The IceCube neutrino telescope has provided upper limits on neutrino emission from gamma ray bursts. These constraints provided by the IceCube detector have been instrumental in investigating the properties of the GRB jet and its emission models. During the prompt phase of gamma ray burst emission, intense radiation components are generated that interact with the shock-accelerated particles within the jet. We study various GRB emission models, such as the internal shock model, the photospheric models, and also include a model-independent case. Based on these models, we calculate the neutrino fluence using the photo-hadronic interaction process. We estimate the bulk Lorentz factor using the well-known correlations between prompt phase observables, which is then used to calculate the emission site for the model-dependent scenarios. For GRB 221009A, we find that a low baryon loading scenario is consistent with the IceCube upper limits; however, for GRB 240825A, a higher value of baryon loading is preferred. Also, the values of the microphysical parameters $ε_e$ and $ε_B$ for GRB 240825A are lower by factors of approximately 10 and 100, respectively, compared to those of GRB 221009A. Further, using neutrino upper limits for these two sources, we estimate the lower limits on the dissipation radius for our models. The current TeV PeV upper limits for GRB 221009A are already useful for constraining parameter space for the BPH and MPH models.

We present new measurements of 27 gamma ray energies ranging from 14 keV to 136 keV, obtained using high-energy-resolution magnetic microcalorimeters for energy-dispersive spectrometry. The spectrometer has eight pixels and achieves an energy resolution between 15 and 30 eV across the entire energy range. It faces a cryogenic source sampler with four movable sources. Each source contains a mixture of radionuclides, including Yb-169 and Co-57 used to calibrate the spectrometer and correct its non-linearity. The gamma-ray energies, emitted through the decay of Co-57, Cd-109, Ba-133, Gd-153, Eu-154, Eu-155, Yb-169, Tm-170, Pb-210, Np-239, Am-241 and Am-243, have been reassessed. The lowest absolute uncertainty achieved is 0.13 eV at 105.3 keV, which corresponds to a relative uncertainty of 1.3 ppm. Of the 27 measured gamma rays, the uncertainties of 19 energies were improved with respect to the available literature: 10 by a factor of 5 and 4 by more than one order of magnitude. Good agreement is observed with energies obtained elsewhere by wavelength-dispersive spectrometry. This work significantly improves upon previously reported gamma energies obtained by energy-dispersive spectrometry using semiconductor detectors, thanks to the ultra-high energy resolution of magnetic microcalorimeters.

Assessing the time scale of biological processes using molecular dynamics (MD) simulations with sufficient statistical accuracy is a challenging task, as processes are often rare and/or slow events, which may extend largely beyond the time scale of what is accessible with modern day high performance computational infrastructure. Recently, the replica exchange partial path transition interface sampling (REPPTIS) algorithm was developed to study rare and slow events involving metastable states along their reactive pathways. REPPTIS is a path sampling method where paths are cut short to reduce the computational cost, while combining this with the efficiency offered by replica exchange between the partial path ensembles. However, REPPTIS still lacks a formalism to extract time-dependent properties, such as mean first passage times, fluxes, and rates, from the short partial paths. In this work, we introduce a Markov state model (MSM) framework to estimate full path lengths and kinetic properties from the overlapping partial paths generated by REPPTIS. The framework results in newly derived closed formulas for the REPPTIS crossing probability, mean first passage times (MFPTs), flux, and rate constant. Our approach is then validated using simulations of Brownian and Langevin particles on a series of one-dimensional potential energy profiles as well as the dissociation of KCl in solution, demonstrating that REPPTIS accurately reproduces the exact kinetics benchmark. The MSM framework is further applied to the trypsin-benzamidine complex to compute the dissociation rate as a test case of a biological system, albeit the computed rate underestimates the experimental value. In conclusion, our MSM framework equips REPPTIS simulations with a robust theoretical and practical foundation for extracting kinetic information from computationally efficient partial paths.

