Estimating a classical parameter encoded in the Hamiltonian of a quantum probe is a fundamental and well-understood task in quantum metrology. A textbook example is the estimation of a classical field's amplitude using a two-level probe, as described by the semi-classical Rabi model. In this work, we explore the fully quantum analogue, where the amplitude of a coherent quantized field is estimated by letting it interact with a two-level atom. For both metrological scenarios, we focus on the quantum Fisher information (QFI) of the reduced state of the atomic probe. In the semi-classical Rabi model, the QFI is independent of the field amplitude and grows quadratically with the interaction time $τ$. In contrast, when the atom interacts with a single coherent mode of the field, the QFI is bounded by 4, a constant dictated by the non-orthogonality of coherent states. We find that this bound can only be approached in the vacuum limit. In the limit of large amplitude $α$, the QFI is found to attain its maximal value $1.47$ at $τ=O(1)$ and $τ=O(α^2)$, and also shows periodic revivals at much later times. When the atom interacts with a sequence of coherent states, the QFI can increase with time but is bounded to scale linearly due to the production of entanglement between the atom and the radiation (back-action), except in the limit where the number of modes and their total energy diverge. Finally, in the continuous-field limit, where the atom interacts with a continuous source of weak coherent states, this back-action can be simply interpreted as spontaneous emission; we find that the optimal atomic QFI rate is finite, depends on the source intensity, and is upper bounded by the constant rate at which the QFI is emitted by the radiation source.

String field theory is supposed to stand to perturbative string theory as quantum field theory stands to single-particle quantum theory; as such, it purports to offer a substantially more general and powerful perspective on string theory than the perturbative approach. In addition, string field theory has been claimed for several decades to liberate string theory from any fixed, background spatiotemporal commitments -- thereby (if true) rendering it `background independent'. But is this really so? In this article, we undertake a detailed interrogation of this claim, finding that the verdict is sensitive both to one's understanding of the notion of background independence, and also to how one understands string field theory itself. Although in the end our verdicts on the question of the background independence are therefore somewhat mixed, we hope that our study will elevate the levels of systematicity and rigour in these discussions, as well as equip philosophers of physics with a helpful introduction to string field theory and the variety of interesting conceptual questions which it raises.

This paper addresses the lifting problem for the Černý conjecture: namely, whether the validity of the conjecture for a quotient automaton can always be transferred (or "lifted") to the original automaton. Although a complete solution remains open, we show that it is sufficient to verify the Černý conjecture for three specific subclasses of reset automata: radical, simple, and quasi-simple. Our approach relies on establishing a Galois connection between the lattices of congruences and ideals of the transition monoid. This connection not only serves as the main tool in our proofs but also provides a systematic method for computing the radical ideal and for deriving structural insights about these classes. In particular, we show that for every simple or quasi-simple automaton $\mathcal{A}$, the transition monoid $\text{M}(\mathcal{A})$ possesses a unique ideal covering the minimal ideal of constant (reset) maps; a result of similar flavor holds for the class of radical automata.

Using a two-fluid approach, we consider the properties of relativistically nonlinear (arbitrary $a_0$), circularly polarized \EM\ waves propagating along magnetic field in electron-ion and pair plasmas. Dispersion relations depend on how wave intensity scales with frequency, $a_0 (ω)$. For superluminal branches, the nonlinear effects reduce the cut-off frequency, while the general form of the dispersion relations $ω(k)$ remains similar to the linear case. For subluminal waves, whistlers and Alfven, a new effect appears: dispersion curves effectively terminate at finite $ω^\ast - k^\ast$, where the group velocity becomes zero. Qualitatively, subluminal modes with fluctuating electric field larger than the guide field, $E_w (ω) \geq B_0$, cannot propagate. In extended systems, e.g., within magnetospheres of neutron stars, this leads to opening of the magnetosphere by a strong wave.

Social media platforms are increasingly adopting features that display crowdsourced context alongside posts, a technique pioneered by X's Community Notes. These systems -- which we term Crowdsourced Context Systems (CCS) -- have the potential to reshape the information ecosystem as major platforms embrace them as alternatives to professional fact-checking. To understand the features and implications of these systems, we conduct a systematic literature review of existing CCS research (n=56) and analyze real-world CCS implementations. Based on our analysis, we develop a framework with two components. First, we present a theoretical model to conceptualize and define CCS. Second, we identify a design space encompassing six aspects: participation, inputs, curation, presentation, platform treatment, and transparency. We also surface normative implications of different CCS design and implementation choices. Our work integrates theoretical, design, and ethical perspectives to establish a foundation for future human-centered research on Crowdsourced Context Systems.

