction is eliminated, conditionally, by vertical duality forced by the full three-dimensional vertical momentum equation.

Motivated by the observed $KD^{(*)}$ molecular candidates $D_{s0}(2317)$ and $D_{s1}(2460)$, their bottom--strange counterparts, $K\bar{B}^{(*)}$ molecular states, are naturally expected, although not yet experimentally established. This discrepancy may reflect sizable heavy-quark flavor symmetry breaking, which introduces significant model uncertainties. Current studies of heavy-quark flavor symmetry breaking effects still exhibit strong parameter dependence, and further experimental input is required to constrain these effects, in particular regarding possible additional $K^{(*)}D^{(*)}$ and $K^{(*)}\bar{B}^{(*)}$ molecular states. In this work, we examine whether additional $K^{*}D^{(*)}$ molecular states can be identified among the observed $D_s$ resonances. Within the Gaussian expansion method, we solve the Schrödinger equation using $σ$, $ρ$, $ω$, $π$, and $η$ exchange potentials, systematically including $S$-wave and higher partial waves. We find that $D_{s1}(2700)$ can be interpreted as a pure $P$-wave $DK^{*}$ molecule, while $D_{s1}(2860)$ and $D_{s3}(2860)$ are well described as $D^{*}K^{*}$ molecular states dominated by the $^{1}P_{1}$ and $^{5}P_{3}$ components, respectively. We also predict additional molecular states with various $J^{P}$ quantum numbers. These results provide a new description of the charmed--strange spectrum and a useful benchmark for heavy-quark flavor symmetry breaking effects.

Under the canonical setting of observational studies for causal inference, we show that the average treatment effect under the overlap weight, the weight that is proportional to the conditional variance of the treatment given the covariates, is bounded between the average treatment effects on the treated and control, under a monotonic relationship between the propensity score and the conditional average treatment effect. We further extend the result to weighted local average treatment effects, under the canonical setting with a binary instrumental variable and a binary treatment. We also extend the results to other weights. Based on the theory, we recommend the ``CP-plot'' of the estimated conditional average treatment effect against the estimated propensity score.

We are developing a compact three-element Wide Field Corrector (WFC) with spherical and aspherical lenses for the 2.34 m Vainu Bappu Telescope (VBT) to enhance its field coverage for imaging and spectroscopic applications. The design consists of three optical elements, with at least one spherical lens movable to serve as an Atmospheric Dispersion Corrector (ADC), while the aspherical elements remain fixed to maintain optical stability. We are currently testing two design configurations, one with two spherical lenses and one aspherical lens, and another with two aspherical lenses and one spherical lens. The ADC is designed to correct atmospheric dispersion for zenith angles ranging from 0 degree to 60 degree. The system is optimized to operate over a wavelength range of 0.4 μm to 0.9 μm, targeting an effective field of view of about 0.5 degree. Considering the limited mechanical space available at the VBT prime focus, the design emphasizes compactness, ease of alignment, and manufacturability. The system achieves a mean D80 better than 0.3 arcsec and 0.23 arcsec for Design 1 and Design 2, respectively, at zenith, and maintains a mean D80 within 0.57 arcsec and 0.45 arcsec up to a zenith angle of 60 degree after atmospheric dispersion correction. Atmospheric dispersion at higher zenith angles (up to 60 degrees) is corrected using a movable lens element, enabling the system to preserve high image quality across the field.

We explicitly compute the axial anomaly in dense matter and show that its form remains unchanged from that in vacuum, even in the massless limit. This result follows from a subtle cancellation in the anomalous Ward identity between the medium-induced contributions to the divergence of the axial current and to the pseudoscalar density. We then revisit the chiral magnetic effect in a fermionic medium coupled to an axial chemical potential under an external magnetic field. We show that the medium supports a persistent, conserved anomalous current carried by fermions. The current is determined by the axial chemical potential and suppressed by the Fermi velocity, in agreement with anomalous axial-current correlation functions. We finally discuss applications to axion physics, where axion dark matter acts as an effective axial chemical potential.

