In this work, initial-boundary value problems for the time-fractional Airy equation are considered on different intervals. We study the properties of potentials for this equation and, using these properties, construct solutions to the considered problems. The uniqueness of the solution is proved using an analogue of the Gronwall-Bellman inequality and an a priori estimate.

Affective alignment in generative AI represents a systemic risk to the developmental autonomy of younger users. Although emotional mirroring is commonly seen as a hallmark of advanced human-machine interaction, it can also manifest as affective sycophancy, reinforcing a user's immediate emotional state. By providing a sense of objectivity to transient anxieties, these systems diminish the cognitive friction necessary for independent emotional management and critical thought. Reward models driven by RLHF could heighten this dilemma by embedding adult-focused definitions of helpfulness, unintentionally promoting emotional dependency in younger users rather than facilitating cognitive reappraisal. This paper exposes the misalignment between adult-labeled reward signals and the developmental requirements of younger users, proposing stoic architectures that emphasize functional neutrality to preserve user autonomy.

For the fully nonlinear stationary logistic equation ${\mathcal F}(x,D^2u)+μu=k(x)u^p$ with $p>1$ and $k(x)\geq 0$, in a bounded domain with Dirichlet boundary condition, we determine, in terms of $μ$, the existence and uniqueness or the nonexistence of a positive solution. Furthermore, we study the asymptotic behavior of the solutions when $μ$ approaches the boundary points of the existence range.

We study various properties of $f$-divergences and Csiszár indices between two probability distributions in very general setups for the convex function $f$ and for the probability distributions. We establish general structural properties of $f$-divergences and show how they are inherited by the associated Csiszár indices, including monotonicity and invariance under suitable transformations. We also study the relationship between Csiszár indices and copula representations of random vectors. When the marginal distributions have atoms, the copula representation is not unique and the Csiszár index of the transformed vectors may increase. We build a large family of interpolating copulas which minimize the Csiszár index and thus preserve the dependence structure of the initial vector.

Speculative fiction has long served an inspiration for genuine scientific inquiry. One notable work that has almost acted in this manner is the the seminal comedic speculative fiction work Cloudy with a Chance of Meatballs. While exoplaneteers reference this work frequently, we have never engaged with the central prediction of this work... until now! We perform detailed microphysical modeling of meatball clouds, both bare and coated with marinara sauce, and find that while meatball condensation is possible in temperate atmospheres, the meatballs do not quite grow to the sizes predicted by Cloudy. We do find, however, that such meatball condensation, across a large enough planet, would be able to sustain humanity calorically.

We consider a structure-preserving finite-volume scheme for the Euler-Korteweg (EK) and Navier-Stokes-Korteweg (NSK) equations. We prove that its numerical solutions converge to energy-variational solutions of EK or NSK under mesh refinement. Energy-variational solutions constitute a novel solution concept that has recently been introduced for hyperbolic conservation laws, including the EK system, and which we extend to the NSK model. Our proof is based on establishing uniform estimates following from the properties of the structure-preserving scheme, and using the stability of the energy-variational formulation under weak convergence in the natural energy spaces.

Recent cosmological surveys and datasets have highlighted a variety of tensions to the concordance model of our universe, $Λ$CDM. Of particular interest is the Hubble tension, the $5.5σ$ discrepancy between measurements of the Hubble constant $H_0$ using high redshift CMB data from Planck ($67.27\pm0.60$km$\text{s}^{-1}\text{Mpc}^{-1}$) and low redshift supernovae from SH0ES ($73.2\pm1.3$km$\text{s}^{-1}\text{Mpc}^{-1}$). To avoid stepping on any toes, we have initiated the CROCS collaboration to resolve this tension, gathering experts from across many fields of cosmology, astrophysics, astronomy, machine learning, data science, philosophy, and astrology. In this paper, we present findings from CROCS Data Release 1, corresponding to the first $\sim3$ days and 27 minutes (rest frame) of observation. We perform a robust statistical analysis, showing that Planck and SH0ES both suffer from imperial biasing systematics (IBS) at $5σ$ significance. Accounting for these errors by converting to metric units reconciles the high and low redshift data, with $H_0 = 69.00\pm0.420$km$\text{s}^{-1}\text{Mpc}^{-1}$. We thus report that our results are sufficient to end the Hubble tension for good.

