We investigate the nature of the unassociated sources detected by the Fermi-LAT close (|b|<10°) to the Galactic plane, representing 16% of all sources in the 4FGL-DR4 catalog. The bulk of these sources (referred to as soft Galactic unassociated sources, SGUs) exhibit properties not found in known classes of gamma-ray emitters, as confirmed by a machine-learning classification approach. In particular, these properties include a steep, curved spectrum peaking below 1 GeV and a specific Galactic-latitude distribution with both a narrow and a broad component (dubbed the spike and the shoulder, respectively). Some source clusters are highlighted. New plausible source classes are explored, but only star-forming regions are found to account for a significant fraction (at most 10%) of the unassociated population. A thorough search for counterparts to the 175 brightest sources brings out a number of plausible counterparts but does not reveal clues about the nature of the whole population. We investigate the possibility that SGUs originate from mismodeled clumps of diffuse emission. Using Monte Carlo simulations, the SGU spectra can be reproduced in this scenario under an ad hoc condition concerning the clump spatial extension. The possible connection between the SGUs and gas not accounted for by the 12CO tracer is explored using the 13CO MOPRA data but leads to inconclusive results. The origin of SGUs being related to diffuse emission remains plausible. However, a scenario whereby SGUs represent a new class of gamma-ray emitters cannot be fully excluded.

Neutral gas transport directly affects the ionization source, propellant utilization, and low-frequency discharge oscillations in Hall thrusters. High-fidelity particle-based neutral models or DSMC methods can describe rarefied gas transport, but they are computationally expensive; in contrast, reduced neutral-continuity models are cheaper but require a closure for the neutral velocity or face-normal flux. Under a low-pressure collisionless approximation, this work adopts a free-molecular preprocessing strategy to provide a reference density field and the mean-velocity or face-normal-flux closure used by the reduced neutral-continuity equation in a manner consistent with the underlying transport this http URL this basis, a particle-based free-molecular faceflux preprocessor is used as a stochastic reference, and an SN-DFEM deterministic free-molecular preprocessor is proposed to generate the corresponding reference density, velocity moments, and face-normal fluxes within a unified free-molecular transport framework. Results show that the SN-DFEM preprocessor preserves the main neutral-density and velocity structures and reduces the statistical error in face-flux closure by about three orders of magnitude in the baseline continuity-recovery test. A prescribed moderate ionization-loss case further demonstrates the extension of the framework to free-molecular preprocessing with volumetric neutral removal.

The asymmetric simple exclusion process (ASEP) is an important particle model with deep connections to orthogonal polynomials. Motivated by this connection, Corteel and Williams introduced the Koornwinder moments $M^{Z}_{\lambda}$ at $ t=q $, which generalize the moments of Askey--Wilson polynomials. They showed that the partition function of the two-species ASEP is equal to $M^{Z}_{\lambda}$ for a one-row partition $ \lambda $. In this paper, we investigate a conjecture of Rains on the positivity of the minimal numerator of the Koornwinder moment $M^{Z}_{\lambda}$. We derive the first explicit formula for this moment, thereby obtaining a precise formulation of the conjecture by determining the minimal denominator of $M^{Z}_{\lambda}$. We also propose a generalization of the conjecture for the more general Koornwinder moments $M^{Z}_{\lambda,\mu}$ indexed by two partitions at special parameter values. We prove the generalized Rains' conjecture in two special cases: $(\xi,q)=(1,0)$ and $(\xi,q)=(1,1)$. For $(\xi,q)=(1,0)$, we construct a lattice path model and obtain a combinatorial formula for $M^{Z}_{\lambda,\mu}$ in terms of non-intersecting lattice paths. For $(\xi,q)=(1,1)$, we establish an explicit product formula for $M^{Z}_{\lambda,\mu}$ and give a combinatorial interpretation using lecture hall tableaux.

We study Fano manifolds of Picard number one equipped with a locally flat VMRT structure whose VMRT at a general point is a smooth linearly non-degenerate complete intersection. We prove that such a manifold is biregular to the standard hyperquadric provided that one of two additional assumptions is satisfied. The proof uses equivariant compactifications of the vector group $\mathbb C^n$, Euler-symmetric projective varieties, fundamental forms, and special birational transformations.