We analyze a theory with non-minimal matter-curvature coupling, considering non-metricity properties with a Weyl connection. This model has the advantage of an extra force term which can mimic dark matter and dark energy, and simultaneously follow Weyl's idea to unify gravity and electromagnetism. Indeed, Schwarzschild-like and Reissner-Nordstrom-like black hole solutions exist in this model, leading to new features, such as an additional horizon, due to the non-metricity vector. We derive the cosmological field equations, considering a minimal coupling, and discuss preliminary results on the scalar cosmological perturbations in this model.

The polarized light of the cosmic microwave background is sensitive to new physics that violates parity symmetry. For example, the interaction of photons with the fields of elusive dark matter and dark energy could cause a uniform rotation of the plane of linear polarization across the sky, an effect known as cosmic birefringence. We extract the cosmological rotation angle, $β$, using Bayesian analysis of parity-violating correlations, $EB$ and $TB$, of polarization data from the Atacama Cosmology Telescope (ACT) Data Release 6. We use prior probabilities for instrumental miscalibration angles derived from the optics model for the ACT telescope and instruments, and marginalize over a residual intensity-to-polarization leakage. We measure $β= 0.215^\circ\pm 0.074^\circ$ (68\% confidence level), which excludes $β=0$ with a statistical significance of $2.9σ$. Although there remain systematics in the ACT data that are not understood and do not allow us to draw strong cosmological conclusions, this result is consistent with previous independent results from the WMAP and Planck missions. It is suggestive that independent data sets and analyses using different methodologies have yielded the same sign and comparable magnitudes for $β$.

We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical transparency properties of stealthy hyperuniform layered media, we compute the localization length using a perturbative expansion of the self-energy. We find that, for fixed energy and small but finite disorder strength $W$, there exists for any finite length system a range of stealthiness $χ$ for which the localization length exceeds the system size. This kind of "effective delocalization" is the result of the novel kind of correlated disorder that spans a continuous range of length scales, a defining characteristic of stealthy systems. Unlike uncorrelated disorder, for which the localization length $ξ$ scales as $W^{-2}$ to leading order for small W, the leading order terms in the perturbation expansion of $ξ$ for stealthy disordered systems vanish identically for a progressively large number of terms as $χ$ increases such that $ξ$ scales as $W^{-2n}$ with arbitrarily large $n$. Moreover, we support our analytical results with numerical simulations. Our results introduce stealthy disorder into quantum tight-binding models and show that enforcing a low-$k$ spectral gap markedly alters the scattering landscape, enabling localization lengths that exceed the system size at fixed disorder strength. Since this mechanism relies only on the spectral properties of the disorder, it carries over directly to photonic and phononic wave systems.

The Vera C. Rubin Observatory LSST is expected to discover tens of millions of new Active Galactic Nuclei (AGNs). The survey's exceptional cadence and sensitivity will enable UV/optical/NIR monitoring of a significant fraction of these objects. The unprecedented number of sources makes spectroscopic follow-up for the vast majority of them unfeasible in the near future, so most studies will have to rely on photometric redshifts estimates which are traditionally much less reliable for AGN than for inactive galaxies. This work presents a novel methodology to constrain the photometric redshift of AGNs that leverages the effects of cosmological time dilation, and of the luminosity and wavelength dependence of AGN variability. Specifically, we assume that the variability can be modeled as a damped random walk (DRW) process, and adopt a parametric model to characterize the DRW timescale ($τ$) and asymptotic amplitude of the variability (SF$_\infty$) based on the redshift, the rest-frame wavelength, and the AGN luminosity. We construct variability-based photo-$z$ priors by modeling the observed variability using the expected DRW parameters at a given redshift. These variability-based photometric redshift (VAR-PZ) priors are then combined with traditional SED fitting to improve the redshift estimates from SED fitting. Validation is performed using observational data from the SDSS, demonstrating significant reduction in catastrophic outliers by more than 10% in comparison with SED fitting techniques and improvements in redshift precision. The simulated light curves with both SDSS and LSST-like cadences and baselines confirm that, VAR-PZ will be able to constrain the photometric redshifts of SDSS-like AGNs by bringing the outlier fractions down to below 7% from 32% (SED-alone) at the end of the survey.

Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed by the Lindblad master equation, has received attention recently with the current state-of-the-art algorithms having an input model query complexity of $O(T\mathrm{polylog}(T/ε))$, where $T$ and $ε$ are the desired time and precision of the simulation respectively. For the Hamiltonian simulation problem it has been show that the optimal Hamiltonian query complexity is $O(T + \log(1/ε))$, which is additive in the two parameters, but for Lindbladian simulation this question remains open. In this work we show that the additive complexity of $O(T + \log(1/ε))$ is reachable for the simulation of a large class of dissipative Lindbladians by constructing a novel quantum algorithm based on quantum trajectories.

Higher-order shear statistics contain part of the non-Gaussian information of the projected matter field and therefore can provide additional constraints on the cosmological parameters when combined with second-order statistics. We aim to provide the theoretical framework for studying shear four-point correlation functions (4PCF) using fourth-order aperture statistics and develop a numerical integration pipeline to compute them. Finally, we forecast the information content of fourth-order aperture statistics. We begin by giving the relation of the $n$-th order aperture statistics, $\langle M_\mathrm{ap}^n\rangle$, to the shear $n$PCF and to the convergence polyspectra. We then focus on the fourth-order case, where we derive the functional form of their filters and test the behavior of these filters by numerically integrating over the 4PCF of a Gaussian random shear field (GRF). Finally, we perform a Fisher forecast on the constraining power of $\langle M_\mathrm{ap}^4\rangle_\rm{c}$, where we develop a novel method to estimate derivatives from a simulation suite with arbitrarily distributed cosmological sets. By analyzing and mitigating numerical effects within the integration pipeline, we achieve a two-percent-level precision on the fourth-order aperture statistics for a GRF, which remains well below the noise budget of Stage IV surveys. We report a minimal improvement in the constraining power of the aperture statistics when including fourth-order statistics to a $\langle M_\mathrm{ap}^2\rangle + \langle M_\mathrm{ap}^3\rangle$ joint analysis for a DES-Y3-like setup, using non-tomographic equal-scale aperture statistics.

High-redshift ($z>2$) blazars, with relativistic jets aligned toward us, probe the most powerful end of the active galactic nuclei (AGN) population. We aim at determining the black hole masses and mass accretion rates of high-$z$ blazars in a common framework that utilizes a Markov Chain Monte Carlo (MCMC) fitting method and the Shakura-Sunayev multi-temperature accretion disk model, accounting also for attenuation due to neutral hydrogen gas in the intergalactic medium (IGM). We compiled a sample of 23 high-redshift blazars from the literature with publicly available infrared-to-ultraviolet photometric data. We performed a Bayesian fit to the spectral energy distribution (SED) of the accretion disk, accounting for upper limits, and determined the black hole masses and mass accretion rates with their uncertainties. We also examined the impact of optical-ultraviolet attenuation due to gas in the IGM. We find that neglecting IGM attenuation in SED fits leads to systematically larger black-hole mass estimates and correspondingly lower Eddington ratios, with the bias becoming more severe at higher redshift. Our MCMC fits yield median black-hole masses in the range $\sim (10^{8}-10^{10})\,M_{\odot}$ and a broad distribution of median Eddington ratios ($λ_{\rm Edd}\sim0.04$ up to $\sim1$). Comparison with previous literature shows no clear method-dependent systematic offsets, although individual mass estimates can differ by up to a factor of a few. We also demonstrate that assumptions about black-hole spin introduce a systematic degeneracy. This work is to our knowledge the first systematic study to model the accretion-disk emission of a large sample of high-$z$ blazars within a single, consistent statistical framework. Our results emphasize the importance of accounting for IGM attenuation and of using uniform fitting methods when comparing disk-based black hole estimates across samples.

