Given an acyclic directed graph (DAG), the space of strength one flows is a lattice polytope called the flow polytope of the DAG. If the DAG admits an ample framing, then the flow polytope is Gorenstein and it linearly projects onto a reflexive polytope called the $\mathbf{g}$-polytope. We provide a combinatorial characterization of amply framed DAGs that have a locally anti-blocking $\mathbf{g}$-polytope, and we characterize the minimal faces of the $\mathbf{g}$-polytope containing a fixed pair of vertices. We prove in this case that the unimodular triangulation of the $\mathbf{g}$-polytope induced by the DKK triangulation of the flow polytope is a pulling triangulation, and we characterize the pulling orders that yield the DKK triangulation. To prove our results, we introduce and study coherence diagrams, a combinatorial model of coherence for amply framed DAGs with locally anti-blocking $\mathbf{g}$-polytopes. We conclude by indicating possible extensions of these results to the setting of $\mathbf{g}$-polytopes for gentle Nakayama algebras.

An over-the-air (OTA) experimental evaluation of concurrent 5G New Radio (5G NR) and Wi-Fi transmission using successive interference cancellation (SIC) in a shielded-box environment is presented. A USRP is used as the receiver, which captures the composite waveform containing both air-interface signals and applies sample-domain SIC to suppress the dominant 5G-NR signal and recover Wi-Fi signal from the residual waveform. The framework reports error vector magnitude (EVM), bit error rate (BER), sample-domain cancellation depth, and channel-estimate suppression, and, at the representative \(18\) dB attenuation point, measures \(11.88\) dB cancellation depth and \(26.96\) dB 5G channel suppression. The proposed methodology provides a practical basis for assessing cross-technology coexistence and receiver-side interference suppression under controlled OTA conditions.

Lattice Boltzmann methods are usually derived under the assumption of isotropy. In this work, we present a derivation of a Lattice Boltzmann method for anisotropic fluid flow. Starting from an anisotropic equilibrium distribution, we show a full derivation of the resulting lattice Boltzmann method. We ensure that our method correctly reproduces macroscopic behavior via Chapman-Enskog analysis for a single-relaxation time collision operator. As a result, we are able to show that a properly discretized anisotropic Maxwell-Boltzmann equilibrium does macroscopically in fact lead to an anisotropic variation of the Navier-Stokes equations. All desired properties of lattice Boltzmann methods, such as locality of the collision operator, isotropic discrete position and velocity space, or mass and momentum conservation are retained. While it is explicitly shown in the context of fluid flow, the presented scheme is straight-forward to adopt to advection-diffusion problems.

Small planets are extremely common in the Galaxy, including planets with masses and radii between those of Earth and Neptune. Characterizing these planets' masses requires ultra-precise radial velocities. The ESPRESSO spectrograph was designed and built for this purpose. We present an overview of the ESPRESSO Guaranteed Time Observations transit follow-up sub-program, aimed at confirming and characterizing small transiting planet candidates from the K2 and TESS space missions. We analyse the global stellar and planetary properties of the sample of 65 planets in 30 systems characterized by this sub-program. This includes six systems presented in this paper, for which we either obtain only upper mass limits, or provide updates to previously published parameters. We also place this sample in the context of the overall population of precisely characterized small planets. Separating the population into insolation regimes, we find a tentative mass threshold at $\simeq6\,M_\oplus}$ for the rocky to volatile-rich composition transition in the medium-insolation regime, and a population of likely stripped massive rocky planets in the high-insolation regime. We likewise find a correlation between planet mass and stellar metallicity, with more massive planets being hosted by more metal-rich stars. We also explore the radius valley, finding that planets below the gap have a tighter mass distribution. We compare planet masses with typical protoplanetary disk masses and draw tentative conclusions about likely formation conditions. Finally, we discuss the impact of our observing strategy on our results. The ESPRESSO transit follow-up sub-program has been highly productive, characterizing a diverse population of small planets that allows us to identify population-level features. Likewise, the lessons learned from this sub-program will be valuable for PLATO follow-up planning.