As mobile application (app) functionalities grow increasingly complex and their iterations accelerate, ensuring high reliability presents significant challenges. While functionality-oriented GUI testing has attracted growing research attention, existing approaches largely overlook interactions across functionalities, making them ineffective at uncovering deep bugs hidden in inter-functional behaviors. To fill this gap, we first design a Functional Flow Graph (FFG), a behavioral model that explicitly captures an app's functional units and their inter-functional interactions. Based on the FFG, we further introduce an inter-functional-flow-oriented GUI testing approach with the dual goals of precise model construction and deep bug detection. This approach is realized through a long-short-term-view-guided testing process. By combining two complementary test-generation views, it can adaptively refine functional boundaries and systematically explore inter-functional flows under diverse triggering conditions. We implement our approach in a tool called FuncDroid, and evaluate it on two benchmarks: (1) a widely-used open-source benchmark with 50 reproducible crash bugs and (2) a diverse set of 52 popular commercial apps. Experimental results demonstrate that FuncDroid significantly outperforms state-of-the-art baselines in both coverage (+28%) and bug detection number (+107%). Moreover, FuncDroid successfully uncovers 18 previously unknown non-crash functional bugs in commercial apps, confirming its practical effectiveness.

About forty years ago, it has been predicted that a charged particle, moving parallel to a charged wall in an electrolyte, should experience a lift force that, contrarily to electrostatic forces, is not screened at large distances. Up to now, such electroviscous lift force has not been directly measured. Here, we use Atomic Force Microscopy to directly measure the electroviscous lift force and quantify its dependency with the distance to the wall, the translation velocity or the particle's size. Observing that existing theories exhibit large discrepancies with our experimental observations, we develop an analytical approach combining lubrication theory to a previously introduced formalism for small screening length. The experimentally observed lift forces are in good agreement with our theoretical predictions and reveal, for the first time, a saturation of the lift force for increasing velocities. Altogether, our results characterize, through direct measurements and analytical approach, the properties of electroviscous forces between charged particles in viscous electrolytes in non-equilibrium conditions.

We study decentralized equilibrium selection in stochastic games under severe information and communication constraints. In such settings, convergence to equilibrium alone is insufficient, as stochastic games typically admit many equilibria with markedly different welfare properties. We address decentralized optimal equilibrium selection, where agents coordinate on equilibria that optimize a designer-specified social welfare objective while allowing heterogeneous tolerance to deviations from strict best responses. Agents observe only the global state trajectory and their realized rewards, and exchange a single randomized bit of feedback per agent per round. This semantic content/discontent signaling mechanism implicitly aligns decentralized learning dynamics with the global welfare objective. We develop explore-and-commit and online variants applicable to general stochastic games, accommodating heterogeneous model-based or model-free methods for solving the induced Markov decision processes, and establish explicit finite-time regret guarantees, showing logarithmic expected regret under mild conditions.

Within the light-front approach in flat space, we study the closure of the Poincare algebra at the quartic order, specifically the nonholomorphic constraint involving both MHV and anti-MHV vertices. We first recover some well-established results: the existence of Yang-Mills theory and gravity, as well as the inconsistency of interacting multi-graviton theories. We explicitly construct several lower-derivative and lower-spin quartic vertices. We then turn to theories involving massless higher-spin fields. It becomes evident that the quartic constraint does not allow many cubic interactions to survive, in accordance with the well-known no-go results. Nevertheless, once higher-derivative cubic vertices are included, we find nontrivial solutions to the full quartic constraint and determine the corresponding quartic vertices. On this basis, we conjecture the complete set of quartic vertices that solve the light-cone consistency conditions. Exploiting this, we find all allowed unitary local higher-spin theories and identify new families of local quasi-chiral higher-spin theories. We then determine all local higher-spin four-point amplitudes using the spinor-helicity formalism together with locality. We conclude with a short discussion on non-locality and propose a ``local'' (at the amplitude level) higher-spin theory in flat space.