We investigate the automorphism groups of non-normal affine toric surfaces. While the connected component of the automorphism group of a normal toric surface is always generated by the acting torus and root subgroups, we prove that this fails for non-normal surfaces in general. Specifically, we show that the property holds if the singular locus contains a one-dimensional torus orbit, but can fail if the singular locus is an isolated point. To illustrate this, we construct an explicit non-normal affine toric surface in $\mathbb{A}^4$ whose connected component of the identity is strictly larger than the subgroup generated by the torus and root automorphisms of the surface.

Android applications (apps) developers increasingly rely on code obfuscation techniques to hinder reverse engineering and protect intellectual property. However, obfuscation also reduces the effectiveness of static analysis and vulnerability detection tools, creating challenges for Android security analysis. Existing approaches for detecting obfuscation in Android apps predominantly rely on handcrafted heuristics, engineered features, or task-specific learning pipelines, which may struggle to generalize across evolving obfuscation strategies. This paper presents a large-scale empirical study investigating the capability of Large Language Models (LLMs) to detect obfuscation in Android apps through semantic reasoning. Our study evaluates whether off-the-shelf LLMs can identify obfuscated code without relying on handcrafted rules, predefined signatures, or dedicated model training. The empirical evaluation is conducted on both a controlled benchmark containing an app obfuscated with multiple techniques and a real-world dataset of Android apps collected from Google Play. The study further examines the impact of prompt design, model selection, and decision thresholds across several open-weight and proprietary LLMs. Finally, the analysis compares LLM-based reasoning with existing SAST-based obfuscation-detection approaches and discusses the broader implications and limitations of applying LLMs to Android security analysis.

We present a multi-line characterisation of how oscillatory power is organised across distinct magnetic environments in an active region using seeing-free, stratospheric near-ultraviolet spectroscopy from the Sunrise-III UV Spectropolarimeter and Imager (SUSI). A two-hour time series of short raster scans in the line-rich 327-329 nm window samples along a single transect that contains the following regions: weak magnetic-field surroundings, a plage, a sunspot, and a pore. From a set of 30 selected, relatively unblended absorption lines, we extract line-core Doppler-velocity time series and compute Morlet-wavelet refined global spectra from which we form band-integrated power maps for three frequency bands (2-4, 4-6, and 6-12 mHz). The stacked, line-resolved maps reveal a clear environment-dependent redistribution of power: 2-4 mHz power is strongest in the weak-field/plage segments but is commonly suppressed in the umbra and pore cores, while 4-6 mHz and 6-12 mHz power becomes relatively enhanced in the strongest-field regions, with line-dependent behaviour in the penumbra and plage. Across the line ensemble, this broad frequency structuring is coherent, but the detailed spatial distribution and relative band ranking are not identical from line to line - even among spectral lines with comparable effective formation depths - demonstrating clear line dependence. This novel result implies that single-line measurements may miss secondary components of the local wave spectrum because different lines weight co-existing perturbations and modes differently; therefore, the SUSI near-UV window provides a uniquely diagnostic-rich mapping of oscillations, offering leverage that is difficult to obtain with traditional one- or two-line approaches.

We explore soliton interactions in a homogeneous spinor $F=1$ Bose Einstein Condensate (BEC) in the presence of a magnetic field, focusing on dark bright dark and bright dark bright configurations. We investigate how these interactions depend on the phase differences among bright solitons and their influence during the dynamics. Our findings align with prior non spinor results, i.e., repulsion among in phase bright solitons and attraction among out of phase pairs in self repulsive atomic BECs. The potential bright soliton attraction, added to the short range repulsion of dark dark soliton interactions, can lead to bound states. However, we find that these bound states break in the presence of spinor interactions due to the particle exchange dynamics between the hyperfine states of the components. Additonally, we develop an effective classical model to describe the soliton dynamics, using a Lagrangian approach. The accuracy of the model is tested by comparing it against numerical simulations. Our results suggest that the proposed model captures the essential features of soliton behavior in the presence of spin interactions, and provides congruent soliton trajectories and interspecies particle exchange dynamics in most of the cases.