In this paper, we establish some modified defect relations for the Gauss map $g$ of a complete minimal surface $S\subset\mathbb R^m$ into $\mathbb P^n(\mathbb C)\ (n=m-1)$ with only a single Fermat hypersurface $Q$ of $\mathbb P^n(\mathbb C)$. In particular, we show that $S$ must have finite total curvature if the image $g(S)$ intersects $Q$ with only a finite number of times and the degree of $Q$ is sufficiently large.

Weexperimentally study the temperature dependence of the magnon-phonon coupling in a yttrium iron garnet (YIG)/gadolinium gallium garnet (GGG) heterostructure. More specifically, we use broadband ferromagnetic resonance to investigate the magneto-elastic coupling between the Kittel mode of a YIG thin film and the transverse acoustic phonon modes of the YIG/GGG high overtone bulk acoustic wave acoustic resonator for in and out-of-plane field directions in the temperature range between T = 5K and 300K. We find that for a magnetic field applied normal to the film surface, magneto-elastic coupling decreases with decreasing temperature, whereas it increases for the in-plane magnetic field configuration. The observed temperature dependence differs from earlier observations on bulk YIG samples, which might be due to the temperature dependent stress imposed by the GGG substrate.

Two meromorphic functions $f$ and $g$ are said to weakly share a small function $a$ with bi-weight $(n,k)$ if the functions $f-a$ and $g-a$ have the same zeros with multiplicities truncated at level $n+1$, while zeros whose multiplicities exceed $k$ are disregarded. In this article, we show that if two meromorphic functions $f$ and $g$ weakly share three small functions $a_i\ (1\le i\le 3)$ with bi-weights $(n_i,k)$ satisfying $n_1n_2n_3>n_1+n_2+n_3+2$ then $$(1-ε-δ_ε)T(r, f)\le (2+ε+δ_ε)T(r, g)+S(r, g)$$ for every positive number $ε$, where $δ_ε$ is explicitly estimated depending only on $ε$ and $k$, so that $δ_ε$ tends to zero as $k$ tends to $+\infty$.

This paper presents a controlled over-the-air (OTA) characterization of dual-user IEEE 802.11be Extremely High Throughput Multi-User (EHT-MU) transmission under transmit-chain imbalance. The objective is to determine whether attenuation applied to one access-point transmit chain produces packet-global degradation or appears primarily as stream-dependent payload degradation after receiver processing. Measurements are performed in a shielded RF enclosure using two NI USRP-2953R and NI USRP-2942R software-defined radios, with one USRP generating a dual-user non-OFDMA EHT-MU waveform and the other implementing synchronized dual-branch packet recovery. A calibrated attenuation sweep is applied to the second AP transmit chain (TX2), and performance is evaluated using bit error rate (BER), EHT-Data error vector magnitude (EVM), control-field success probability, payload-success probability, and subcarrier-level EVM distributions. The results show that the stream decoded as User~1 remains at the BER floor over the tested range, while the stream decoded as User~2 exhibits progressive EVM degradation followed by threshold-like BER and payload-success collapse. Common signaling fields remain recoverable, indicating that the dominant observed failure mode is stream-local at the receiver output than the packet-global. Replacing User~2 binary convolutional coding (BCC) with low density parity check (LDPC) coding delays the BER and payload-success collapse by approximately \(5\)~dB of TX2 attenuation, demonstrating a measurable coding-dependent robustness margin for the more sensitive stream.

We prove backward uniqueness for a class of ultraparabolic operators with coupled linear drift. The main difficulty is that the Fourier transform in the degenerate variables turns the coupled drift into a transport operator in the dual frequency variables, so the classical Littlewood--Paley Carleman argument does not apply directly. We overcome this by introducing an invariant frequency variable and establishing a frequency-localized Carleman estimate adapted to the transport structure. The result gives a partial answer to the question of W. Wang and L. Zhang $\left[ \emph {Methods Appl. Anal.}, \ 20 \ (1) \ (2013) \ 79-88 \right]$ for constant coupled drift, with diffusion and lower-order coefficients depending on time and the diffusive variables. As an application, for a jerk-driven control model, we prove backward uniqueness for the equation describing the position, velocity, acceleration, or jerk error: under bounded lower-order coefficients, zero final error in $L^2$ implies zero error at all earlier times.