The European Union's Digital Services Act (DSA) introduced regulatory mechanisms which serve as a way to manage harmful content online. The recognition of Trusted Flaggers (TFs) is one such mechanism which accredits entities with experience, platform independence, and skill in identifying and reporting illegal content. With the DSA's TF role being roughly one year old, we interviewed representatives of seven such TF organizations to learn about their experiences of becoming a TF and how it impacts their interactions with online platforms and with individual users. We additionally ran a workshop involving TF representatives, primarily as it was requested by TFs themselves, who collectively wanted to share experiences of their new role and learn from each other rather than be isolated. Notably, we found that accreditation as a TF can be cumbersome, that resources for TFs remain the same despite an increasing workload, and that platforms priorities often diverge from TFs. We conclude with recommendations for future research into understanding user representation within the DSA and the need for standardization measures tailored to the needs and resource constraints of TFs.

The suspended end mirror of the input mode cleaner cavity in the Advanced Virgo Plus interferometer was equipped with an instrumented baffle in spring 2021, serving as a demonstrator of the technology in preparation for the installation of large instrumented baffles in the main arms of the interferometer. This baffle includes tens of sensors positioned near the mirror to enable monitoring of stray light within the cavity. In this contribution, we assess the performance and stability of the instrument after four years of operation. After introducing the main characteristics of the baffle, we study the distribution of stray light and show that the instrumented baffle can be used to monitor laser stability and alignment within the cavity. Finally, we assess the noise level during the final stages of the O4b commissioning to monitor the impact of the baffle, and conclude that the baffle does not introduce any additional disturbance to the normal operation of the interferometer.

Applications of the Ryu-Takayanagi formula to evaporating black holes are known to reproduce the Page curve, although leaving open the microscopic origin of the necessary black hole degrees of freedom responsible for the entanglement and microstates. Here, we fill this gap by utilizing a recently proven generalized Ryu-Takayanagi formula which keeps the contact to the theory's Hamiltonian phase space. Precisely, we show that in any diffeomorphism invariant field theory containing stationary black holes with bifurcate Killing horizons the phase space states distinguishable by their Hamiltonian surface charges over the bifurcation surface must provide the degrees of freedom responsible for the black hole's Wald entropy. This result is part of a larger program where measurable quantities of a quantum theory are expressed as weighted sums over paths in the theory's phase space. Suited reorganization tools for those sums make then physical phenomena evident which might be obscured in a naive summation relying on spacetime notions such as field configuration spaces and Feynman diagrams. Besides presenting this result, we provide here a conceptual overview of the program as an entry point for unfamiliar readers explaining the central notion of the program and why it reveals the results obtained so far. These include especially the gravitational entropy bound and the here applied generalized Ryu-Takayanagi prescription shown earlier within the program. Using the information paradox as a leitmotif, our proposed program uncovers black hole hair that may be hidden within a naive spacetime interpretation.

We present a systematic derivation of the Heisenberg evolution of a trilinear bosonic Hamiltonian system in presence of a strong drive beyond the standard approximation of a classical, undepleted driving field. We employ a perturbative expansion of the Hamiltonian propagator in orders of the input field amplitudes, as opposed to the standard Baker-Campbell-Hausdorff (BCH) expansion of the propagator in orders of time. Our method automatically provides time-closed expressions; and converges considerably faster than BCH, especially in the regime of high parametric gain because the small parameter it uses is natural to the problem. We obtain the well-known quantum solution for optical parametric amplification of down-conversion simply as the first order of the expansion, and present the rigorous procedure to derive higher order corrections one by one. To demonstrate the utility of higher corrections, we discuss the 2nd order correction to the pump field as an ideal detector of time-energy entanglement in parametric down-conversion. We also use the 3rd order correction to calculate the limits on the fidelity of quantum state-transfer from one optical mode to another using sum/difference frequency generation, due to the quantum properties of the strong driving field.

