We investigate how non-Markovian mechanical dissipation affects exceptional points in linearized optomechanical systems with red-sideband drive. For a chosen non-Ohmic mechanical bath, we derive analytical conditions for the memory-renormalized exceptional point by employing a pseudomode mapping, thereby demonstrating that structured environments displace the mode coalescence away from the Markovian prediction. Crucially, we reveal that failing to account for this memory-induced shift suppresses the divergent Petermann factor by orders of magnitude, showing that accurate bath modeling is essential for the successful operation of exceptional-point-based devices whenever reservoir-induced memory is non-negligible. We finally show that non-Markovianity modifies the cavity reflection spectrum, manifesting as a shallower optomechanically-induced-transparency dip, providing therefore an experimentally-accessible signature of structured mechanical environments.

We consider the algebra of square matrices of bounded non-commutative (NC) functions over NC operator unit balls (unit balls corresponding to finite-dimensional operator spaces) and characterize cyclic matrix free polynomials with respect to the canonical weak-* topology. More precisely, we show that a matrix free polynomial generates a weak-* dense left/right ideal if and only if it is stable, i.e., non-singular at every point in the NC operator unit ball. To this end, we establish a version of the Neuwirth--Ginsberg--Newman inequality for stable matrix free polynomials. We combine our techniques with the theory of realizations to establish cyclicity of stable NC rational functions that are uniformly continuous across the boundary, and we recover known results about cyclicity of NC rational functions in the matrix-valued free Hardy space over the NC unit row-ball. Lastly, we introduce the NC parallel sum function: a stable NC rational function that is contractive over the NC bidisk, which cannot be extended uniformly across the boundary, and determine its cyclicity using properties of accretive operators.

Advanced Air Mobility (AAM) has emerged as a key pillar of next-generation transportation systems, encompassing a wide range of uncrewed aerial vehicle (UAV) applications. To enable AAM, maintaining reliable and efficient communication links between UAVs and control centers is essential. At the same time, the highly dynamic nature of wireless networks, combined with the limited onboard energy of UAVs, makes efficient trajectory planning and network association crucial. Existing terrestrial networks often fail to provide ubiquitous coverage due to frequent handovers and coverage gaps. To address these challenges, geostationary Earth orbit (GEO) satellites offer a promising complementary solution for extending UAV connectivity beyond terrestrial boundaries. This work proposes an integrated GEO terrestrial network architecture to ensure seamless UAV connectivity. Leveraging artificial intelligence (AI), a deep Q network (DQN) based algorithm is developed for joint UAV trajectory and association planning (JUTAP), aiming to minimize energy consumption, handover frequency, and disconnectivity. Simulation results validate the effectiveness of the proposed algorithm within the integrated GEO terrestrial framework.

We prove asymptotics for mollified first and second moments of subfamilies of Dirichlet $L$-functions given by shrinking angular restrictions on the root number. Using these moments, we prove that for even primitive characters with prime conductor $q$, a positive proportion of the central values $L(1/2,χ)$ do not vanish as $q\to\infty$.

In this work we present a comprehensive analysis of a post-selective attack on quantum key distribution protocols employing phase-encoded linearly independent coherent states (or similar alternatives). The attack relies on multimode projection onto a Fock subspace and enables probabilistic extraction of information by an eavesdropper. We derive analytical expressions for the information accessible to the adversary and show that it depends only on three protocol parameters: the mean photon number of the signal states, the phase separation in the information basis, and the expected optical loss of the quantum channel. Several optical realizations of phase-encoded quantum key distribution protocols are analyzed to illustrate the applicability of the results. Possible countermeasures against the proposed attack are also discussed.