We develop a theory for the acoustic radiation force on a liquid particle in a 2D standing-wave field beyond the Rayleigh limit. The theory is valid for any frequency, includes the traveling-wave components due to the Rayleigh angle, and is thus applicable to a large class of surface acoustic wave applications. The analytical results are validated with respect to finite-element models. Using our analytical solution, we determine the parameter space for which Rayleigh-limit methods, such as the Gor'kov framework, remain applicable. This range is shown to depend on the particle properties, the Rayleigh angle, and even the particle position in the acoustic field. We propose a general form for the acoustophoretic contrast factor applicable to any wavelength of 1D standing-wave field, broadening the applicability of the classical Gor'kov framework. We show that the Rayleigh-angle effect can substantially weaken the acoustic radiation force, an effect that has been largely overlooked. We also confirm a frequency-dependent topological transition of the acoustic landscape that induces a switching of the field attractors and particle equilibrium points. These results advance the quantitative theory of acoustic forces, unveil previously unresolved dynamical features of acoustofluidic fields, and provide a theoretical foundation for SAW-based cell trapping, separation, and enrichment in acoustofluidics.

Submarine eruptions, accounting for over 80% of Earth's volcanic activity, primarily occur along mid-ocean ridges, where shallow magmatic systems are accessible to high-resolution imaging. Yet, their remoteness often leaves them undetected. Recent seismic studies at the East Pacific Rise (EPR) 9°50'N-one of the most dynamic ridge segments, imaged the detailed architecture of the shallowest magma lens, but no data-constrained model yet explains how magma accumulates, migrates, or triggers eruptions. Similarly, the formation of oceanic crust remains poorly understood. While 2-D seismic data reveal only a few vertically stacked, transient magma lenses, our study applies matrix imaging, a novel technique in controlled-source seismology, to map the inner structure of on- and off-axis magma reservoirs. We uncover a conical on-axis reservoir and interconnected magma-rich zones throughout the crust. Combined with ophiolite evidence, these findings reveal that magma channels dominate the first 3 km for lower crust formation, while in situ crystallization prevails in the final 1 km, resolving a long-standing debate.

Two meromorphic functions $f$ and $g$ are said to weakly share a small function $a$ with bi-weight $(n,k)$ if the functions $f-a$ and $g-a$ have the same zeros with multiplicities truncated at level $n+1$, while zeros whose multiplicities exceed $k$ are disregarded. In this article, we show that if $f$ and $g$ weakly share three distinct small functions with suitable bi-weights and are not related by a quasi-Möbius transformation, then for every other small function $c$, the counting function $N(r,ν_f^c)$ is asymptotically equivalent to the characteristic function $T(r,f)$. Moreover, the truncated counting function $N_{(3}(r,ν_f^c)$, which counts only zeros of multiplicity at least $3$, is negligible. As an application, we further prove that $f$ and $g$ must be related by a quasi-Möbius transformation provided that they satisfy an additional condition, which is weaker than the usual assumption that they share a fourth pair of small functions.

The Resource Public Key Infrastructure (RPKI) secures the Internet's routing system by defining a complex trust and validation framework for certificates, Route Origin Authorizations (ROAs), manifests, and Certificate Revocation Lists (CRLs). These mechanisms are specified across dozens of RFCs. This paper presents the first comprehensive analysis of the causal link between flaws in RPKI Requests for Comments (RFCs) and vulnerabilities in implementations and real-world deployments. We reveal how vague, conflicting, or underspecified requirements in 50 RPKI RFCs propagate into inconsistent implementation behavior and operational failures. We conduct the first large-scale, impact-driven evaluation of RPKI specifications. Our methodology combines differential fuzzing of major RPKI implementations with Internet-wide crawling and validation log analysis, enabling us to trace practical vulnerabilities back to flawed RFC requirements. We uncover 61 previously undocumented inconsistencies in validation behavior, trace 23 directly to RFC flaws, and identify two novel vulnerabilities that were assigned CVEs. Our findings reveal that these are not isolated coding errors but rather systemic issues inherent in how RPKI standards are written, interpreted, and implemented. To mitigate these threats, we propose concrete recommendations and introduce a novel alerting service that monitors and reports live inconsistencies in RPKI deployments. Our open-source datasets, code, and tools support reproducibility and further research.