As the LIGO-Virgo-KAGRA collaboration's (LVK's) gravitational-wave transient catalog grows, we are learning a wealth of information from the population properties of binary black hole mergers. Events in the catalog are represented with posterior samples describing the astrophysical parameters for each event. Population studies combine these samples to measure the distribution of astrophysical parameters such as black hole masses and spins. However, the posterior-sample representation of each event is only approximate. We demonstrate that when $\gtrsim 300$ events are combined, the numerical error can become large enough that the resulting population inference is unreliable. We consider two solutions. In the short term, we show that nested samples (already produced by LVK analyses) can be used to more accurately describe each event in population studies. But this will only grant a temporary reprieve until the nested-sample representation becomes inadequate. In the longer term, we propose to represent each event with a normalizing flow. Each normalizing flow can be used to generate an arbitrarily large number of new posterior samples in order to represent each event with sufficient accuracy.

In this paper, we introduce and evaluate Selective Field Transmission (SFT), a middleware mechanism that decouples transmission content from statically defined message types in publish-subscribe systems. Industrial and robotics developers often face a dilemma: They can follow established best practices and use standard message types, such as in the Robot Operating System 2 (ROS 2) and COVESA projects, to benefit from reusable and interoperable interfaces, or they can introduce proprietary, project-specific message types tailored to receiver requirements to reduce bandwidth. SFT resolves this trade-off by dynamically adapting the transmitted message components to each receivers actual needs while preserving unmodified standard interfaces. Receivers declare or automatically derive the required message components, which are communicated to the publisher. The publisher then serializes and transmits only the required component subset per receiver with minimal developer intervention. Our evaluation shows that SFT achieves significant bandwidth reductions without measurable per-message latency overhead, with savings proportional to the number and size of unused fields.

Non-trivial alignments between vorticity and the strain-rate tensor play an important role in the evolution of velocity gradients and the energy cascade in isotropic turbulence. Here we explore how alignments between the fluctuating and mean density gradients impact the mechanisms governing the turbulent kinetic energy (TKE) and available potential energy (APE) across scales in stably stratified turbulence. This is motivated by analytical results that demonstrate a connection between them, and is conducted using direct numerical simulations (DNS) of statistically stationary, stably stratified turbulence for $Pr = 1, 7, 50$ in the strongly stratified regime. After demonstrating how the gradient field alignments depend on scale and $Pr$, we show that the alignments are intimately connected to the reversal of the buoyancy flux at small-scales, and that regions of strong alignment and misalignment correspond to regions where the horizontal TKE inter-scale flux becomes weak. The same is also true of the APE flux, except that at larger scales, regions of strong alignment are associated with an upscale APE flux. The TKE and APE dissipation rates, and the mixing coefficient also show a strong dependence on the alignment, especially for $Pr=1$. Finally, we explore the connection between the local alignment and stability of the flow, and we find a non-trivial relationship, with regions of strong alignment surprisingly occurring most often in stable regions. This demonstrates that the dynamical significance of the alignments on the flow energetics cannot be understood through a simple connection between the local alignments and local stability of the flow.

Quantum walks provide a versatile framework for quantum algorithms across a wide range of applications. We develop efficient classical simulation methods for Szegedy quantum walks that avoid explicit construction of the full unitary evolution operator. Unlike previous approaches restricted to a particular walk formulation, our framework is built from fundamental update and reflection operators, enabling the simulation of a broader class of Szegedy walk formulations. We further extend these methods to phase-estimation-based algorithms coupled to the walk, including implementations suitable for large sparse graphs. The resulting methods achieve optimal $O(N^2)$ complexity for dense graphs with $N$ nodes. For sparse graphs, the computational cost scales linearly with the number of edges, which is $O(N)$ in many cases. We implement the framework in the Python package SQWLib and illustrate its capabilities through simulations of representative algorithms, including quantum simulated annealing and quantum search on graphs. These results provide a practical tool for studying Szegedy-walk-based algorithms numerically beyond purely analytical treatments.