Generation and Transmission Expansion Planning (GTEP) problems co-optimize generation and transmission expansion, enabling them to provide better planning decisions than traditional Generation Expansion Planning or Transmission Expansion Planning problems, but GTEPs can be computationally complex or intractable. Benders Decomposition (BD) has been applied to expansion planning problems, with various methods applied to accelerate convergence. In this work, we test strategies for improving the performance of BD on GTEP models with nodal resolution and DCOPF constraints. We also present an alternative approach for handling the bilinear constraints that can result in these problems. These tests included combinations of using generalized Benders decomposition (GBD), hot-starting via a transport constrained model, using linear relaxations of the master problem, and using regularization. We test these methods on mixed-integer linear programming GTEP models with up to 146 buses (10 million continuous variables and 400 mixed-integer decisions). With selected accelerated Benders decomposition approaches, the problems can be solved to under a 1\% gap in as little as 5 hours where they were otherwise intractable. Results also suggest that using regularization on these initial hot-starting and relaxation steps and turning it off after they are complete was generally the best combination of strategies.

Existing mezzanine image codecs lack specialized screen content coding tools and therefore struggle to maintain high image quality under bandwidth constraints, especially in areas with dense text. Although distribution codecs offer advanced screen content compression techniques, their high computational complexity makes them impractical for mezzanine coding. To address this shortfall, we introduce the High-quality Lightweight Codec (HLC), a solution centered on enabling practical, high-throughput palette for mezzanine coding. The core innovation is a novel data-dependency-free palette that eliminates the throughput bottlenecks. To ensure its effectiveness across all content, a co-designed rate-distortion optimization module arbitrates between the palette and traditional prediction modes, while a data reuse strategy between rate estimation and entropy coding minimizes the overall hardware resources required for the system. Experimental results show that, compared with a 4K@120fps JPEG-XS encoder, HLC achieves the same throughput while using only half the LUT resources and delivers BD-PSNR improvements of 3.461dB, 3.299dB, and 5.312dB on gaming, natural, and text content datasets, respectively.

We propose a least-squares penalization as a means to extend the discontinuous Petrov-Galerkin (DPG) method with optimal test functions to a class of semilinear elliptic problems. The nonlinear contributions are replaced with independent unknowns so that standard DPG techniques apply to the then linear problem with non-trivial kernel. The nonlinear relations are added as least-squares constraints. Assuming solvability of the semilinear problem and an Aubin-Nitsche-type approximation property for the primal variable, we prove a Cea estimate for the approximation error in canonical norms. Numerical results with uniform and adaptively refined meshes illustrate the performance of the scheme.

Discrete events alter how parameter influence propagates in hybrid systems. Prevailing Fisher information formulations assume that sensitivities evolve smoothly according to continuous-time variational equations and therefore neglect the sensitivity updates induced by discrete events. This paper derives a Fisher information matrix formulation compatible with hybrid systems. To do so, we use the saltation matrix, which encodes the first order transformation of sensitivities induced by discrete events. The resulting formulation is referred to as the salted Fisher information matrix (SFIM). The proposed framework unifies continuous information accumulation during flows with discrete updates at event times. We further establish that hybrid persistence of excitation provides a sufficient condition for positive definiteness of the SFIM. Examples are provided to demonstrate the merit of the proposed approach, including a three bus generator wind turbine differential algebraic power system

The structure of the nonlinear inverse problem arising from capillarity-driven imbibition in porous media is investigated, considering a degenerate parabolic PDE with compactly supported diffusivity and boundary-driven fluxes as the governing forward model. The inverse problem -- inferring hydraulic model parameters from sparse integral absorption measurements -- is inherently ill-posed: the nonlinear forward operator induces anisotropic parameter sensitivity and structured correlations that render the calibration landscape non-convex and partially unidentifiable. To characterise this structure rigorously, Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) is adopted as a likelihood-free inferential framework, bypassing the analytical intractability of the likelihood while providing full posterior distributions over the parameter space. Two physically motivated parameterisations of the diffusivity function are analysed -- the Natalini-Nitsch (NN) and the BkP formulations. It is shown that the posterior geometry obtained via ABC-SMC encodes, in directly readable form, the sensitivity structure of the nonlinear forward operator: the principal component decomposition of the posterior covariance provides a natural hierarchy of parameter sensitivity, with low-variance eigendirections identifying the parameter combinations to which the forward map is most responsive. This geometric decomposition constitutes a principled and computationally efficient alternative to classical sensitivity analysis, arising as a byproduct of the calibration procedure. These findings are established through both synthetic experiments, confirming accurate parameter recovery, and real laboratory imbibition data from materials of cultural heritage relevance.