Composite optimization problems, formulated as the minimization of three functions, are ubiquitous in large-scale machine learning and signal processing. While state-of-the-art splitting methods such as Condat-Vũ (CV) [Condat, 2013, Vũ, 2013], Primal-Dual Davis-Yin (PDDY) [Salim et al., 2022b], and Primal-Dual Twice Reflected (PDTR) [Malitsky and Tam, 2026] are highly versatile, they inherently exhibit non-accelerated convergence rates. Existing accelerated primal-dual splitting results either focus on special structures like one of the functions being zero, or linearly constrained problems, or smooth regimes, or directly use Nesterov-type momentum. Our contribution is a unified Bregman primal-dual framework that yields four variants and a common Lyapunov analysis. By applying the Chambolle-Pock algorithm [Chambolle and Pock, 2011] to primal-dual reformulations, we systematically derive four novel accelerated algorithms: Accelerated Condat-Vũ (ACV-I and ACV-II) and Accelerated Primal-Dual Twice Reflected (APDTR-I and APDTR-II). Through a simplified Lyapunov-based analysis, we establish iteration complexities for both smooth and nonsmooth cases, successfully removing the restrictive assumptions restrictions required by prior works.

We consider the problem of testing whether an unknown unitary is close to a specified level of the Clifford hierarchy. Bu, Gu, and Jaffe proposed a candidate tester for this task based on a connection with noncommutative analogues of the Gowers uniformity norms. The complexity of this tester -- whose analysis depends on a robust characterization of the near-extremizers of these norms -- was left open. We establish such a characterization for the fourth noncommutative uniformity norm and, as a consequence, obtain an efficient tester for the third level of the Clifford hierarchy. We further discuss possible routes toward resolving the problem of testing for all higher levels, highlighting the main barriers that remain.

The spectra of RR Tau star, which belongs to the family of young irregular variable UX Ori type stars, in its different brightness states have been studied using a comparative analysis. Selected spectra of the star that are obtained with the Nordic Optical Telescope at various times when its brightness ranged from $10.6^m$ to $13.9^m$ have been presented. The veiling of spectral lines at brightness minima by circumstellar emission has been considered, and its origin has been discussed.

The dynamical Markov and Lagrange spectra are subsets of the real line widely studied and that share some similarities with the classical spectra, e.g. typical dynamical spectra, associated to horseshoes with Hausdorff dimension greater than one, have nonempty interior and, in the conservative setting, the intersections of the spectra with half-lines determine a continuous function. Here we study some similar questions in the context of skew products of surface diffeomorphisms with unit circle fiber.

A precision measurement of X-ray transitions in kaonic boron, performed by the SIDDHARTA-2 collaboration at the DA$Φ$NE collider, is reported. The energies and yields of the $5g\rightarrow4f$ and $4f\rightarrow3d$ transitions were determined for both boron isotopes, kaonic $^{10}\text{B}$ and kaonic $^{11}\text{B}$. For the $5g\rightarrow4f$ transition, the measured energies are $7064.62 \pm 16.93\,\text{(stat.)} \pm 2.00\,\text{(sys.)}$~eV for kaonic $^{11}\text{B}$ and $6920.96 \pm 58.23\,\text{(stat.)} \pm 2.00\,\text{(sys.)}$~eV for kaonic $^{10}\text{B}$. For the $4f\rightarrow3d$ transition, the corresponding values are $15293.33 \pm 4.80\,\text{(stat.)} \pm 5.30\,\text{(sys.)}$~eV and $15180.11 \pm 20.86\,\text{(stat.)} \pm 5.30\,\text{(sys.)}$~eV, respectively. The yields for the $5g\rightarrow4f$ transition are $0.076 \pm 0.013\,\text{(stat.)}^{+0.011}_{-0.012}\,\text{(sys.)}$ for kaonic $^{11}\text{B}$ and $0.0189 \pm 0.0032\,\text{(stat.)}^{+0.0028}_{-0.0030}\,\text{(sys.)}$ for kaonic $^{10}\text{B}$. For the $4f\rightarrow3d$ transition, the corresponding yields are $0.115 \pm 0.006\,\text{(stat.)}^{+0.002}_{-0.005}\,\text{(sys.)}$ and $0.0286 \pm 0.0015\,\text{(stat.)}^{+0.0007}_{-0.0014}\,\text{(sys.)}$, respectively. No statistically significant deviation from pure electromagnetic (QED) calculations is observed in the measurement of the $4f\rightarrow3d$ X-ray transition in kaonic $^{11}\text{B}$. Interpreted as upper limits, these results impose stringent constraints on the strong-interaction energy shift and width of the 3d level in light nuclei. Translating these limits into bounds on phenomenological kaon-nucleus optical potentials and, within specific theoretical models, on the complex scattering amplitude, we constrain and disfavor scenarios that predict large shifts or widths in boron.