The paper studies the existence of \emph{polynomial} measures of dependence between two random variables: polynomial functions of the joint distribution that (i) vanish on independence and (ii) cannot increase under post-processing of either variable (the data processing inequality, DPI). Mutual information satisfies both properties but is transcendental in the joint distribution, making it impossible to estimate without bias from finitely many samples. A polynomial alternative would admit an exact finite-sample unbiased estimator, with the polynomial degree controlling the required sample size. The main result is negative: in the asymmetric setting where the variables have different alphabet sizes (\(|X| > |Y|\)), no nonzero polynomial can simultaneously satisfy DPI on the larger-alphabet side and vanish on independence. In the symmetric case \(|X| = |Y| = n\), we establish a structural result: every such polynomial is divisible by \((\det U)^2\), where \(U\) denotes the \(n \times n\) joint distribution matrix. Consequently, any nontrivial candidate must have degree at least \(2n\). The determinant-based mutual information attains this lower bound. These algebraic results have direct consequences for \emph{multi-task peer prediction}, a mechanism-design problem in which a principal incentivizes honest reports from agents who observe correlated signals but no ground truth. Every such mechanism running on \(\ell\) independent tasks gives rise to a polynomial measure of dependence of degree at most \(\ell\), so our lower bounds on polynomial degree translate directly into lower bounds on the number of tasks: in the asymmetric case no finite-task mechanism exists on the larger-alphabet side at all, while the symmetric case requires at least \(\ell \geq 2n\) tasks.

The advent of photonic integrated circuits (PICs) will allow the replacement of the large aperture of an optical telescope by a dense array of small apertures combined interferometically. The light coming from aperture pairs can be combined by a PIC in order to extract interferogram characteristics known as complex visibilities, from which the observed object can then be reconstructed. In such a compact interferometric imager, the optical components dedicated to image formation in a regular telescope are no longer necessary. In particular, such a concept is relevant for space missions where weight and size are critical. In this communication, we study such an instrument concept, focusing on signal-to-noise considerations. We recall the design basis for the field and the spatial resolution, and we show that the spectral resolution must be no less than the field to resolution ratio. Then, we analyze the signal-to-noise ratio of this concept, assuming that each spatial frequency is recorded only once, and compare the signal-to-noise ratio with that of a monolithic telescope. We perform the comparison in Fourier space for an identical number of recorded photons. We show that the noise propagation of the interferometric imager is identical to that of a monolithic telescope that would have a flat Modulation Transfer Function with a level roughly given by the ratio of the small apertures' diameter to the maximum baseline. We conclude that the noise propagation in low and medium spatial frequencies is unfavorable for the interferometric imager.

The intelligent evolution of mission-critical networks, such as the Internet of vehicles (IoV) and the low-altitude economy (LAE), requires sixth-generation (6G) networks to move beyond discrete physical parameter estimation toward deeper environmental understanding. However, existing integrated sensing and communications (ISAC) studies mainly focus on target-level sensing, which provides fragmented snapshots of the physical world and lacks the behavioral semantic capability to interpret intent. This limitation hinders the intelligent evolution of such networks and prevents 6G from acquiring the essential sensing foundation to evolve into an "intelligent service engine". To bridge this gap, ISAC must advance toward event-level sensing, which models continuous-time states to enable persistent recognition and prediction of target intent and behavioral semantics. This article presents a comprehensive overview of event-level sensing in 6G ISAC networks. We first introduce its fundamental concepts, sensing types, and representative scenarios. We then review key enabling techniques across waveform design, target state estimation and tracking, and event recognition. Furthermore, focusing on IoV and LAE scenarios, we discuss representative applications of ISAC event-level sensing and the intelligent enhancement of downstream operational functions enabled by event-level information. Finally, we highlight future research trends and potential directions to further advance ISAC event-level sensing toward intelligent and proactive 6G networks.