This article focuses on some rings of integers of number fields which are known to be norm-Euclidean domains, but for which no explicit algorithm computing the Euclidean division has yet been studied or implemented. The rings of integers we are interested in were proven to be Euclidean by H.W. Lenstra, Jr in 1978; they include the $n$-th cyclotomic rings for $n=15,20,24$. We present an algorithm performing Euclidean division in these rings based on Lenstra's proof and a closest vector computation by Conway and Sloane, and study its complexity. We give a complete implementation of the algorithm in SageMath. We also estimate the size of the remainders obtained when computing Euclidean divisions with this algorithm.

The `Inverse Distance Ladder' uses relative-distance measurements with type Ia supernovae (SNe Ia), anchored to an absolute distance scale from Baryon Acoustic Oscillations (BAO) and the cosmic microwave background (CMB), to provide an alternative measurement technique for the local expansion rate $H_0$. Using SNe Ia from the Dark Energy Survey and BAO measurements from the Dark Energy Spectroscopic Instrument, we show that the inverse distance ladder is unable to explain the Hubble Tension, anchored as it is to the CMB and its value of $H_0 = 67.4 \pm 0.5$ kms$^{-1}$ Mpc$^{-1}$. To do so, we first show that the suite of systematics considered in cosmology analyses with SNe Ia only move the inferred $H_0$ by $<0.1$kms$^{-1}$ Mpc$^{-1}$, and second, we investigate the scale of redshift-dependent magnitude changes necessary to change the inferred inverse distance ladder $H_0$ from $67$ to the local network of distance measurements value of $73$, and the impact that this would have on other cosmological inferences with SNe Ia. We find that a change of $dμ/dz = 0.2$ mag would be necessary to infer an $H_0$ in concordance with local distance measurements, and that this $dμ/dz$ value would result in a Flat $Λ$CDM $Ω_M = 0.23$, $10σ$ discrepant with other cosmological probes, {indicating that the precision of SNe Ia measurements preclude the necessary redshift evolution for an $H_0$ of 74 kms$^{-1}$ Mpc$^{-1}$}. Therefore, we conclude that current SN Ia cosmology leaves little freedom for the inverse distance ladder to yield $H_0$ values significantly different from $67$ kms$^{-1}$ Mpc$^{-1}$.

The most precise theoretical predictions for the total cross section for the associated production of a Higgs boson with a top-antitop quark pair at the LHC, first presented in \cite{Balsach:2025tth}, are reported. The calculation combines NNLO QCD corrections that include an approximation of the two-loop virtual contribution, with soft-gluon resummation at NNLL accuracy in two independent frameworks (SCET and direct QCD), and complete NLO electroweak corrections.

The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity of the mild solution to the stochastic Cahn-Hilliard equation, shedding light on the intricate behavior of solutions under such complex perturbations. Second, it introduces a fully discrete numerical scheme designed to solve the equation effectively. This scheme integrates the finite difference method for spatial discretization with the tamed exponential Euler method for temporal discretization. The analysis demonstrates that the proposed scheme achieves a strong convergence rate of $O\big(h^{1-ε}+τ^{H_1-\frac{1}{8}-\fracε{2}}\big)$, where $ε$ is an arbitrarily small positive constant, providing a solid foundation for the numerical treatment of such equations.

We study probability measure on $\mathrm{Hom}(H,G)$, where $G$ is a finite group and $H$ a finitely generated subgroup of a finitely generated free group $F$, obtained by pushing forward the uniform random homomorphisms $\mathrm{Hom}(F,G)$ via restriction map to $\mathrm{Hom}(H,G)$. This framework generalizes the word measures arising from single elements of a free group. We formalize the notion of profinite rigidity for subgroups via these induced measures. Our main result shows that a finitely generated subgroup is profinitely rigid if and only if any (equivalently, every) ordered generating tuple is profinitely rigid, thereby extending the notion of rigidity from individual word maps to arbitrary tuples. We also obtain a generalization of a result of \cite{puder2015measure}.