In this study, we report direct experimental observations of self-sustaining CH4-air rotating flames formed spontaneously in an unheated, open, circular Hele-Shaw cell. These flames are observed under fuel-rich conditions and exhibit stable traveling-wave patterns, with edge velocities that can significantly exceed the nominal flame speed of the unburned mixture. PLIF measurements across the central plane reveal that the flame front consists of a bibrachial structure, with a diffusion branch gliding along the side edges of the cell and a premixed branch extending into the interior. Complementary numerical simulations suggest that the formation of rotating flames is driven by a dynamic balance between local flame speed and unburned-gas velocity near the cell edges, where both wall heat loss and flow expansion play critical roles in stabilizing the rotation pattern. A parametric study is conducted for various equivalence ratios, flow rates, and gap distances, from which the regime diagrams of flame modes and rotation frequencies are obtained. At low flow rates, the rotating flames are single-headed, with a positive dependence of rotation frequency on the flow rate. For this type of flames, a semi-empirical model is established to predict their rotation frequencies and shapes as functions of mass flow rate and surface temperature. At elevated flow rates, the flames split into multiple heads at approximately equal spacing, and the product of number of heads and rotation frequency increases with the flow rate. Mode transition from rotating flames to steady ring-shaped flames anchored at the burner edges occurs at sufficiently high flow rates, while at sufficiently low flow rates, flame extinction occurs due to thermal quenching. These findings can provide useful guidance for the advancement of micro-combustion technologies.

When medical chatbots provide advice that conflicts with users' lived care experiences, users are left to interpret, negotiate, and evaluate the legitimacy of that guidance. In India, the widespread overuse of antibiotics, antidiarrheals, and injections has shifted patient expectations away from the guideline-aligned advice that chatbots are trained to provide. We present a mixed-methods, vignette-based study with 200 urban Indian adults examining preferences for and against guideline-aligned, norm-divergent advice in chatbot transcripts. We find that a majority of users reject such advice, drawing on diverse rationales grounded in their lived expectations. Through the design and introduction of context-aware nudges, we support expectation alignment that shifts preferences towards transcripts containing guideline-aligned advice. In doing so, we surface key tensions in the equitable design of medical chatbots in the Global South.

Deductive verification provides strong correctness guarantees for code by extracting verification conditions (VCs) and writing formal proofs for them. The expertise-intensive task of VC proving is the main bottleneck in this process, and has been partly automated owing to recent advances in Large Language Model (LLM) agents. However, existing proof agents are not able to discover helper lemmas - auxiliary lemmas that aid in proving - and thus fall short as programs grow in size and complexity. In this paper, we argue that VC proving for program verification is more than a purely mathematical task, and benefits considerably from program comprehension. Our key insight is that human-proof engineers often discover and apply helper lemmas based on their understanding of the program semantics, which are not directly reflected in the VCs produced by VC generators. Inspired by this insight, we propose an LLM agent, LemmaNet, that discovers helper lemmas in two ways. Specifically, the agent first synthesizes lemmas offline by directly analyzing the source code and specifications, and then relating this semantic understanding to the mechanical, verbose encoding produced by VC generators. As the proof unfolds, LemmaNet then adapts existing helper lemmas online to accommodate evolving proof states, enabling the agent to effectively discharge complex VCs on-the-fly. We evaluate LemmaNet on SV-COMP and established real-world subjects, including modules of the Linux kernel, Contiki OS, standard C++ library, and X.509 parser. Our experimental results demonstrate that LemmaNet significantly outperforms state-of-the-art approaches, highlighting the importance of program comprehension-aided lemma discovery in agentic program verification.

Access to healthcare facilities is a critical issue in developing countries, where limited resources and significant challenges hinder progress toward universal health coverage, one of the targets pursued by the United Nations. As a result, the Operations Research (OR) community has become increasingly active in addressing this issue, employing various techniques, particularly optimization. However, making long-term strategic decisions remains challenging, as these often require substantial investments and directly affect large populations. Moreover, much of the existing literature is predominantly theoretical. This paper reviews studies published over the past two decades that use optimization techniques to inform strategic planning decisions aimed at improving health accessibility and specifically contain a case study conducted in a developing country. The review explores the nature of the problems tackled, considering factors such as the level of care, service delivery channels, objectives, criteria, or potential hierarchy, uncertainty, and multi-period settings. Additionally, we discuss the modeling approaches, solution methodologies, and the extent of practical implementation. The goal of this survey is not only to summarize existing work but also to provide a roadmap for future research, offering valuable insights for OR practitioners in the field.