In this article we give regularity results for the geodesic X-ray transform on nonsmooth simple manifolds. As an application, we improve previous injectivity results for the geodesic X-ray transform acting on $L^p$ functions. The results are based on symbol smoothing arguments for the normal operator and mapping properties of pseudodifferential operators with low regularity symbols.

Convex-concave saddle point problems with nonlinear coupling term have wide applications in signal processing, machine learning, robust optimization, and generative models, among others. Primal-dual algorithms are widely used for convex-concave saddle point problems. However, when handling nonlinear coupling term in convex-concave saddle point problems, primal-dual algorithms usually encounter geometric mismatches between variable and mapping spaces, delayed gradient information, and strong dependence on linesearch, resulting in less stable performance and complex convergence analysis. To address these issues, we propose a new primal-dual algorithm named PDAce by combining convex combination and extrapolation strategies. More specifically, in the update of the primal variable, we construct a convex combination point to replace the current iterative point and compute the Jacobian matrix of the vector function in the nonlinear coupling term at the convex combination point. Besides, we use the latest information of convex combination points to extend extrapolation to the mapping space in the update of the dual variable. The core innovations lie in performing linearization of the vector function in the nonlinear coupling term at convex combination points and shifting extrapolation from the variable space to the nonlinear mapping space. This design completely eliminates nonlinear residual terms and allows for rigorous convergence analysis without linesearch. Under mild convex assumptions, we construct a new Lyapunov potential function to prove that PDAce is globally convergent with an ergodic convergence rate of $\mathcal{O}(1/N)$. Moreover, we develop an accelerated version of PDAce, termed aPDAce, which achieves $\mathcal{O}(1/N^2)$ rate under strong convexity of the primal function, and linear convergence when both the primal and dual functions are strongly convex.

In this paper, we propose three extensions to the Real-Time Publish Subscribe wire protocol, on which Data Distribution Service (DDS) is based, to improve bandwidth efficiency. First, a stream negotiation mechanism exchanges static header information during discovery, replacing the full RTPS header at runtime with a compact 2 B identifier. Second, a payload aggregation scheme aggregates samples for the same locator into single UDP packets, reducing IP and UDP header costs. Third, a predictive heartbeat suppression strategy reduces control traffic by omitting heartbeats for periodic communication patterns, falling back upon detected loss or timing violations. All three mechanisms preserve Real-Time Publish Subscribe(RTPS) compatibility by extending DDS discovery to activate these features when supported. Experimental results show that stream headers reduce bandwidth consumption by up to 27.9 % compared to conventional RTPS under best-effort transport, and that heartbeat suppression yields a further 22.7 % reduction on top of stream headers under reliable transport, while preserving transmission latency in both cases.

Physical vapor deposition (PVD) provides a route to prepare highly stable and anisotropic organic glasses that are utilized in multi-layer structures such as organic light-emitting devices. While previous work has demonstrated that anisotropic glasses with uniaxial symmetry can be prepared by PVD, here, we prepare biaxially aligned glasses in which molecular orientation has a preferred in-plane direction. With the collective effect of the surface equilibration mechanism and template growth on an aligned substrate, macroscopic biaxial alignment is achieved in depositions as much as 180 K below the clearing point $T_{LC-iso}$ (and 50 K below the glass transition temperature $T_g$ ) with single-component disk-like (phenanthroperylene ester) and rod-like (itraconazole) mesogens. The preparation of biaxially aligned organic semiconductors adds a new dimension of structural control for vapor-deposited glasses and may enable polarized emission and in-plane control of charge mobility.

This thesis establishes a connection between the coarse homotopy theory of Euclidean cones and the shape theory of compact metric spaces. For a compact metric space $X$, the coarse homotopy groups of the Euclidean cone $cX$ are determined by pointed shape invariants of $X$, fitting into a $\varprojlim^1$ sequence involving the Čech homotopy groups. Using inverse mapping telescopes and strong shape theory, we prove that two compact metric spaces are strong shape equivalent if and only if their Euclidean cones are coarsely homotopy equivalent. We also prove a version of the coarse Whitehead theorem for Euclidean cones. In contrast, we derive a similar $\varprojlim^1$ sequence for arbitrary proper metric spaces, and construct a counterexample showing that the coarse Whitehead theorem fails in this general setting.