We report the multi-temperature structure of the intracluster medium (ICM) in the Centaurus cluster core observed with XRISM/Resolve. Thanks to its high energy resolution, Resolve enables us to measure fine structures of highly ionized emission lines from Si to Fe and to directly determine the excitation temperature and the ionization temperature from the emission line ratio diagnostics. The observed spectrum in the Centaurus core is well-represented by a double-temperature thermal plasma at collisional ionization equilibrium state rather than an isothermal one. The line ratio diagnostics also support this biphasic temperature structure. Particularly, the observed line ratios show a trend of increasing ionization temperature with atomic mass, while the ionization and excitation temperatures of Fe show nearly the same temperature. The resultant line ratios, which are well-represented by the two temperatures ICM, ~ 1.6 and ~ 3 keV, are also fairly consistent with the expected numbers when assuming the radial single-temperature ICM was projected in the cluster core along the line of sight. Due to the limited low-energy sensitivity of the Resolve with the gate valve closed, we investigated the effect of the cool component using the XMM-Newton/RGS spectrum, but it ultimately did not affect our results. The observed flux ratio between the Fe XXV He alpha resonance and forbidden lines shows an about 20% reduction, suggesting the presence of resonant scattering.

Shattered pellet injection (SPI) as primary mitigation method for major disruptions in ITER has a large parameter space available for optimization including the total amount of injected material, the size of the individual pellet fragments, the material composition, and the timing of multiple injections. This flexibility needs to be exploited to simultaneously minimize thermal heat loads, electromagnetic vessel forces, and formation of relativistic electrons and their impacts on plasma facing components. In this article, we apply 3D non-linear magnetohydrodynamic modelling to SPI experiments in the ASDEX Upgrade tokamak, going beyond our previous work [Tang et al Nucl. Fusion 65 116003 (2025)] by resolving some discrepancies between simulations and experiment and thus opening the path to quantitative model validation and experiment interpretation. The key element that enables the transition from merely qualitative comparisons to quantitatively reliable predictions of the thermal quench duration and the radiation fraction is the incorporation of a simplified treatment of parallel heat-flux limiting. The work increases the confidence of matching the key processes of disruption mitigation with this high fidelity modelling in view of predictive studies for ITER.

A reader browsing through an online article is highly likely to encounter an advertorial, often without realizing it. Advertorials represent a relatively new marketing strategy where advertisements are deliberately designed to resemble the style and tone of editorial content. Despite their appearance, they are, in fact, paid content intended to promote a product, brand, or service. Studies indicate that advertorials are significantly more effective (81%) and less intrusive than traditional banner ads or pop-ups. Despite ongoing regulatory efforts to ensure clear disclosure of paid content, concerns persist about the deceptive nature of advertorials. Advertorials can mislead readers into believing that they are consuming unbiased editorial content. In doing so, they gain undeserved legitimacy, by draping themselves in the credibility of the publication's design; not to inform or inspire genuine interest, but to deceive. In this study, we conduct the first large-scale and systematic study of advertorials. We propose a novel automated methodology for detecting advertorials in the wild, and we collect 185K ad URLs over a period of 5 months. We investigate the prevalence of problematic advertorials and explore their structural and linguistic characteristics. We find that advertorials appear in 1 out of 3 news sites, including some of the most popular and credible outlets worldwide (e.g., The Guardian, EuroNews, CNN). We further highlight that legal disclaimers intended to inform users of the promotional nature of the content, are often deliberately obscured or difficult to recognize, raising concerns about user protection.