In this article, we obtain the exact distribution of a linear combination of bilateral gamma (BG) random variables (r.v.s). Next, we discuss the distributional properties of the linear combination of BG r.v.s, including probability density function, cumulant generating function and characteristic function. A Stein characterization is developed, which leads us to several distributional approximation results with explicit error bounds in both Kolmogorov and Wasserstein distances. Related limit theorems are also discussed. Furthermore, we show that the associated Lévy processes are finite-variation processes with BG distributed increments having random parameters. Finally, we apply our results in exponential stock models.

Graphene quantum point contacts (QPCs) in the quantum Hall regime host competing transport mechanisms including chiral edge propagation, valley degeneracy, and gate-induced mode mixing. Their interplay is not visible in conductance alone. Shot noise directly probes the statistics of transmission eigenvalues, revealing microscopic mode partitioning that conductance cannot access. We develop a hybrid framework combining tight-binding simulations of gate-defined graphene QPCs with random matrix theory (RMT) to predict shot noise and Fano factor signatures across different quantum Hall regimes, validated against experimental conductance maps of hBN-encapsulated graphene Hall bars. Three distinct regimes are identified: adiabatic propagation, sharp mode filtering, and multi-mode mixing driven by localized states beneath the split gate. For higher Landau levels ($N_L > 0$), complete mode mixing produces the universal chaotic-cavity limit $F \simeq 1/4$. Strikingly, the zeroth Landau level ($N_L = 0$) converges to $F = 1/3$. This distinct value originates in the sublattice polarization of the $N_L = 0$ edge state: coupling to mixed-sublattice localized states beneath the gate is suppressed, confining transport to an effective single channel ($N = 1$). Complete mixing within this single channel yields a flat transmission eigenvalue distribution and hence exactly $F = 1/3$ from single-channel RMT, numerically coincident with but mechanistically distinct from pseudo-diffusive zero-field graphene transport. The $F = 1/3$ versus $F = 1/4$ crossover is a Landau-level-resolved noise signature absent in conductance, providing a direct discriminator between single-channel and multi-channel chaotic transport in graphene QPCs.

We study the formation of multiphase gas in the post-accretion-shock regions of cosmic sheets, filaments, and the circumgalactic medium (CGM) of haloes, i.e., cosmic web objects (CWOs). Local instabilities in the hot medium result in fragmentation and cooling, eventually forming small-scale overdensities with temperatures of $\sim 10^{4}{\,\rm K}$ in pressure equilibrium with the hot environment. Such dense, ionised inhomogeneities can affect the propagation of radio waves from fast radio bursts (FRBs), thereby offering us a way to probe their presence and properties in CWOs through scattering signatures in the observed FRB flux. We find that high-$z$ filaments \& sheets have a negligible contribution to the total observed scattering. The high rates of FRBs expected even at high redshifts may still allow detection from high-temperature filaments along rare sightlines, and we suggest other methods for such systems in a companion paper. Our model further predicts that if turbulent cloudlets exist in the CGM of intervening massive haloes with a volume-filling fraction of $f_{\rm v}\gtrsim 10^{-3}$, they are expected to cause considerable cumulative scattering along an average sightline, resulting in a significant correlation between the total scattering time and source redshifts. The lack of such a correlation in current observations may imply that the cool gas in the CGM has substantial non-thermal pressure, reducing its density, or significant damping of small-scale density fluctuations. Forthcoming localised FRB samples can map these constraints into bounds on volume-filling fractions, densities, cloud sizes, and the strength of turbulence.