Pseudo entropy is a complex-valued generalization of entanglement entropy defined from a reduced transition matrix. We study the pseudo entropy associated with a real-time transition matrix between an initial pure state and its unitary time evolution. For a subsystem $A$, we show that the short-time behavior of real-time pseudo entropy is governed by the correlation between the physical Hamiltonian $H$ and the modular Hamiltonian $K_A=-\log\rho_A$ of the initial reduced state, $ S_A(t,0)=S_A(0)-it \langle K_A(H-\langle H\rangle)\rangle + \mathcal{O}(t^2)$. For Hermitian dynamics, the initial imaginary response is controlled by the symmetrized covariance of $H$ and $K_A$ with an overall minus sign, while the initial real response is governed by their commutator. Thus the imaginary part of real-time pseudo entropy is not merely a branch artifact: it is a time-oriented modular response generated by the correlation between microscopic time evolution and subsystem coarse graining. We clarify the relation of this result to the known first law of pseudo entropy, derive an all-order expression in a Schmidt-diagonal model, recover thermal pseudo entropy as a special case, illustrate the covariance/commutator decomposition in a two-qubit model, and confirm the covariance response in transverse-field Ising-chain quenches, including a finite-size study of a modular susceptibility near the Ising critical region. We discuss how this amplitude-level oriented response can be related to ordinary entropy production, and also give a concrete $\mathcal{PT}$-symmetric toy-model illustration of the non-Hermitian extension.

Resolving the spectral Raman signature of molecules grafted on a metallic support is often a difficult task, in which quantum chemistry methods allow for precious additional rationalization and signal attributions, especially to probe the formation of a bond with the support. In the specific case of gold-organic architectures based on a Au-C bond, only a limited amount of experimental and theoretical reference data are available in the literature, and Raman simulations based on quantum mechanics quickly become unaffordable with the size of the system. In this work, we evaluate the precision of a cost-efficient DFTB method to simulate Raman spectra of gold-organic systems at different scales, from gold complexes to functionalized gold surfaces. After a validation of the method through a careful comparison of DFTB Raman spectra of organometallic gold(I) and (III) complexes to DFT and experimental reference data, we discuss the case of molecules grafted on gold aggregates. For these simulations, the choice of the model (cluster or periodic surface) appears to be critical, and significant differences arise (positions and intensities of the peaks) when considering a full metallic slab, as allowed by the low computational cost of the method.

Fourier analysis has become a crucial tool for understanding the expressivity of Variational Quantum Circuit (VQC) models, as well as an important indicator of barren plateaus (BP). While existing literature has only studied angle-embedded VQCs in a noiseless environment, here we develop the Fourier analysis of VQCs with non-linear data embedding, with particular focus on amplitude embedding, which provides a naturally compact encoding scheme. We first investigate a subtle difference in the domain of input features within amplitude embedding that leads to a distinct expressivity of the zero-frequency Fourier coefficient. By assuming that the ensemble of unitaries generated from the parameter space forms at least a 2-design with respect to the unitary group, we derive, via Weingarten calculus, that the mean of the Fourier coefficients is concentrated at zero, and the variance scales at an exponentially decaying order with respect to the multi-dimensional frequency magnitude. When a noise channel with unitary Kraus operators and probabilities $\{p_k\}$ is taken into account, the variance is further suppressed by a factor $\left(\sum_k p_k^2\right)^{Q}<1$, where $Q$ is the number of channel instances applied. Furthermore, we demonstrate and validate the analytical results through simulations, both noiseless and noisy, including a case where target functions are decomposed into non-integer frequencies, highlighting the practical utility of the approach. Our results establish a rigorous Fourier framework for amplitude-encoded VQCs, offering both theoretical guarantees on expressivity, hence trainability scaling in the frequency domain, as well as practical simulations for deployment on noisy quantum devices.