We present a scheme for laser cooling and magneto-optical trapping of the Group IV (a.k.a. Group 14 or tetrel) atoms silicon (Si), germanium (Ge), tin (Sn), and lead (Pb). These elements each possess a strong Type-II transition ($J \rightarrow J' = J-1$) between the metastable $s^2p^2 \,^3P_1$ state and the excited $s^2ps'\, ^3P_0^o$ state at an accessible laser wavelength, making them amenable to laser cooling and trapping. We focus on the application of this scheme to Sn, which has several features that make it attractive for precision measurement applications. We perform numerical simulations of atomic beam slowing, capture into a magneto-optical trap (MOT), and subsequent sub-Doppler cooling and compression in a blue-detuned MOT of Sn atoms. We also discuss a realistic experimental setup for realizing a high phase-space density sample of Sn atoms.

The ATLAS experiment has performed a measurement of coherent exclusive $J/ψ\toμ^+μ^-$ production in ultraperipheral Pb+Pb collisions at $\sqrt{s_{\textrm{NN}}}=5.36$ TeV. The data was recorded at the Large Hadron Collider (LHC) during 2023, and corresponds to an integrated luminosity of 79 $μ$b$^{-1}$. Exclusive $J/ψ$ candidates were selected with a dedicated track-sensitive trigger based on the ATLAS transition radiation tracker. The analysis involves reconstruction of the dimuon invariant mass based on muon tracks from the inner detector, as the muon transverse momentum range of interest precludes the use of the standard muon reconstruction and identification algorithms. Differential cross sections are measured as a function of $J/ψ$ rapidity and are compared with theoretical predictions. After extrapolation to $\sqrt{s_{\textrm{NN}}}=5.02$ TeV, they are also compared with previous measurements performed by other experiments using data from LHC Run 2. While the results agree reasonably well with theoretical predictions, they are in tension with previous Run-2 results for the central rapidity region.

We present the calibration of stellar and active galactic nucleus (AGN) feedback in the subgrid model for the new COLIBRE hydrodynamical simulations of galaxy formation. COLIBRE directly simulates the multi-phase interstellar medium and the evolution of dust grains, which is coupled to the chemistry. COLIBRE is calibrated at three resolutions: particle masses of $m_{\rm gas} \approx m_{\rm dm} \sim 10^7$ (m7), $10^6$ (m6), and $10^5~\mathrm{M_\odot}$ (m5). To calibrate the COLIBRE feedback at m7 resolution, we run Latin hypercubes of $\approx 200$ simulations that vary up to four subgrid parameters in cosmological volumes of ($50~\mathrm{cMpc}$)$^{3}$. We train Gaussian process emulators on these simulations to predict the $z=0$ galaxy stellar mass function (GSMF) and size - stellar mass relation (SSMR) as functions of the model parameters, which we then fit to observations. The trained emulators not only provide the best-fitting parameter values but also enable us to investigate how different aspects of the prescriptions for supernova and AGN feedback affect the predictions. In particular, we demonstrate that while the observed $z=0$ GSMF and SSMR can be matched individually with a relatively simple supernova feedback model, simultaneously reproducing both necessitates a more sophisticated prescription. We show that the calibrated m7 COLIBRE model not only reproduces the calibration target observables, but also matches various other galaxy properties to which the model was not calibrated. Finally, we apply the calibrated m7 model to the m6 and m5 resolutions and, after slight manual adjustments of the subgrid parameters, achieve a similar level of agreement with the observed $z=0$ GSMF and SSMR.

We introduce a generalisation of Schütz and Trimper's elephant random walk to finitely generated groups. We focus on the simplest non-abelian setting, i.e. groups whose Cayley graphs are homogeneous trees of degree $d \ge 3$. We show that the asymptotic speed of the walk does not depend on the memory parameter $p \in [0, 1)$ and equals $\frac{d - 2}{d}$, the asymptotic speed of simple random walk on these graphs. We also establish upper bounds on the rate of convergence to the limiting speed. These upper bounds depend on $p$ and exhibit a phase transition at the critical value $p_d = \frac{d + 1}{2d}$. Numerical experiments suggest that these upper bounds are tight. Along the way, we also obtain estimates on the return probability.

We propose a new approach to coarse-grained description of quantum evolution that provides an explicit recipe to construct and evaluate multi-time decoherent histories in a controlled way, applicable to non-Markovian and integrable systems. Specifically, we study local interaction quench of a local degree of freedom (an open quantum system) within a noninteracting integrable environment. This setting allows us to identify the environmental degrees of freedom that irreversibly store records of the system's past. These modes emerge sequentially in time and define the projectors required for decoherent histories. We show numerically that the off-diagonal elements of the decoherence functional are exponentially suppressed relative to a significance threshold.