In this paper we propose a detectability condition for nonlinear continuous-time systems with irregular/infrequent output measurements, namely a sample-based version of incremental integral input/output-to-state stability (i-iIOSS). We provide a sufficient condition for an i-iIOSS system to be sample-based i-iIOSS. This condition is also exploited to analyze the relationship between sample-based i-iIOSS and sample-based observability for linear systems, such that previously established sampling strategies for linear systems can be used to guarantee sample-based i-iIOSS. Furthermore, we present a sample-based moving horizon estimation scheme, for which robust stability can be shown. Finally, we illustrate the applicability of the proposed estimation scheme through a biomedical simulation example.

The high energy consumption of buildings presents a critical need for advanced control strategies like Demand Response (DR). Differentiable Predictive Control (DPC) has emerged as a promising method for learning explicit control policies, yet conventional DPC frameworks are hindered by three key limitations: the use of simplistic dynamics models with limited expressiveness, a decoupled training paradigm that fails to optimize for closed-loop performance, and a lack of practical safety guarantees under realistic assumptions. To address these shortcomings, this paper proposes a novel End-to-End Differentiable Predictive Control (E2E-DPC) framework. Our approach utilizes an Encoder-Only Transformer to model the complex system dynamics and employs a unified, performance-oriented loss to jointly train the model and the control policy. Crucially, we introduce an online tube-based constraint tightening method that provides theoretical guarantees for recursive feasibility and constraint satisfaction without requiring complex offline computation of terminal sets. The framework is validated in a high-fidelity EnergyPlus simulation, controlling a multi-zone building for a DR task. The results demonstrate that the proposed method with guarantees achieves near-perfect constraint satisfaction - a reduction of over 99% in violations compared to the baseline - at the cost of only a minor increase in electricity expenditure. This work provides a deployable, performance-driven control solution for building energy management and establishes a new pathway for developing verifiable learning-based control systems under milder assumptions.

Interlayer coupling plays a critical role in van der Waals materials by governing lattice stability and emergent quantum phases, yet its impact on few-layer hexagonal CoTe$_2$ remains unclear. Here, using first-principles calculations, we systematically investigate monolayer and bilayer CoTe$_2$ with an emphasis on their electronic structures, lattice dynamics, and electron-phonon coupling, and elucidate the underlying mechanisms driven by interlayer interactions. Our results show that monolayer CoTe$_2$ exhibits pronounced dynamical instability at low temperatures, whereas interlayer coupling stabilizes the bilayer crystal structure and gives rise to phonon-mediated superconductivity with a predicted critical temperature of about $4.7$~K. The stabilization and superconductivity in bilayer CoTe$_2$ are primarily attributed to interlayer-coupling-induced Te-$p_z$ charge redistribution and the associated modification of the Fermi surface and electron-phonon coupling. Finally, we discuss how spin-orbit coupling in bilayer CoTe$_2$ weakens the EPC and suppresses superconductivity. Our work clarifies how interlayer coupling can jointly tune structural stability and superconductivity in few-layer CoTe$_2$, providing insights for engineering quantum phases in layered transition-metal dichalcogenides.

Machine-learned interatomic potentials hold the promise to enable the modeling of highly concentrated liquids over meaningful timescales, far from reach for current ab initio electronic structure methods. Here we evaluate the performances of various MACE potentials in modeling a $21 m$ water-in-salt electrolyte based on lithium bis(trifluoromethanesulfonyl)imide. We test out-of-the-box foundation models, as well as both fine tuning and from scratch training strategies. Our simulations demonstrate that surrogate models allow to overcome sampling limitations of ab initio molecular dynamics, reaching an excellent agreement with experimental observables such as the structure factor. We also demonstrate the benefit of fine tuning a foundation model over training from scratch: in terms of data efficiency, but most importantly as a means to provide information regarding configurations hard to sample, such as short Li$^+$--Li$^+$ distances. Finally, we show that depending on the reference exchange-correlation functional, empirical dispersion correction schemes can be detrimental. All in all, our work shows that machine-learned interatomic potentials are a good fit for the modeling of highly concentrated electrolytes over long timescales.