Sum-rank codes provide a generalized framework for Hamming and rank-metric codes, with codewords represented as tuples of matrices and weight given by the sum of the block ranks. In this paper, we introduce and study a block-tensor-rank invariant for sum-rank metric codes. To each code, we associate its \emph{block tensor rank}: the smallest number of block-simple tensors, namely rank-one matrices supported inside single blocks, whose linear span contains the code. In general, determining the block tensor rank of a sum-rank code is challenging. Our main structural result shows that the block tensor rank decomposes additively across the blocks of the code, thereby reducing its computation to a tensor-rank problem on each block projection. Consequently, we derive two complementary lower bounds on the block tensor rank, referred to as the \emph{projection-wise bound} and the \emph{coordinate-code bound}. Moreover, by combining the coordinate-code bound with the classical Singleton and Griesmer bounds for codes in the Hamming metric, we obtain explicit lower bounds, called the \emph{Singleton coordinate-code bound} and the \emph{Griesmer coordinate-code bound}, respectively. We further construct families of sum-rank codes whose block tensor ranks attain the Singleton or Griesmer coordinate-code bounds. These constructions are based on Hamming-metric codes achieving the corresponding classical bounds. Finally, we show that, in certain cases, the block tensor ranks of two known families of sum-rank codes in the literature do not attain the Singleton coordinate-code bound.

We study the simultaneous estimation of partial-transpose moments $p_j(\rho_{AB})=\mathrm{Tr}[(\rho_{AB}^{T_B})^j]$, $j=2,\ldots,K$, of an unknown bipartite $n$-qubit state from independent copies under an explicit active-memory constraint. We give a sequential qubit-reuse realization of the partial-transpose permutation that uses at most $2n+1$ active qubits, independent of $K$, and estimates all moments $p_2,\ldots,p_K$ to uniform additive error $\epsilon$ with total copy complexity $O(K\log K/\epsilon^2)$. We also prove two converse bounds. First, any uniformly accurate simultaneous estimator requires $\Omega(K/\epsilon^2)$ copies in the worst case. Second, the same scaling holds on an explicit isospectral two-qubit negative-partial-transpose (NPT) family whose ordinary moments are constant while the partial-transpose moments vary. These results characterize the copy complexity of the partial-transpose moment hierarchy up to a logarithmic factor and extend simultaneous nonlinear-functional estimation from ordinary state powers to partial-transpose spectral data under active quantum memory independent of the target moment order.

We consider the transmission of data encoded into binary messages, with the goal of minimizing the Hamming distance, i.e., the number of bit-flips, between consecutive messages. This problem is relevant for enhancing the longevity of Non-Volatile Memories and reducing transition-induced energy consumption in data buses. Known as Write-Efficient Memory coding in the literature, this challenge has traditionally been addressed using optimal but complex schemes. In low-power computer systems the same topic is known as bus encoding. In this paper, we derive closed-form expressions to evaluate the average number of bit-flips for practical, sub-optimal encoding schemes, and propose two new schemes assisted by predefined random codebooks. We demonstrate that low-complexity solutions achieve performance very close to the optimal schemes, making them attractive for implementation in energy-sensitive and memory-critical applications. For instance, by adding 8 extra bits to 64-bits data, sub-optimal schemes can achieve a bit-flip reduction (related to energy saving) of approximately 24.7%, compared to the 26.4% reduction offered by the significantly more complex optimal scheme.

Text-to-SQL aims to translate natural language questions into executable SQL queries over structured databases. Existing benchmarks mainly focus on closed-domain settings with predefined database schemas and well-specified questions, but they fall short in addressing the challenges of open-domain scenarios, such as ambiguous questions, unspecified databases, and cross-database querying. To bridge this gap, we introduce TACO, a benchmark for open-domain Text-to-SQL with Ambiguous and Cross-database queries. TACO consists of 1,500 real-world Text-to-SQL examples based on a smart city data service and 13,000 high-quality synthetic examples generated based on large-scale open data portals, covering diverse domains such as transportation, healthcare, and finance. To construct the synthetic examples, we develop an effective data synthesis pipeline that preserves the complexity of real-world queries. To demonstrate the utility of TACO, we introduce a baseline TACO-SQL composed of question rewriting, table linking, and query planning, to illustrate the challenges posed by TACO and to better understand the limitations of existing Text-to-SQL approaches. Extensive experiments on TACO using a variety of recent Text-to-SQL approaches show that, while TACO-SQL achieves the best results, a significant gap still remains between the existing approaches and human-written SQL. These findings highlight the difficulty of open-domain Text-to-SQL and position TACO as a valuable benchmark to drive future research.