The classical p-adic Cauchy theorem asserts that formal solutions of ordinary p-adic differential equations are convergent. In this article we establish a geometric analogue of this result for arbitrary smooth rigid-analytic varieties. More precisely, we show that the horizontal sections functor defined using the overconvergent de Rham period structure sheaf agrees with Scholze's horizontal sections functor defined using OBdR. Equivalently, every formal solution arising from Scholze's construction is already overconvergent. As an application, we identify Scholze's horizontal sections functor with the de Rham functor for D-cap-modules on vector bundles with flat connection.

In this article, we present a new approach to studying multivariate period rings that is more consistent with classical theory and provides a clearer description of their structure. We also prove that the category of $B$-admissible representations forms a Tannakian subcategory of the category of representations of $G_{K,Δ}$ by defining an analogue of $(F,G)$-regular rings, which is central to the classification of representations in multivariate $p$-adic Hodge theory.

During the evolution of a binary black hole, energy and angular momentum are exchanged between the orbital motion and the individual black holes through horizon absorption, modifying both the binary dynamics and the black hole masses and spins. This leaves an imprint on the emitted gravitational waves that may be relevant for the accurate modeling of signals observed by current and future detectors, while also offering a probe of the nature of compact objects. In this work, we derive, for the first time and at leading order in the post-Newtonian expansion, the effect of horizon absorption in binary black hole inspirals with both orbital eccentricity and spin-induced precession, and we incorporate these corrections into the pyEFPEHM waveform model. We then quantify their impact through analytical estimates of the orbital dephasing, waveform mismatches, and Bayesian parameter-estimation studies. The effect is largest for systems with large spin components (anti-)aligned with the orbital angular momentum ($|\vecχ_i \cdot \hat{l}| \sim 1$), highly unequal mass ratios ($q=m_2/m_1 \ll 1$), and long inspirals spanning a wide frequency range ($\log(f_\mathrm{max}/f_\mathrm{min}) \gg 1$). For such systems, neglecting horizon absorption biases the recovered binary parameters at moderate signal-to-noise ratios. In quasi-circular binaries these biases largely absorb the effect, rendering it difficult to detect. In eccentric binaries, however, the richer signal morphology breaks this degeneracy, making horizon absorption potentially measurable in high signal-to-noise-ratio events.

Artificial intelligence is driving intense interest in alternative computing hardware capable of neural information processing beyond conventional charge-based electronics. Among emerging approaches, wave-based computing promises highly parallel and energy-efficient operation, but scalable physical neural hardware has remained elusive because wave systems generally lack cascadable nonlinear neurons with signal regeneration and phase-robust operation. Here we demonstrate integrated magnonic neural circuits based on nonlinear threshold neurons realized in nanoscale yttrium iron garnet waveguides. The neurons perform weighted summation of multiple spin-wave inputs, while a pump-controlled nonlinear activation defines continuously tunable firing thresholds. Owing to deeply nonlinear spin-wave dynamics, the activated neurons emit self-normalized outputs whose intensities are largely independent of the input amplitudes, while nonlinear phase self-adjustment suppresses sensitivity to the relative input phases, enabling deterministic neuron-to-neuron cascading without external signal restoration. We experimentally realize programmable threshold neurons, reconfigurable weighted classification and deterministic cascading between sequential neuronal stages, and further demonstrate reconfigurable physical pattern recognition in a seven-neuron integrated magnonic circuit through experimental classification of the binary letter patterns 'HUST'. These results establish nonlinear magnons as a scalable platform for integrated neural hardware and position nonlinear wave dynamics as a general paradigm for physical neuromorphic computing.