While rectangular and box-shaped objects dominate the classic discourse of theoretic investigations, a fascinating frontier lies in packing more complex shapes. Given recent insights that convex polygons do not allow for constant competitive online algorithms for diverse variants under translation, we study orthogonal polygons, in particular of small complexity. For translational packings of orthogonal 6-gons, we show that the competitive ratio of any online algorithm that aims to pack the items into a minimal number of unit bins is in $Ω(n / \log n)$, where $n$ denotes the number of objects. In contrast, we show that constant competitive algorithms exist when the orthogonal 6-gons are symmetric or small. For (orthogonally convex) orthogonal 8-gons, we show that the trivial $n$-competitive algorithm, which places each item in its own bin, is best-possible, i.e., every online algorithm has an asymptotic competitive ratio of at least $n$. This implies that for general orthogonal polygons, the trivial algorithm is best possible. Interestingly, for packing degenerate orthogonal polygons (with thickness $0$), called skeletons, the change in complexity is even more drastic. While constant competitive algorithms for 6-skeletons exist, no online algorithm for 8-skeletons achieves a competitive ratio better than $n$. For other packing variants of orthogonal 6-gons under translation, our insights imply the following consequences. The asymptotic competitive ratio of any online algorithm is in $Ω(n / \log n)$ for strip packing, and there exist online algorithms with competitive ratios in $O(1)$ for perimeter packing, or in $O(\sqrt{n})$ for minimizing the area of the bounding box. Moreover, the critical packing density is positive (if every object individually fits into the interior of a unit bin).

Learning-based Model Predictive Control (MPC) has emerged as a powerful strategy for building demand response. However, its practical deployment is often hindered by the non-convex optimization problems induced by standard neural network models. These problems lead to long solver times and suboptimal solutions, making real-time control over long horizons challenging. While Input Convex Neural Networks (ICNNs), such as Input-Convex Long Short-Term Memorys (IC-LSTMs), are developed to address the convexity issue, their recurrent architectures suffer from high computational cost and gradient instability as the prediction horizon increases. To overcome these limitations, this paper introduces the Input-Convex Encoder-only Transformer (IC-EoT), a novel architecture that synergizes the parallel processing capabilities of the Transformer with the guaranteed tractability of input convexity. The IC-EoT was developed and evaluated in a high-fidelity co-simulation framework using the Energym Python library to interface with the EnergyPlus building simulator, and compared against its recurrent convex counterpart (IC-LSTM) and standard non-convex models. The results demonstrate that the IC-EoT is structurally immune to the gradient instability that affects recurrent ICNNs while maintaining comparable predictive accuracy. More critically, it substantially reduces MPC solver times; this speed advantage grows with the prediction horizon, with the IC-EoT proving 2.7 to 8.3 times faster than the IC-LSTM across horizons spanning from one to eight hours. This leap in computational efficiency makes the IC-EoT a robust and practical solution, enabling effective, real-time MPC for building energy management under realistic horizon decision-making scenarios.

Bounded model finding is a key technique for validating software designs, usually obtained by translating high-level specifications into SAT/SMT problems. Although effective, such translations introduce a semantic gap and a dependency on external tools. We present the \emph{Maude Model Finder} (MMF), a native approach that brings bounded model finding to the Maude rewriting logic framework. MMF provides a schema-parametric engine that repurposes symbolic reachability for structural solving, generating finite object configurations from class declarations and graph and data constraints without bespoke generators. Technically, MMF explores a constrained symbolic rewriting system over runtime states modulo an equational theory; SMT is used only to prune states by constraint satisfiability and to discharge entailment checks for subsumption and folding. We contribute a bounded, obligation-driven calculus that separates object creation from reference assignment and supports symmetry reduction by folding via Maude's ACU matching. We establish termination, soundness, and completeness of the bounded construction within the declared bounds, and justify folding via a coverage-preserving subsumption test. We focus on the calculus and its properties, illustrating it on running examples supported by a Maude prototype.