In the reinforcement learning literature, strong theoretical guarantees have been obtained for algorithms applicable to LTI systems. However, in the nonlinear case only weaker results have been obtained for algorithms that mostly rely on the use of function approximation strategies like, for example, neural networks. In this paper, we study the applicability of a known output-feedback Q-learning algorithm to the class of nonlinear systems that admit a Koopman linear embedding. This algorithm uses only input-output data, and no knowledge of either the system model or the Koopman lifting functions is required. Moreover, no function approximation techniques are used, and the same theoretical guarantees as for LTI systems are preserved. Furthermore, we analyze the performance of the algorithm when the Koopman linear embedding is only an approximation of the real nonlinear system. A simulation example verifies the applicability of this method.

Recent studies have shown that Trotter errors are highly initial-state dependent and that standard upper bounds often substantially overestimate them. However, the mechanism underlying anomalously small Trotter errors and a systematic route to identifying error-resilient states remain unclear. Using interaction-picture perturbation theory, we derive an analytical expression for the leading-order Trotter error in the eigenbasis of the Hamiltonian. Our analysis shows that initial states supported on spectrally commensurate energy ladders exhibit strongly suppressed error growth together with persistent Loschmidt revivals. We refer to such states as Trotter scars. To identify such states in practice, we further introduce a general variational framework for finding error-minimizing initial states for a given Hamiltonian. Applying this framework to several spin models, we find optimized states whose spectral support and dynamical behavior agree with the perturbative prediction. Our results reveal the spectral origin of Trotter-error resilience and provide a practical strategy for discovering error-resilient states in digital quantum simulation.

Recent advancements in the text-rendering capabilities of image generation models have made the end-to-end creation of graphic design content, such as posters, increasingly feasible. However, existing reward models fall short of accurately assessing design quality, as they primarily focus on global image aesthetics while overlooking the critical dimensions of typography and layout. Furthermore, the scarcity of domain-specific preference data remains a significant bottleneck, which limits the further development of graphic design evaluation and generation. To bridge this gap, we introduce an automated pipeline to construct a high-quality dataset of 70k poster preferences by leveraging the consensus of multiple Multi-modal Large Language Models (MLLMs) to simulate human-like judgment. Utilizing this dataset, we develop PosterReward, a reward model specifically designed for high-precision poster assessment through a cascaded, multi-stage training strategy. We also provide multiple variants of the model to cater to different application scenarios. Finally, we introduce PosterRewardBench and PosterBench to evaluate the performance of existing reward models in poster assessment and the generation capabilities of current text-to-image models in poster creation, respectively.

We report the first measurement of the $e^{+}e^{-}\to K^{+}K^{-}$ cross sections around the $ψ(2S)$ resonance using the energy scan method. The analysis is based on $e^{+}e^{-}$ collision data corresponding to an integrated luminosity of 495~pb$^{-1}$ collected with the BESIII detector at BEPCII. By analyzing the cross section line-shape, we extract the relative phase $Φ$ between the strong and electromagnetic amplitudes of the $ψ(2S)$ resonance, a fundamental parameter in charmonium physics, based on the assumption that the relative phase between the electromagnetic amplitude of the $ψ(2S)$ resonance and the continuum is zero. Two distinct solutions for the branching fraction $\mathcal{B}$ of $ψ(2S)\to K^{+}K^{-}$ are observed: a constructive interference solution with $\mathcal{B}=(7.49\pm0.41)\times10^{-5}$ and $Φ=(110.1 \pm6.7)^\circ$, and a destructive interference solution with $\mathcal{B}=(10.94\pm0.48)\times10^{-5}$ and $Φ=(-106.8\pm5.7)^\circ$. A significant correlation between $Φ$ and $\mathcal{B}$ is established, demonstrating that interference effects must be taken into account in the $ψ(2S)$ branching fraction measurements. Additionally, the first results for both the $ψ(2S)$ strong form factor, which characterizes the strong coupling between $ψ(2S)$ and $K^{+}K^{-}$, and the energy-dependent electromagnetic form factor of the charged kaon in this energy region are here reported.