The development of scalable quantum networks requires coherent interfaces capable of converting microwave photons used in superconducting quantum processors into optical photons suitable for long-distance fiber transmission. This review surveys recent progress in microwave-to-optical quantum transduction across optomechanical, electro-optic, and magneto-optic platforms, with emphasis on conversion efficiency, bandwidth, added noise, and operating temperature. In addition to standard metrics, we propose the internal efficiency eta_in and the magnon decay rate kappa_m/2pi as normalized parameters that enable fairer comparison across heterogeneous implementations. Optomechanical systems achieve internal phonon-to-photon efficiencies of 93% with sub-quantum added noise of 0.25 quanta at millikelvin temperatures. Electro-optic devices based on LiNbO3 and AlN have advanced from room-temperature efficiencies below 1% to millikelvin systems with internal efficiencies approaching 99.5%, added noise as low as 0.16 quanta at 60 mK, and bandwidths extending to several tens of megahertz. Magneto-optic (optomagnonic) platforms exhibit the lowest efficiencies (typically $10^{-10}$ to $10^{-8})$, but offer intrinsic non-reciprocity and broadband magnonic operation, with emerging approaches based on topological heterostructures and magnon squeezing predicting enhancements up to $10^{-4}$. Optomechanical systems appear promising for high-fidelity quantum state transfer, electro-optic transducers for high-bandwidth coherent links, and magneto-optic devices for non-reciprocal network components. We discuss the fundamental trade-off between efficiency and added noise across all three platforms, and argue that heterogeneous microwave-optical transduction is emerging as a key enabling technology for distributed quantum computing and large-scale quantum networks.

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. However, the estimation of the multiple nonlinear eigenvectors is associated with an increased computational cost. We present an implementation of a direct multiway spectral clustering algorithm in the $p$-norm, for $p\in(1,2]$, using a novel C++ GraphBLAS API. The key operations are expressed in linear algebraic terms and are executed over the resulting sparse matrices and dense vectors, parameterized in the algebra pertinent to the computation. We demonstrate the effectiveness and accuracy of our shared-memory algorithm on several artificial test cases. Our numerical examples and comparative results against competitive methods indicate that the proposed implementation attains high quality clusters in terms of the balanced graph cut metric. The strong scaling capabilities of our algorithm are showcased on a range of datasets with up to $8$ million nodes and $48$ million edges.

In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary genus - or equivalently a Teichmüller modular form in any genus. As a first application, we connect the geometry of the moduli space of curves to the classification program for holomorphic vertex algebras. We then discuss how to use the theory of holomorphic vertex algebras to reach new results about the moduli space of curves. In the last part of the paper we study how the above mentioned forms can be used to reconstruct the vertex algebra.

To support the adoption of electric transport systems, public charging opportunities are becoming increasingly important. In this dynamic environment, a central challenge for route planning and charging scheduling is forecasting charging-station availability under fluctuating demand. In this work, we propose a fluid-based forecasting method that accounts for uncertainty in both known and unforeseen electric vehicle arrival patterns while respecting station capacity constraints. We further evaluate the congestion forecasting method by applying it to an electric vehicle scheduling problem. Compared to scheduling frameworks that rely on standard baselines, charging schedules based on the fluid congestion forecasting model reduce waiting-related downtime by up to 14%. Finally, we quantify how increased knowledge of vehicle arrivals and different levels of station congestion affect overall system performance.