Objective(s): T$_2$* and susceptibility ($χ$) MRI mapping provide complimentary measures of the haemodynamic environment in the placenta. The aims of this work were to use these simultaneously obtained measures to investigate the role of oxygen distribution on the well-established reduction of T$_2$* with gestational age found in healthy pregnancies and explore differences in both measures in compromised placentas. Methods: T$_2$* and $χ$ were measured simultaneously from a double echo, echo planar scan of the whole placenta, across a range of gestational ages and pregnancy complications. Regional variations across the placenta were investigated. Results: Whole placental mean T$_2$* was more correlated with standard deviation of $χ$ than mean $χ$ indicating it is more driven by increasing local inhomogeneities rather than bulk deoxygenation with healthy gestation. Compromised placentas also showed increased standard deviation of $χ$ as well as lower mean T$_2$* suggesting flow/uptake mismatch and reduced oxygenation. Regionally, the susceptibility was lowest (most oxygenated) and least variable in the central region of the placenta indicating good mixing and refreshment of blood in this area. The susceptibility was highest (most deoxygenated) and most variable at the fetal side, suggesting less effective perfusion in this region. Compromised cases showed the greatest difference on the fetal side for both mean and standard deviation of $χ$. T$_2$* was lowest at the fetal side for healthy and compromised cases but the maternal and central regions better distinguished between the two groups. Conclusion(s): T$_2$* and susceptibility can be mapped simultaneously from a single MRI scan and provide complimentary information about the function of the placenta across healthy gestational development, and as a potential indicator of placental compromise.

Recommender systems play an essential role in online services by providing personalized item lists to support users' decision-making processes. While collaborative filtering methods can achieve high accuracy, it is crucial to consider not only accuracy but also the diversity of recommended items to improve user satisfaction. Although financial portfolio theory has been applied to balance these factors, existing models are often sensitive to estimation errors in rating statistics. To overcome these challenges, we establish a computational framework of distributionally robust optimization (DRO) for recommendation selection. We first formulate a cardinality-constrained DRO model based on moment-based ambiguity sets to select a specified number of items for each user. We then design a penalty alternating direction method (PADM) to efficiently compute high-quality solutions and prove its convergence properties. Computational experiments using three publicly available rating datasets demonstrate that our DRO model generates more diverse recommendations than existing models while maintaining the same level of accuracy. Additionally, our solution method computes these recommendations for each user in just a few seconds, proving its practical effectiveness. This study establishes a DRO framework that has the potential to enhance the recommendation quality of various collaborative filtering methods.

Strongly coupled theories are of phenomenological interest, for example as dark matter candidates. Theories that can undergo first order thermal phase transitions are particularly appealing as potential sources of a stochastic gravitational wave background. Determining the expected gravitational wave signal from a first order phase transition requires accurate information on the bubble nucleation rate, but thus far for strongly coupled models these have relied on semiclassical methods. As a first step towards determining the nucleation rate, in this paper we study the confinement-deconfinement phase transition in a 4D SU(8) pure gauge model, using multicanonical Monte Carlo. Resolving the critical bubble for the first time in a pure Yang-Mills model, we determine the critical bubble probability and compare it to results from thin wall calculations. We also compare the effectiveness of different lattice pseudo-order parameters at resolving the condensation transition between the metastable phase and critical bubble branch, and point out the choice of order parameter is crucial to accurately resolve the critical configurations.