In this paper we study the local geometry of the stack of pointed $A_r$-stable curves. In particular, we analyze the deformation theory of $A_r$-stable curves and their automorphism groups in order to study the combinatorics of families of curves over $[\mathbb{A}^1/\mathbb{G}_m]$, and use this to classify all closed points of the stack of $A_r$-stable curves. As a byproduct, we also classify all open substacks of the moduli stack of degree $2$ cyclic covers of $\mathbb{P}^1$ that admit a separated good moduli space. This is the first in a series of three papers aimed at studying obstructions for the existence of good moduli spaces for stacks of curves with $A$-type singularities, and using these to find an open substack of the stack of $A_r$-stable curves that admits a proper non-projective good moduli space when $r=5$.

Electrification of marine transport is a promising solution to reduce sector greenhouse gas emissions and operational costs. However, the large upfront cost of electric vessels and the required charging infrastructure can be a barrier to the development of this technology. Optimization algorithms that jointly design the charging infrastructure and the operation of electric vessels can help to reduce these costs and make these projects viable. In this paper, we present a mixed-integer linear programming optimization framework that jointly schedules ferry operations, charging infrastructure and ship battery size. We analyze our algorithms with the case of the China Zorrilla, the largest electric ferry in the world, which will operate between Buenos Aires and Colonia del Sacramento in 2025. We find that the joint system and operations design can reduce the total costs by 7.8\% compared to a scenario with fixed power limits and no port energy management system.

In this work, we propose a simple method to resolve the eigenstates located at the band gap edges of an electronic eigenspectrum using only the quasi-purified one-particle density matrix as input. The theoretical framework relies on the decomposition of the occupation number variance into a particle and hole moment. These moments, when purified using power narrowing iterations, allow to isolate the higher occupied and lower unoccupied single state projectors, giving readily access to the corresponding eigenpairs. We demonstrate that when degeneracy is encountered, power narrowing remains able to deliver relevant mixed states. From a benchmark of selected molecules, we show that the method is robust and efficient since it requires no more that a dozen of matrix-matrix multiplications at worst. The possibility of reducing the computational cost using Lanczos subspace approach is discussed. The very low algorithmic complexity of power narrowing makes it very easy to implement in electronic structure codes or libraries already featuring Fermi operator expansion or density matrix purifications.

Causal inference in brain networks has traditionally relied on regression-based models such as Granger causality, structural equation modeling, and dynamic causal modeling. While effective for identifying directed associations, these methods remain descriptive and acyclic, leaving open the fundamental question of intervention: what would the causal organization become if a pathway were disrupted or externally modulated? We introduce a unified framework for counterfactual causal analysis that models both pathological disruptions and therapeutic interventions as an energy-perturbation problem on network flows. Grounded in Hodge theory, directed communication is decomposed into dissipative and persistent (harmonic) components, enabling systematic analysis of how causal organization reconfigures under hypothetical perturbations. This formulation provides a principled foundation for quantifying network resilience, compensation, and control in complex brain systems.

The decoupling strategy allows one to obtain the value of the strong coupling in QCD from the running in pure gauge. Here we present our strategy to determine the running in the $SU(3)$ Yang-Mills theory. We use a finite-volume scheme with twisted boundary conditions and a step-scaling approach based on a gradient-flow coupling. We show preliminary results for the continuum extrapolation of the step-scaling function. Compared with other finite-volume approaches, we expect a reduced statistical error and absence of linear cutoff effects due to the translational invariance of the boundary conditions.