The goal of this short paper is to investigate the regularity of the solutions of the Dyson equation. In the work of Bertucci and al. [3, 4, 5], a new notion of solutions for the Dyson equation has been introduced using the viscosity solutions theory and they proved a regularization of solutions in L^{$\infty$} . According to the work of Biane [6] we should expect a regularization in C^{1/3} of solutions (and not better). In the spirit of the works of Bertucci and al., we shall prove using PDE methods that for almost all time t \ge 0 the solution is as expected in C^{1/3} . Our approach allows us to extend this result in addition to a drift term in the Dyson equation for which the semi explicit solutions is not necessarily known. We shall also give an application of this result, proving that the solutions of the periodic Dyson equation converge in long-time toward the uniform distribution on the circle in L^{$\infty$} norm which was an open question in [5].

Understanding student difficulties in programming is a complex challenge due to the wide range of topics and the abundant varieties of misconceptions and errors. This paper presents the design and development of a fine-grained taxonomy that categorizes novice programmers' difficulties specifically related to reading and understanding the control flow constructs selection and iteration. Building upon prior research and our own empirical data from quizzes and interviews with students, the taxonomy is constructed through the iterative methodology of the Extended Taxonomy Design Process (ETDP). Key contributions include clear distinctions between different student difficulties and a detailed analysis of common student misunderstandings concerning conditional statements and loops. The taxonomy aims to aid computing education researchers by providing a harmonized framework to classify and analyze student errors, fostering deeper theoretical insights and informing pedagogical strategies. Future work will involve applying the taxonomy to novel student data and evaluating its usability among educators and researchers.

The baryonic Faber-Jackson relation (BFJR) links the baryonic mass of pressure-supported systems to their mean velocity dispersion. For elliptical galaxies, the BFJR is thought to be a projection of the fundamental plane (FP), which includes the stellar half-mass radius as a third variable. We study the BFJR and FP across eight orders of magnitude in baryonic mass, encompassing galaxy groups, ellipticals, dwarf ellipticals, and dwarf spheroidals. We compile and homogenize data for 1400 pressure-supported systems and measure their mean internal baryonic acceleration $\langle g_\mathrm{bar}\rangle$. We find that the properties of the BFJR and FP systematically depend on the internal acceleration of the sampled systems, with a transition around the acceleration scale $a_0\simeq 1.2\times10^{10}$ m s$^{-2}$. For low-acceleration systems with $\langle g_\mathrm{bar}\rangle < 0.6\,a_0$ (dwarf galaxies and galaxy groups), the BFJR relation takes the form $\log_{10}(M_\mathrm{bar}/M_{\odot}) = (4.19 \pm 0.10) \log_{10}(σ_{\rm los}/\rm{km s}^{-1}) + (2.55^{+0.16}_{-0.16})$ with an orthogonal intrinsic scatter of $0.11 \pm 0.01$ dex. The FP expected from the Newtonian virial theorem is followed by high-acceleration systems (massive ellipticals with $\langle g_\mathrm{bar}\rangle \gtrsim 6 \,a_0$), whereas low-acceleration systems deviate from the FP at both low masses (dwarf galaxies) and high masses (galaxy groups). Our results generally agree with the expectations of MOND: high-acceleration systems follow the Newtonian virial theorem in which a radial variable explicitly appears (the FP), while low-acceleration systems follow the MOND virial theorem in which the radial dependence disappears (the BFJR). On average, the MOND external field effect seems to play a secondary role in dwarf galaxies in galaxy groups and clusters.