When scaling up quantum processors in a cryogenic environment, it is desirable to limit the number of qubit drive lines going into the cryostat, since fewer lines makes cooling of the system more manageable and the need for complicated electronics setups is reduced. However, although time multiplexing of qubit control enables using just a few drive lines to steer many qubits, it comes with a trade-off: fewer drive lines means fewer qubits can be controlled in parallel, which leads to an overhead in the execution time for quantum algorithms. In this article, we quantify this trade-off through numerical and analytical investigations. For standard quantum processor layouts and typical gate times, we show that the trade-off is favorable for many common quantum algorithms $\unicode{x2014}$ the number of drive lines can be significantly reduced without introducing much overhead. Specifically, we show that couplers for two-qubit gates can be grouped on common drive lines without any overhead up to a limit set by the connectivity of the qubits. For single-qubit gates, we find that the serialization overhead generally scales only logarithmically in the number of qubits sharing a drive line. These results are promising for the continued progress towards large-scale quantum computers.

When solving time-dependent partial differential equations(PDEs), traditional physics-informed neural networks (PINNs) have inherent limitations: due to the lack of temporal causality, the network is forced to learn the later-time control equations while fully capturing the initial conditions, resulting in the continuous accumulation of errors during the integration process. Meanwhile, the limited expressivity of a single network hinders its ability to capture diverse physical behaviors across multiple subdomains. To address these issues, we propose a domain-decomposition-based causal PINNs (DDC-PINNs) framework. This framework enhances spatial representation through domain decomposition and employs a causal strategy to constrain the temporal learning sequence, thereby improving the accuracy and generalization ability of solutions to time-varying problems. Within this framework, an approximate solution is first obtained through PINNs with domain decomposition. Subsequently, the time derivative term in the PDE is retained, while other solution-dependent terms are replaced with this approximate solution, thereby simplifying the original PDEs into ordinary differential equations (ODEs). Finally, classical numerical methods for solving ODEs are employed to obtain the time-dependent solution. DDC-PINNs not only preserve the inherent computational efficiency and flexibility of PINNs but also effectively incorporate causality when solving time-dependent PDEs. Numerical experiments verify the effectiveness of the proposed method.

Data generated in studies of cellular regulatory systems are often qualitative. For example, measurements of signaling readouts in the presence and absence of mutations may reveal a rank ordering of responses across conditions but not the precise extents of mutation-induced differences. Qualitative data are often ignored by mathematical modelers or are considered in an ad hoc manner, as in the study of Kocieniewski and Lipniacki (2013) [Phys Biol 10: 035006], which was focused on the roles of MEK isoforms in ERK activation. In this earlier study, model parameter values were tuned manually to obtain consistency with a combination of qualitative and quantitative data. This approach is not reproducible, nor does it provide insights into parametric or prediction uncertainties. Here, starting from the same data and the same ordinary differential equation (ODE) model structure, we generate formalized statements of qualitative observations, making these observations more reusable, and we improve the model parameterization procedure by applying a systematic and automated approach enabled by the software package PyBioNetFit. We also demonstrate uncertainty quantification (UQ), which was absent in the original study. Our results show that PyBioNetFit enables qualitative data to be leveraged, together with quantitative data, in parameterization of systems biology models and facilitates UQ. These capabilities are important for reliable estimation of model parameters and model analyses in studies of cellular regulatory systems and reproducibility.

The wettability of monolayer and multilayer graphene remains a topic of longstanding debate. Here, we combined first-principles molecular dynamics simulations accelerated with the atomic cluster expansion machine learning interatomic potential to investigate how substrate, graphene layer number, and intercalated water molecules influence graphene's wettability. Simulated vibrational sum-frequency generation (vSFG) spectra revealed that the experimentally observed hydrophilic behavior of monolayer graphene on hydrophilic substrates arose not from wetting transparency, but from signal cancellation induced by intercalated water. Energetic analyses further showed that intercalated water molecules were thermodynamically favorable for monolayer graphene on hydrophilic substrates, but not for multilayer systems, leading to changes in the vSFG response in line with experimental observations. These results offer a mechanistic understanding of graphene-water interactions and have broad implications for the design of graphene-based interfaces and devices.