This work studies the likely dust seeding processes arising from alkali metal and alkaline earth ionisation, epoxidation (epoxide bond formation via oxygen atom insertion into C=C bonds), and grain charge disproportionation (the existence around the uncharged state of oxidised cationic and reduced anionic states) at (sub-)nanometre size scales. The chemical, physical, and photon-initiated processes leading to dust seeding are explored within the framework of the size-dependent physical, optical, and photoelectric properties of the THEMIS carbonaceous nanoparticles. The critical grain charge states at (sub-)nanometre size scales are derived as a function of the interstellar and circumstellar physical conditions. Photo-initiated low-energy ionisation, epoxide reactions, and disproportionation-driven electrostatic effects could play key roles in seeding dust nucleation and growth. The size-dependent seed cluster and nanograin charge distribution is shown to encompass both positive and negative charges where the ionisation is driven by low ionisation metals or by weak attenuation. Cluster seeding via ionisation and epoxidation could help to explain the co-spatial and contemporaneous nucleation and growth of both carbon-rich and oxygen-rich dust in the same regions. This may be enhanced by electrostatic effects, driven by charge disproportionation, between negatively-charged, nucleation-seeding, polyatomic clusters and positively-charged ions or larger (nano)particles. Such processes could occur in the dust-forming regions in novae, Wolf-Rayet, and Luminous Blue Variable systems and electrostatic effects may also aid the accretion of nanoparticles in the outer regions of molecular clouds.

In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a broad class of gauge-variant and gauge-invariant spin-network states. This algorithm is later used to calculate the coherent state expectation value and coherent state matrix elements of the volume operator. By comparing the results generated by our numerical model with the analytical results in various scenarios at the near-semiclassical region, not only is our numerical model validated with high accuracy, but it also provides a complete picture of how the full quantum action of the volume operator connects with its semiclassical approximations. We further find that the maximal eigenvalue approaches the classical polyhedral volume in the semiclassical regime. For irregular geometries, we also observe that the relative volume magnitudes can change in the deep quantum regime.

We classify which of the 672 oriented diffeomorphism types of closed, simply-connected spin 7-manifolds with the cohomology ring of $S^2\times S^5$ admit a free circle action. In addition, we show that whenever such an action exists, there exist infinitely many pairwise non-equivalent free circle actions. Finally, in almost all cases where such an action exists, we construct invariant Riemannian metrics of positive Ricci curvature.

Fully inhomogeneous spin Hall-Littlewood symmetric rational functions $F_λ$ arise as partition functions of certain path configurations in the $\mathfrak{sl}_2$ higher spin six vertex models. They are multiparameter generalizations of the classical Hall-Littlewood symmetric polynomials. We establish two new generalizations of the classical Littlewood identity, where we express a weighted sum of $F_λ$'s over all partitions $λ$ as a product of the Littlewood kernel and another simple product in one case, and a product of the Littlewood kernel and a Pfaffian in the other case. As a corollary we obtain a novel Littlewood identity for Hall-Littlewood symmetric polynomials. We also elaborate on the newly established connection between the fully inhomogeneous spin Hall-Littlewood symmetric rational functions $F_λ$ and the modified Robbins polynomials, the latter being multivariate generating functions for alternating sign matrices. This connection allowed us to discover the two generalizations of the Littlewood identity and we provide a bijection between the underlying combinatorial models in the case where $λ$ is strictly decreasing.

The SPHEREx near-infrared space telescope is an all-sky spectroscopic survey mission launched on March 12th, 2025 UTC. In addition to providing the community with a spectral database applicable to a wide range of investigations, it is optimized to address three core science goals: to survey the large scale structure of the Universe for signatures of non-Gaussianity during inflation; to conduct intensity mapping studies of the extragalactic background light for probing the history of galaxy evolution; and to survey the plane of the Milky Way for the prevalence and distribution of water and other biogenic ices. Each of these science goals imposes unique requirements on the performance of the instrument. We detail the design and testing strategies and report the performance results for the full instrument test campaign, ranging from component-level screening to in-orbit tests during the commissioning phase. The instrument, currently operating in full science survey mode, meets all of its driving requirements including optical performance, point source sensitivity, thermal stability and correlated noise minimization.