A contact form is called K-contact if its Reeb vector field is Killing with respect to some Riemannian metric. In this paper we classify K-contact forms whose Reeb vector field admits at least one non-periodic orbit, on three-dimensional manifolds. We prove that if a compact three-manifold carries such a contact form, then it is diffeomorphic to a lens space and admits exactly two periodic Reeb orbits, whose periods have irrational ratio. We further classify, up to (global) diffeomorphism, these contact forms in terms of the periods of their closed Reeb orbits. We conclude by relating these periods to spectral invariants of the sub-Laplacian, confirming a conjecture of Y. Colin de Verdière in the irregular K-contact case.

Accurate forecasting of patient arrivals at emergency departments (EDs) is vital for efficient resource allocation and high-quality patient care. In this study we investigate the relevance of exogenous variables, namely tourism, weather, calendar and demographic variables, in forecasting ED visits in the reference hospital in Palma de Mallorca, a city with significant seasonal population fluctuations due to tourism. Using a machine learning approach, we develop a model that predicts ED visits based solely on these exogenous variables. We test different machine learning algorithms (random forests, support vector machines, and feedforward neural networks) with different combinations of input variables and compare their symmetric mean average percentage errors (SMAPEs). Our findings reveal that calendar information, resident, and tourist population data are statistically significant for the accuracy of the predictions, while the addition of weather data does not provide any further improvement. Comparison of non-time-series with time-series prediction models reveals that the latter provide better accuracy for short prediction horizons (e.g. shorter than a week). Furthermore, time-series models become less or equally accurate to models relying only on exogenous variables for long prediction horizons (e.g. fortnight or month). Our study highlights the importance of carefully selecting predictive variables to ensure short- and long-term, robust and reliable forecasts. This demonstrates that, despite their lower complexity, non-time-series models with well-chosen input variables can be as effective as time-series models when predicting for long time horizons.

This paper is devoted to a class of finite horizon deterministic mean field games with Grushin type dynamics, state constraints and nonlocal coupling. First, we consider the optimal control problem that each agent aims to solve when the evolution of the population is given and we establish some properties as: the existence of an optimal trajectory for any starting point $(x,t)$, the closed graph property for the multivalued map which associates to each point $(x,t)$ the set of optimal trajectories starting from that point, endowed with a suitable notion of convergence, the continuity of the value function. The main issue to overcome is due to the local interplay at boundary points between the set of state constraints and the degenerate dynamics. To this end, we shall point out two different sets of assumptions which are both sufficient for these properties. Afterwards, we tackle the mean field games; taking advantage of the aforementioned properties, we prove the existence of a relaxed equilibrium (which describes the evolution of the game in terms of a probability on the set of admissible trajectories) and derive the existence of a mild solution (which is a couple formed by the value function for the generic player and a family of time dependent measures on the state).

In this paper, we investigate the performance of RIS-aided orthogonal time frequency space (OTFS) and orthogonal frequency division multiplexing (OFDM) systems in the presence of oscillator phase noise. OFDM is known to be sensitive to phase noise, which could limit the potential gains promised by RIS systems. OTFS, on the other hand, is a compelling potential waveform for RIS-aided systems in the presence of phase noise due to it's resilience to time-varying channels. However, the effect of phase noise on OTFS has not been fully analyzed in the literature as of yet. Additionally, no existing works in the literature consider the effect of phase noise on an RIS-aided OTFS system. Hence, we propose a joint RIS channel and phase noise estimation technique using a Wiener filtering approach. Our proposed method exploits the statistical nature of both the phase noise and the Doppler spread channel in a setup with RIS. Our numerical analysis demonstrates the significant gain of RIS-aided OTFS offers compared to RIS-aided OFDM in the presence in the presence of phase noise. Additionally, our results demonstrate the superiority of our proposed estimation technique, with gains of up to 3~dB in terms of bit error rate (BER), over existing methods in the literature.