Solar radio bursts (SRBs) are intense emissions observed in radio wavelengths most frequently during solar transients, such as coronal mass ejections (CMEs) and flares. SRBs are direct signatures of accelerated electrons in the solar atmosphere. These solar transients have a direct impact on the near-Earth atmosphere. SRBs serve as key diagnostic tools for plasma processes, particle accelerations, magnetic field dynamics in the solar corona and the heliosphere, which are the root cause of these solar transients. There are several key science question which solar radio observations can answer, such as: When $\&$ where is the bulk of the energy released in flares?, what are the physical properties of the energy release site?, what are the properties of heated plasma $\&$ accelerated particles?, how does the transport of heated plasma $\&$ accelerated particles?, what bearing do flares have on the question of coronal heating? The Square Kilometre Array (SKA), with its unprecedented sensitivity, temporal, spectral, and spatial resolution, as well as dynamic range, is expected to provide an enhanced understanding of the physics behind solar transients with unprecedented detail.

Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this paper we prove a direct analogue of that result in all dimensions. In order to do so we develop a lifting technique that allows us to handle manifolds that are collapsed at infinity. This new method also gives an alternative way of handling collapsed manifolds in the known three-dimensional case. As part of this approach, we prove a Ricci flow curvature estimate of a type that would normally be derived from the Harnack inequality, but without requiring the strong curvature positivity hypothesis demanded by Harnack. We give an improved gap theorem as a further application.

WISPIT 2 is a nearby young star with a multi-ringed disk which was recently confirmed to host a ~4.9 MJup gas giant planet embedded in a large (60 au) gap at a radial separation of 57 au from the host star. We confirm and characterise a second, close-in planet in the WISPIT 2 system using a combination of new VLT/SPHERE H-band dual-polarisation imaging and VLTI/GRAVITY K-band interferometric observations of the WISPIT 2 system. The GRAVITY detection is consistent with a point-like source while its extracted K-band spectrum shows CO band-head absorption at 2.3 microns and a continuum shape consistent with a young giant planet. From the GRAVITY data we extract a medium resolution K-band spectrum of the companion and fit atmospheric model grids using the species tool with nested sampling to constrain its effective temperature, radius, and luminosity. We infer Teff of 1500-2600 K, a radius of 0.91-2.2 RJup, and a luminosity of (-3.47)-(-3.63). Comparison with evolutionary tracks implies a mass range of 8-12 MJup, approximately twice as massive as the previously confirmed WISPIT 2b. The astrometry rules out a background source and marginally detects orbital motion of WISPIT 2c, which needs further follow-up observations for confirmation. WISPIT 2 now becomes an analogue to PDS 70, offering a second laboratory for studying the formation and early evolution of a multi-planet system within its natal disk.

We introduce a low-cost every-$K$-step correction for one-dimensional Euler computations. The correction uses differentiated Riemann variables (DRVs) -- characteristic derivatives that isolate the left acoustic wave, the contact, and the right acoustic wave -- to locate the current wave packet, sample the surrounding constant states, perform a short Newton update for the intermediate pressure and contact speed, and conservatively remap a sharpened profile back onto the grid. The ingredients are elementary -- filtered centered differences, local state sampling, a single Newton step, and conservative cell averaging -- yet the effect on accuracy is disproportionate. On a long-time severe-expansion benchmark ($N=900$, $t=0.4$), intermittent correction drives the intermediate-state errors from $O(10^{-2})$ to $O(10^{-13})$, i.e. to machine precision. On a long-time LeBlanc benchmark ($N=800$, $t=1$), the method crosses a qualitative threshold: one-shot final-time reconstruction fails entirely (shock location error $2.7\times 10^{-1}$), whereas correction every three steps recovers an almost exact sharp solution with contact and shock positions accurate to machine precision. The same detector-and-Newton mechanism handles two-shock and two-rarefaction packets without case-specific logic, with plateau improvements of four to sixteen orders of magnitude. In an unoptimized Python prototype the wall-clock overhead is below a factor of two even on the most aggressively corrected benchmark. To our knowledge, no comparably lightweight fixed-grid add-on has been shown to recover this level of coarse-grid accuracy on the long-time LeBlanc and related near-vacuum problems.