Multireference alignment (MRA) is the task of recovering a hidden "signal" vector, given many noisy copies that have been cyclically shifted by unknown offsets. This task belongs to the class of orbit recovery problems, in which the observed samples are affected by some group action. These problems have a variety of practical motivations, including the reconstruction of 3-dimensional molecular structure from cryogenic electron microscopy (cryo-EM) images. We consider two variants of MRA: dihedral MRA, where the cyclic group is replaced by the dihedral group, allowing for reversals of the vector in addition to shifts; and projected MRA, where the observations are passed through a projection operator akin to the tomographic projection present in cryo-EM. We apply the method of moments and aim to recover the signal from the third moment tensor of the samples. This inverse problem is well understood for basic MRA, but for the variants we consider there is no polynomial-time algorithm known to succeed for generic signals. We give the first such algorithm for both of these variants. Our method requires the signal length to be a power of two, and recursively subdivides the problem into smaller problems of half the size. The algorithm's success for generic signals is proven, conditional on a conjecture about the rank of a certain symbolic matrix of polynomials. For any given problem size, this conjecture can be verified on a computer.

Large language model (LLM) rerankers have become an important component of modern retrieval and retrieval-augmented generation pipelines, but their high computational cost limits their applicability to long candidate lists. In this paper, we propose \textbf{CompRank}, a token-efficient reranking framework that reduces redundant computation by aligning reranker design with the sparsity of ranking signals. CompRank decouples document representations from candidate order and query context, enabling reusable document-side states; applies segment-wise token compression to reduce query--document interaction cost; and introduces a CopyNet-style objective that directly aligns attention-based document scoring with training supervision. Experiments on seven BEIR datasets show that CompRank achieves strong reranking performance while retaining only 10.2\% of document tokens, reaching an average NDCG@10 of 39.2 compared with 39.7 under full-token attention. Further scaling experiments on TREC-COVID show that CompRank remains stable when evaluated on candidate lists of up to 500 documents after training on 30-document lists, while achieving $4.9\times$--$9.5\times$ end-to-end speedup over generation-based listwise reranking and approximately $1.3\times$ speedup over the full-token CompRank variant. These results suggest that token-level compression and decoding-free attention scoring provide an effective path toward scalable LLM-based reranking.

In this paper, we investigate finite and infinite decomposition formulas for zero mean curvature (ZMC) graphs in three-dimensional spaces with different metrics, including Euclidean space, Lorentz--Minkowski space, and isotropic 3-space. We first derive new Euler--Ramanujan-type identities yielding decompositions for the conjugate of Scherk's first minimal surface in terms of dilated catenoids. We then employ Weierstrass factorisation and power series techniques to obtain infinite decompositions for a broad class of ZMC graphs in isotropic 3-space into helicoids, logarithmoids of revolution, and Enneper surfaces. We further extend these decomposition results to larger families of ZMC surfaces across these spaces by considering surfaces arising from the López--Ross transformation, Bonnet rotation, and a one-parameter family of metric deformations. We also investigate finite decompositions, establishing finite analogues of Scherk tower decompositions in both Euclidean and isotropic settings. In addition, we prove a theorem characterising finite decompositions of isotropic minimal surfaces. Finally, we discuss applications of the resulting decomposition theory to lamellar structures.

Similar to the behavior of elementary particles, such as photons and electrons, the interference of phonon waves in artificial periodic nanostructures coherently modulates phonon band structures, serving as the foundation for phonon band engineering. However, direct observation of such coherently modulated phonon band structures remains challenging despite substantial insights from existing literature. Here, utilizing high-resolution inelastic X-ray scattering, we observed coherently modulated phonon band structures with phononic band gaps in a short-period GaAs/AlAs superlattice at 300 K and 500 K. Our findings provide the first direct evidence of phonon coherence at and above room temperatures, signifying a major advancement in the artificial engineering of phonon band structures. Furthermore, our experimental observations and ab initio lattice dynamics revealed that the coherently modulated phonon band structure enhances three-phonon scattering channels, strengthening high-order anharmonic effects such as three-phonon scattering and optical phonon softening. Our observations demonstrate the robustness of phonon coherence at high temperatures, and opens new routes for engineering phonon band structure and high-order phonon-phonon scattering by employing a flexible, bottom-up nanostructuring approach, with extensive applications in phononic metamaterials, microelectronics, and thermoelectrics.