We consider the most general parity symmetric effective scalar tensor theory in four dimensions containing terms up to fourth derivative order in the Lagrangian. It has been shown [H.S. Reall, Phys. Rev. D 103 (2021), 084027] that this theory has three polarizations generically goverened by different (nested) propagation cones, neither of which in general coincides with the lightcone as defined by the metric. Consequently, the notion of black hole horizon must be defined relative to the widest propagation cone, and not with respect to the metric. We provide two theorems stating that, nevertheless, the horizon of a \emph{stationary} black hole is null with respect to the metric, and that, in fact, all three propagation cones touch on the horizon. The conditions in these theorems allow for rotating black holes. Our theorems thereby suggest that the notion of Killing horizon, central in most discussions of black hole thermodynamics, retains its fundamental status, and that certain thermodynamic paradoxes associated with multiple propagation cones are evaded.

Channel State Information (CSI) provides a detailed description of the wireless channel and has been widely adopted for Wi-Fi sensing, particularly for high-precision indoor positioning. However, complete CSI is rarely available in real-world deployments due to hardware constraints and the high communication overhead required for feedback. Moreover, existing positioning models lack mechanisms to detect when users move outside their trained regions, leading to unreliable estimates in dynamic environments. In this paper, we present FPNet, a unified deep learning framework that jointly addresses channel feedback compression, accurate indoor positioning, and robust anomaly detection (AD). FPNet leverages the beamforming feedback matrix (BFM), a compressed CSI representation natively supported by IEEE 802.11ac/ax/be protocols, to minimize feedback overhead while preserving critical positioning features. To enhance reliability, we integrate ADBlock, a lightweight AD module trained on normal BFM samples, which identifies out-of-distribution scenarios when users exit predefined spatial regions. Experimental results using standard 2.4 GHz Wi-Fi hardware show that FPNet achieves positioning accuracy above 97% with only 100 feedback bits, boosts net throughput by up to 22.92%, and attains AD accuracy over 99% with a false alarm rate below 1.5%. These results demonstrate FPNet's ability to deliver efficient, accurate, and reliable indoor positioning on commodity Wi-Fi devices.

We study the TMF-valued $(3+1)$-dimensional TQFT of Gukov--Krushkal--Meier--Pei and give an explicit description of the TMF-module state space assigned to a closed $3$-manifold. Our starting point is the torsion linking pairing on $H_1$, viewed as a discriminant form. We construct a canonical, computable package of invariants for torsion linking pairings (uniformly for odd and $2$-primary parts), and from it a canonical tokenization together with an explicit symmetric integral matrix representative realizing the same stable class. This yields an explicit model for the GKMP state space in terms of a rank-one TMF-module $L_b$ with a canonical degree shift determined by signature data. As applications we identify the values on $CP^2$ and, conditional on a natural functoriality/duality statement in GKMP, on $S^2\times S^2$ with the Hopf elements $\pmν$ and $η$, respectively. Finally, we establish a rank-one time-reversal duality $L_{(-n)}\simeq L_{(n)}^\vee[1]$ for all integers $n$.

We present an overview of CHIME/Slow, a real-time transient search backend under development to search for second-duration radio transients using the CHIME telescope, and results obtained from a pilot survey carried out using the prototype version of the search pipeline. The prototype CHIME/Slow pipeline was tested on archival data obtained in December 2022, January 2023 and February 2023 with a total on-sky time of 17 days with an instantaneous Field of View (FoV) of $\sim$13 deg$^2$ . In this pilot survey, we detected nine bursts, one from a new non-repeating source and eight from the known hyperactive repeating source FRB 20220912A. Out of these nine bursts, two bursts from the repeater were not detected by CHIME/FRB, while the non-repeater was detected in the side-lobe of a beam in the CHIME/FRB exhibiting shorter pulse width and narrower bandwidth compared to the CHIME/Slow detection. Here we report properties of the bursts, discuss the sensitivity and completeness of the current version of the CHIME/Slow pipeline, and outline future development to improve its performance. Finally, based on these results, we report the all-sky rate (95% credible region) of radio transients with pulse widths between 16 ms to 5 s, fluence above 5 Jy ms and observing frequency of 600 MHz to be between 184 and 4556 bursts sky$^{-1}$ day$^{-1}$.