In a recent work we studied the first nonlinear stage of modulation instability (NLSMI) of x-periodic anomalous (rogue, freak, extreme) waves (AWs) of physically relevant multidimensional (generalizations of the focusing) nonlinear Schrödinger (MNLS) equation, like the non integrable elliptic and hyperbolic nonlinear Schrödinger (NLS) equations in d+1 dimensions, d = 2, 3, in the quasi one dimensional (Q1D) regime in which the wavelength in the direction of propagation x is small with respect to the wavelengths in the transversal directions. We showed that, at leading order, the first NLSMI is universal, independent of the particular MNLS model, and described by suitable adiabatic deformations of the quasi-homoclinic Akhmediev breather solution of NLS, in excellent agreement with numerical simulations. In the present work we focus on the recurrence of x-periodic AWs in the Q1D regime. We show that, although the first nonlinear stage of MI is essentially universal for all MNLS equations, the recurrence dynamics exhibit significant O(1) differences among different models. Moreover, successive nonlinear stages generally display increasingly complex combinations of fission and fusion processes, leading to progressively richer dynamical choreographies. Since MNLS equations in the Q1D regime can be viewed as multidimensional perturbations of the integrable NLS equation, we use the recently developed finite gap perturbation theory of NLS AWs to give an analytic and quantitative description of the recurrence of Q1D AWs, in excellent agreement with numerical simulations. Due to the physical relevance of the MNLS equations considered in this work, and due to the universality of the processes discussed in this paper, it is plausible that they be observable in many fields of physics, like water waves, nonlinear optics, plasma physics, Bose-Einstein condensates, etc . . .

Extreme-scale data centers are the backbone of next-generation computing, enabling breakthroughs in science, artificial intelligence, and global innovation through unprecedented processing power and scalability. This work examines leaf-spine network topologies that offer extreme scalability--connecting a vast number of endpoints--while delivering strong performance at low cost. It takes as a starting point two alternatives to the widely used Fat-Tree topology: the Orthogonal Fat-Tree and the Random Folded Clos. The resulting Multipass Random Leaf-Spine (MRLS) networks inherit their advantages and surpass Fat-Trees in both throughput and flexibility. To fully leverage the topological properties of these networks, various non-minimal routing strategies are considered. An exhaustive evaluation using an interconnection network simulator provides insight into the trade-offs and scalability of these topologies under realistic conditions, positioning them as a promising solution for extreme-scale systems. The MRLS achieves a 50% speedup against a Fat-Tree for an All2All collective comprising 100k endpoints, and 100% against Dragonfly networks for the same collective.

We review and numerically study a protocol for Liouvillian learning based on randomized Pauli states and measurements. In particular, in the two-body, long-range interactions, and single-body noise setting, we describe the complete workflow to obtain the coefficients of the Liouvillian in an efficient and pairwise manner, meaning that the required classical memory is independent of the system size. We also provide guidelines for choosing the parameters for data acquisition and postprocessing that minimize the total reconstruction error.

In recent years, progress in adaptive graph signal processing algorithms has provided effective solutions for processing signals defined on graph structures. As a classical strategy in information theory, the Generalized Maximum Correntropy Criterion (GMCC) exhibits good resistance to non-Gaussian noises. When non-Gaussian noise interferes with the graph signal, the graph signal processing algorithm based on GMCC (GSP GMCC) algorithm shows better performance. However, the GSP GMCC algorithm itself has three parameters that need to be manually tuned, and the process of manually tuning the parameters is complex and tedious. Meanwhile, the non-concave and non-convex nature of the GMCC function itself limits its own convergence rate and adaptive estimation accuracy. To solve the above problems, based on the strongly convex function half-quadratic criterion (HQC), the GSP HQC algorithm is proposed in this paper. The performance analysis of the GSP HQC algorithm is implemented in this paper. Simulation experiments demonstrate that the GSP HQC algorithm achieves superior performance in terms of convergence rate and adaptive estimation accuracy while maintaining computational complexity comparable to existing algorithms

We study the problem of allocating a finite estate among agents whose total claims exceed the available resources, a standard framework in the theory of claims problems. Two canonical rules embody competing fairness ideals: the Proportional rule allocates in proportion to claims, while the Constrained Equal Awards (CEA) rule equalizes awards as much as possible subject to claim-boundedness. We introduce the P-CEA family of compromise rules, which assigns each agent a fixed baseline award, capped by her claim, and distributes the remaining estate proportionally to residual claims. By varying the baseline parameter, this family generates a continuum of allocation rules that interpolates between the Proportional and CEA benchmarks. We provide an axiomatic characterization based on two threshold-dependent principles: No Advantageous Reallocation, which prevents agents with claims above the threshold from benefiting through coordinated claim redistribution that preserves the threshold condition, and Sustainable Lower Bound, which guarantees each agent at least the minimum of her claim and the threshold. We further develop a dual analysis that reallocates losses instead of awards and characterize the corresponding dual family using the dual versions of our axioms.