Incremental nonlinear dynamic inversion (INDI) is a prominent flight-control strategy valued for its robust disturbance rejection; however, its formal stability verification has traditionally been limited to linearized dynamical models. This paper presents a formal nonlinear stability certificate for a saturated INDI pitch-rate controller for a hybrid vertical take-off and landing (VTOL) aircraft by representing the INDI controller via an equivalent recurrent equilibrium network (REN). By casting the saturated INDI architecture as a REN, the closed-loop dynamics are exactly mapped to an augmented state-feedback system. This structural equivalence enables the use of sum of squares (SOS) programming to synthesize a locally valid Lyapunov function without relying on conservative bounding approximations. The resulting certificate yields an inner estimate of the region of attraction (RoA) that explicitly accounts for actuator saturation, formally verifying the controller's stability in operating regimes where standard linear margins lose their validity.

Next-generation gravitational-wave observatories will observe binary neutron-star mergers with much higher signal-to-noise ratios, over much longer durations and across broader frequency bands than current detectors. These long-duration signals present a major computational challenge for Bayesian parameter estimation. Reduced-order quadrature is a promising approach for accelerating inference, but in this regime its standard construction encounters severe memory and accuracy limitations. We present a practical reduced-order quadrature construction for long binary neutron-star signals with time-dependent detector response and full effects of the observatories' free-spectral range. Our approach combines improved adaptive frequency sampling, disk-backed streaming, and subbanded reduced-order quadrature construction, enabling efficient and accurate reduced-order models for signals that were previously intractable. We demonstrate for the first time reduced-order Bayesian inference on an approximately 2 h binary neutron-star signal extending down to 5 Hz and with signal-to-noise ratio 2090. We show the resulting reduced-order quadrature remains sufficiently accurate for practical inference. The full analysis is carried out in about 48 h using 128 CPU cores. We also find that, when time-dependent detector-response effects are included, a single Cosmic Explorer detector can localize such a signal to a 90% credible sky area of approximately $41~\mathrm{deg}^2$, with important implications for multimessenger astronomy and cosmology. These results demonstrate that reduced-order methods can make next-generation binary neutron-star inference computationally feasible.

In a sawtooth spin chain, competing nearest- and next-nearest-neighbor interactions suppress long-range order, yielding novel quantum states such as a spin-dimer singlet, 1/2 magnetization plateau, and spin contraction. Here, we investigate the magnetic properties of the orthorhombic semiconductor ZnYb$_2$S$_4$, in which Yb$^{3+}$ ions with an effective spin-1/2 form a sawtooth chain along the $b$-axis. The specific heat exhibits a sharp peak at ${T}_{\rm m}$ $=$ 1.4 K, at which the magnetic entropy $S_{\rm m}$ reaches only 27% of $R$ln2. This reduced $S_{\rm m}$ at $T_{\rm m}$ indicates the entropy release of the ground state doublet of Yb$^{3+}$ even for $T$ $>$ $T_{\rm m}$. The isothermal magnetization $M(B)$ at 0.28 K exhibits hysteresis for $\left|B\right| \leq 0.2$ T and increases monotonically for $B > 0.2$ T. The spontaneous magnetization is only 0.1 ${\it \mu}_{\rm B}$$/$Yb, an order of magnitude smaller than that expected for the ground state doublet of Yb$^{3+}$. Moreover, in powder neutron diffraction measurements, no superlattice reflections due to antiferromagnetic order are observed for $T$ $<$ $T_{\rm m}$. Therefore, in the ground state, the Yb moments are ferromagnetically aligned, but their amplitude is reduced by magnetic frustration in the sawtooth Yb chain.