We present PrestaLine: Gorynych, a comprehensive numerical tool designed to model the dynamical, chemical, and spectral evolution of collapsing molecular cores from the prestellar phase to protostellar accretion. The code integrates three key components: (1) Kamelung, a 1D hydrodynamics module simulating gravitational collapse up to first hydrostatic core (FHSC) formation followed by an accretion of envelope onto a young star; (2) Presta, a chemical evolution module post-processing density and temperature profiles to compute time-dependent molecular abundances; and (3) Uran(IA), a radiative transfer module generating synthetic molecular line spectra. We apply Gorynych to compare low-mass (5 Msun) and high-mass (50 Msun) cores, finding that their dynamical evolution is remarkably similar, with differences primarily in spatial scaling. Chemical evolution reveals sharp abundance changes during the FHSC transition, particularly for CO, H2O, and HCO+, though pre-collapse chemical initialization has minimal impact on most species. Spectral maps of 13CO(2-1), HCO+(3-2), and H2O(110--101) lines show distinct kinematic signatures of infall and depletion, with high-mass cores exhibiting spatially extended emission. Our results highlight Gorynych's utility to couple theoretical collapse models and observations, providing a framework to diagnose core evolution and initial conditions from molecular line data.

Charging energy ($E_C$) is essential in quantum dot (QD) devices. Previous studies on PbTe QDs have reported both the presence and absence of $E_C$. To resolve this ambiguity, we vary the QD size, i.e. the cross-sectional area of PbTe nanowires, and track the evolution of $E_C$. For large crosssectional areas ($\sim$ 16000 nm$^2$), the PbTe QDs exhibit no measurable $E_C$, while quantized levels are well resolved. Decreasing this area successively to 5000, 1500, and 500 nm$^2$, $E_C$ becomes finite and increases to 80, 160, and 210 $μ$eV, respectively. We further demonstrate the strong tunability of local gates, which can tune the PbTe device from the QD regime to the regime of ballistic transport. These results address concerns regarding the large dielectric constant of PbTe and provide key insights in engineering advanced PbTe quantum devices.

We present a robust computational framework for Hele-Shaw tumor growth with necrotic cores, a problem identified as the incompressible limit of the Porous Media Equation. Simulating this system presents a fundamental challenge: while the outer boundary evolves via advection, the inner necrotic interface is defined by an obstacle problem and lacks an explicit advection structure, causing standard schemes to fail. To address this, we introduce a stabilized predictor-corrector strategy that iteratively resolves the bidirectional coupling between the nutrient-pressure fields and the domain geometry, ensuring robust time-stepping for both the advection-driven outer surface and the obstacle-defined necrotic core. We establish rigorous convergence theory for the single-interface case and demonstrate the method's robustness in capturing the topological transition of necrotic core nucleation and complex geometric evolution.

In this paper, we introduce and analyze a space-time $p$-adaptive discontinuous Galerkin method for nonlinear acoustics. We first present the underlying mathematical model, which is based on a recently derived formulation involving, in particular, only first order in time derivatives. We then propose a spacetime discontinuous Galerkin discretization of this model, combining a symmetric Friedrichs systems discretization for symmetric hyperbolic systems with an interior penalty discretization for damping terms. The resulting nonlinear system is solved using Newton's method. Next, we present a well-posedness analysis of the discrete problem. The analysis begins with a linearized system, for which stability is shown. Using a fixed point argument, these results are extended to the fully discrete nonlinear system, yielding a priori error estimates in a natural discontinuous Galerkin norm. Finally, we present numerical experiments demonstrating the parallel solvability of the spacetime formulation and the effectiveness of p-adaptivity. The results confirm the theoretical convergence rates and show that adaptive refinement can reduce the number of degrees of freedom required to accurately approximate selected goal functionals. Moreover, the experiments demonstrate that the model reproduces characteristic phenomena of nonlinear acoustics, such as harmonic generation, thereby validating the proposed model.