The C-MetaLL project has provided homogeneous spectroscopic abundances of 290 Classical Cepheids (DCEPs) for which we have the intensity-averaged magnitudes in multiple optical and near-infrared (NIR) bands, periods, pulsation modes, and Gaia parallaxes. Our goal is to derive updated period-Wesenheit-metallicity (PWZ) relations using the largest and most homogeneous metallicity sample ever used for such analyses, covering a range of $-1.3<$[Fe/H]$<+0.3$ dex. We computed several optical and NIR Wesenheit magnitudes using 275 DCEPs with reliable parallaxes, by applying a robust photometric parallax technique, which simultaneously fits all parameters -- including the global Gaia parallax counter-correction -- and handles outliers without data rejection. We find a stronger metallicity dependence ($γ\approx -0.5$ mag/dex in optical, $-0.4$ mag/dex in NIR) than recent literature reports. Gaia parallax zero-point conter-corrections ($ε$) vary smoothly across bands, with an average value of $\sim$10 $μ$as, aligning with previous determinations. Applying our PWZ relations to LMC Cepheids yields distances generally consistent within $1σ$ with geometric estimates. The choice of reddening law has a negligible impact, while using only fundamental-mode pulsators significantly increases the uncertainties. Including $α$-element corrections increases $|γ|$ and reduces $ε$. However, we find statistically consistent $γ$ values with the literature, particularly for the key Wesenheit magnitude in the HST bands, by restricting the sample to the brighter (i.e. closer) objects, or by including only pulsators with $-0.7<$[Fe/H]$<$0.2 dex. Our results hint at a large $γ$ or a non-linear dependence on metallicity of DCEP luminosities at the metal-poor end, which is difficult to quantify with the precision of parallaxes of the present dataset.

We review the cosmic generalisation of the virial theorem known as the Layzer-Irvine equation, also independently derived by Dmitriev and Zeldovich. This equation has been studied in the literature for dark matter-dark energy interaction models, as well as in the context of alternative theories of gravity. We discuss results from the previous scenarios and point out future directions.

We present a matrix product operator construction that allows us to represent the lattice Hamiltonians of (abelian or non-abelian) gauge theories in a local and manifestly translation-invariant form. In particular, we use symmetric matrix product states and introduce link-enhanced matrix product operators (LEMPOs) that can act on both the physical and virtual spaces of the matrix product states. This construction allows us to study Hamiltonian lattice gauge theories on infinite lattices. As examples, we show how to implement this method to study the massless and massive one-flavor Schwinger model and adjoint QCD$_2$.

The 21 cm signal contains a wealth of information about the formation of the first stars and the reionization of the intergalactic medium during the Cosmic Dawn (CD) and Epoch of Reionization (EoR). The timing of these important milestones has only roughly been constrained through indirect measurements, such as from the cosmic microwave background (CMB) optical depth, and Lyman-$α$ forest. Therefore, inferring the neutral fraction over cosmic time is a goal of upcoming 21 cm experiments, such as the Square Kilometer Array (SKA). We contrast two approaches to infer astrophysical parameters and ionization history from 21 cm 2D power spectra (2DPS). We develop an emulator of the 21 cm 2DPS, trained on 21cmFAST simulations, taking into account the expected instrumental noise from the SKA and sample variance. We then perform simulation based inference (SBI) using neural posterior estimation (NPE). We compare training on datasets of noisy 2DPS obtained from 21cmFAST simulations and an emulator, to infer astrophysical parameters of interest. Using an emulator of the ionization history, which has been trained on simulations from the same astrophysical parameters, we then obtain posterior distributions of the ionization history over the redshift range z $\sim$ 5-12. We demonstrate that both methods are capable of accurately recovering the ionization history and astrophysical parameters. However, coverage tests indicate that adding emulated samples does not improve predictions. This work suggests that due to the stochastic nature of the 2DPS, using an emulator of this summary statistic may result in poorer inference.

We prove a non Archimedean Darboux's Theorem: any two symplectic forms on a $p$-adic analytic manifold are locally isomorphic. Understanding local problems such as the existence of flows or the normalization of singularities in the theory of integrable systems, is essential to understand the physics behind these systems. Our result tells us that the phase space defined by a $p$-adic manifold is locally standard, allowing us to concentrate on the equations defining the dynamics rather than on the space itself. Our proof uses a non Archimedean version of Moser's Path Method to push one symplectic form onto another one by a flow. A central technical contribution of the paper is the proof that the flow is given by a power series with \emph{non zero radius of convergence}, which requires geometric analytic estimates and does not follow from algebraic considerations. As a global application, we derive a classification of second-countable $p$-adic analytic symplectic manifolds in terms of $p$-adic volume, which generalizes a classical theorem of J-P. Serre.