A randomly perturbed graph $G^p = G_α\cup G_{n,p}$ is obtained by taking a deterministic $n$-vertex graph $G_α= (V, E)$ with minimum degree $δ(G)\geq αn$ and adding the edges of the binomial random graph $G_{n,p}$ defined on the same vertex set $V$. For which value $p$ (depending on $α$) does the graph $G^p$ contain a $K_r$-factor -- a spanning collection of vertex-disjoint copies of $K_r$ -- with high probability? The order of magnitude of the minimum such $p$ was determined whenever $α\neq 1- \frac{s}{r}$ for an integer $s$ by Balogh, Treglown and Wagner, and by Han, Morris and Treglown. In earlier work, the first three authors determined this threshold probability $p_s$ up to a constant factor for all values of $α= 1-\frac{s}{r}\leq \frac 12$. Here, we complete the picture by establishing $p_s$ in the remaining case $α> \frac12$. A key ingredient in our approach is an extremal result of independent interest: we prove a fractional stability version of a tiling theorem due to Shokoufandeh and Zhao.

We show that the nonlocal Fisher information - defined as the entropy dissipation of the Boltzmann entropy for nonlocal heat equations - admits a natural lifting in the sense of Guillen and Silvestre (2025). Important examples include the discrete Fisher information arising in Markov chains and the fractional Fisher information $i_s$ associated with the fractional Laplacian $(-Δ)^{s}$ on $\mathbb{R}^d$, $s\in (0,1)$. We further establish a Blachman-Stam inequality (BSI) for the fractional Fisher information $i_s$, and prove that, for a large class of functions, $i_s$ converges to the classical Fisher information as $s\to 1$. Through this nonlocal-to-local limit, we recover the classical BSI and the lifting property of the classical Fisher information.

The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of its spectrum and eigenfunctions. We find that the nature of the spin-wave excitations, whether they are hydrodynamic or localized modes, depends crucially on the relevance/irrelevance - in the renormalization group sense - of the correlations induced by the underlying classical order in the spin-wave Hamiltonian matrix elements: low-energy excitations around magnetically ordered states are delocalized, whereas those around spin-glass ordered states are localized, albeit weakly. Remarkably, in the magnetically ordered case, spin-wave delocalization is robust with respect to the presence of disorder, even in two spatial dimensions. We interpret this phenomenology by relating the spontaneous breaking of spin-rotation symmetry in the original Heisenberg model to the symmetry and universality class of the resulting quadratic spin-wave Hamiltonian. We conjecture that the hydrodynamic picture can be recovered through the inclusion of interactions among the spin-wave excitations at higher order in the semiclassical expansion, favoring the onset of ergodic behavior.

We study a coupled system formed by a conservative wave equation and a dissipative Moore-Gibson-Thompson (MGT) equation on a bounded domain. The wave component is driven by the logarithmic source $f(u)=|u|^{γ-2}u\ln|u|$, $2<γ<\frac{2(n-1)}{n-2}$, and carries no direct damping. Rather than employing cross-multiplier arguments, we introduce the coupled variable $w=v+τv_{t}$, which reveals the exact energy structure associated with the interaction term. This formulation yields a genuine coupled energy together with a coercive quadratic form $Q_α(u,w)=\norm{\nabla u}_{2}^{2}+\norm{\nabla w}_{2}^{2}+2α(u,w)$, provided that $|α|<λ_{1}$. Based on this structure, we construct a coupled potential well and prove global well-posedness of weak solutions for initial data lying below the corresponding well depth and inside the stable set. We also show that the energy is strictly dissipative through the MGT component. In addition, a modal analysis of the linearized system identifies a high frequency spectral obstruction to uniform exponential decay, quantifying the weakness of the dissipation transfer to the wave branch. Finally, assuming the relative compactness of the trajectory in the natural energy space and imposing $0<|α|<λ_1$, we apply LaSalle's invariance principle to establish conditional asymptotic stability of the zero equilibrium. The result provides a structurally consistent indirect stabilization theorem for the coupled wave--MGT dynamics without relying on unjustified exponential decay claims.