We discuss the open/closed version of the Gromov-Witten/Hurwitz correspondence. The duality equates the relative Gromov-Witten invariants and the count of covers of the target space with prescribed holonomies at boundaries. We clarify the projective large N limit as well as the role of the completed versus the ordinary cycles associated to the bulk and the boundary vertex operators respectively. We provide an example check of both the correspondence and the fact that cycles dual to closed strings need to be completed. Moreover, we identify the connected world sheets that contribute to an equivariantly localized amplitude in the bulk that is solely due to a completion term. We also propose a picture for the completed cycle combinatorics that involves a localization diagram glued to a cut-and-join string interaction.

We prove existence and multiplicity results for the nonlinear and nonlocal PDE $$ - Δu + (I_α\star |u|^p)\, |u|^{p-2}\, u = f(|x|,u) \quad \textrm{in} \,\,\mathbb {R}^N, $$ where $N \geq 2$, $I_α: \mathbb{R}^N \setminus \{0\} \rightarrow \mathbb{R}$ is the Riesz potential of order $α\in (1,N),$ $p>1,$ and the local nonlinearity $f: [0,\infty) \times \mathbb{R} \rightarrow \mathbb R$ is subject to a new class of assumptions. We find solutions to this zero-mass problem in a Coulomb-Sobolev space using a new scaling based approach in critical point theory, by which we classify the possibly different behaviour of the nonlinearity $f$ at zero and at infinity in terms of the scaling properties of the left hand side of the equation. This is accomplished identifying a scaling invariant PDE which can be interpreted as a nonlinear eigenvalue problem, for which a sequence of eigenvalues $\{λ_k\}$ is conveniently defined via the ${\mathbb{Z}}_2$-cohomological index of Fadell and Rabinowitz. This index allows us to use new critical group estimates (and scaling-based linking sets) which might not be possible via the classical genus. Within a fairly broad set of parameters $N,α, p$ and class of assumptions on the local nonlinearity $f,$ we establish compactness results for an associated action functional and find multiple solutions as critical points, whose existence and number is sensitive to the ''resonance'' of $f$ with the sequence of eigenvalues for the scaling invariant problem, a construction which is at places reminiscent, in the present nonlinear setting, of the classical Fredholm alternative. As a byproduct of our analysis, letting $p\neq 2$ allows us to capture general nonlinearities $f$ of Sobolev-subcritical, critical, or supercritical growth.

While ex-ante screening and static price caps are global standards for mitigating price volatility, Singapore's electricity market employs a unique dual-defense mechanism integrating vesting contracts (VC) with a temporary price cap (TPC). Using high-frequency data from 2021 to 2024, this paper evaluates this mechanism and yields three primary findings. First, a structural trade-off exists within the VC framework: while VC quantity (VCQ) suppresses average prices, it paradoxically exacerbates instability via liquidity squeezes. Conversely, VC price (VCP) functions as a tail-risk anchor, dominating at extreme quantiles where VCQ efficacy wanes. Second, a structural break around the 2023 reform reveals a fundamental re-mapping of price dynamics; the previously positive pass-through from offer ratios to clearing prices was largely neutralized post-reform. Furthermore, diagnostics near the TPC threshold show no systematic evidence of strategic bid shading, confirming the TPC's operational integrity. Third, the dual-defense mechanism exhibits a critical synergy that resolves the volatility trade-off. The TPC reverses the volatility penalty of high VCQ, shifting the elasticity of conditional volatility from a destabilizing 0.636 to a stabilizing -0.213. This synergy enables the framework to enhance tail-risk control while eliminating liquidity-related stability costs. We conclude that this dual-defense mechanism successfully decouples price suppression from liquidity risks, thereby maximizing market stability.