Investigation of the approximation properties, convergence, and stability of the ADER-DG method for solving an ODE system is carried out. The ADER-DG method is $A$- and $AN$-stable, $L$-stable, $B$- and $BN$-stable, and algebraically stable. Several other relations useful for an application and implementation of the ADER-DG method are proved. Applications of the ADER-DG method demonstrated compliance with the expected theoretical results.

The influence of turbine-turbine interactions on sound propagation is investigated using numerical simulations. Three configurations are examined: turbines aligned downstream of each other, placed side by side, and arranged in a staggered pattern. The simulation framework combines large-eddy simulations for aerodynamic interactions, an aeroacoustic source model to simulate turbine sound emission, and parabolic equation methods for sound propagation. When a second turbine is positioned directly downstream, wake-induced flow focusing enhances sound pressure levels (SPL) and amplitude modulation (AM) by several decibels downwind. In side-by-side and staggered configurations, SPL increases are limited (<2 dBA), and AM is generally reduced due to spatial averaging. Distinct AM patterns emerge in regions where acoustic contributions from both turbines are comparable. For identical rotor speeds, AM is strongly affected by the angular offset between rotors. When rotor speeds differ slightly, beating effects occur, resulting in intermittent AM. These findings highlight the sensitivity of AM to rotor dynamics, a key factor influencing sound perception, with implications for environmental impact and turbine siting.

Using cosmological radiation-hydrodynamical simulations, we study the effect of accreting supermassive black holes (SMBHs) on nearby dark-matter (DM) haloes in the very early universe. We find that an SMBH with a spectral energy distribution (SED) extending from the near-ultraviolet to hard X-rays, can produce a radiation background sufficient to delay gravitational collapse in surrounding DM haloes until up to $10^7$ M$_\odot$ of zero-metallicity gas is available for the formation of Population III (Pop III) stars or direct-collapse black holes (DCBHs). We model three scenarios, corresponding to an SMBH located at physical distances of 10, 100, and 1000 kpc from the Pop III host DM halo. Using these three scenarios, we use the SED to compute self-consistent photoionization, photoheating, and photodissociation rates. We include the effects of Compton scattering and gas self-shielding. The X-ray portion of the spectrum maintains an elevated free-electron fraction as the gas collapses to high density. This stimulates H2 formation, allowing the gas to cool further while counteracting the dissociation of H2 by Lyman-Werner radiation. As a result, a large cluster of Pop III stars is expected to form, except in the case with the most intense radiation in which a DCBH may instead form. Our simulated Pop III clusters have comparable HeII 1640 luminosities to the recently discovered Pop III host candidate near GN-z11, observed by the James Webb Space Telescope. In two of the scenarios we consider, the resulting clusters could be detectable using the telescope's NIRSpec instrument out to z ~ 15.

Transformer-based language models for code have shown remarkable performance in various software analytics tasks, but their adoption is hindered by high computational costs, slow inference speeds, and substantial environmental impact. Model compression techniques such as pruning, quantization, and knowledge distillation have gained traction in addressing these challenges. However, the impact of these strategies on the robustness of compressed language models for code in adversarial scenarios remains poorly understood. Understanding how these compressed models behave under adversarial attacks is essential for their safe and effective deployment in real-world applications. To bridge this knowledge gap, we conduct a comprehensive evaluation of how common compression strategies affect the adversarial robustness of compressed models. We assess the robustness of compressed versions of three widely used language models for code across three software analytics tasks, using six evaluation metrics and four commonly used classical adversarial attacks. Our findings indicate that compressed models generally maintain comparable performance to their uncompressed counterparts. However, when subjected to adversarial attacks, compressed models exhibit significantly reduced robustness. These results reveal a trade-off between model size reduction and adversarial robustness, underscoring the need for careful consideration when deploying compressed models in security-critical software applications. Our study highlights the need for further research into compression strategies that strike a balance between computational efficiency and adversarial robustness, which is essential for deploying reliable language models for code in real-world software applications.