This work presents a mathematical model of an adsorption column to study the evolution of contaminant concentration and adsorbed quantity along the longitudinal axis of the filter. The model is formulated as a system of partial differential equations (PDEs) and analysed using a travelling-wave approach, which reduces the system to a second-order ordinary differential equation depending on the inverse Péclet number, typically a small parameter. By neglecting this parameter, the model is simplified via a singular perturbation to a leading-order approximation, which can be interpreted as a slow-fast system. We rigorously justify this reduction by proving the persistence of the heteroclinic connection associated with the travelling wave. Using analytical continuation, we conclude that, at least for small values of the inverse Péclet number, the concentration profile transitions from a clean downstream state of the adsorbent matrix to fully upstream saturation. Numerical simulations are presented to validate the analytical results and to assess the accuracy of the reduced model. A sensitivity analysis demonstrates that the travelling-wave approximation remains remarkably robust for moderate values of the inverse Péclet number.

This study explores the vulnerability of direct data driven control, particularly in the linear quadratic regulator (LQR) problem, to adversarial perturbations in offline collected data. We focus on stealthy attacks that subtly alter training data to destabilize the closed-loop system while evading detection. To craft such attacks, we propose Directed Gradient Sign Method (DGSM) and its iterative variant (I-DGSM), which adapt techniques from adversarial machine learning to align perturbations with the gradient of the closed-loop spectral radius. A key technical contribution is an efficient and exact gradient computation method using implicit differentiation through the Karush-Kuhn-Tucker conditions of the underlying semidefinite program. For defense, we introduce two strategies: (i) regularization to reduce controller sensitivity, and (ii) robust data-driven control that ensures stability under bounded perturbations. Experiments across benchmark systems reveal that even imperceptibly small perturbations, up to ten times smaller than random noise, can lead to instability, while the proposed defenses significantly reduce attack success rates with minimal performance loss. We also assess transferability under partial knowledge, demonstrating the importance of protecting training data. This work highlights critical security risks in data driven control and proposes practical methods for both attack and defense.

We use the characterization of the case of equality in Barthe's Geometric Reverse Brascamp-Lieb inequality to characterize equality in Liakopoulos's volume estimate in terms of sections by certain lower-dimensional linear subspaces.

We report on the observation and measurement of astrometry, photometry, morphology, and activityof the interstellar object 3I/ATLAS, also designated C/2025 N1 (ATLAS) with the NSF-DOE Vera C. Rubin Observatory. Comet 3I/ATLAS, the third known interstellar object, was discovered on UT 2025 July 1. Rubin Observatory had coincidentally collected images of the object's region of the sky during routine commissioning. Facilitated by Rubin's high resolution and large aperture, we successfully recovered object detections from Rubin observations spanning UT 2025 June 21 (10 days before discovery, when 3I/ATLAS was 4.5 au from the Sun) through the date of discovery, and we acquired additional images through UT 2025 July 20 as part of commissioning. We measure on-sky locations of 3I/ATLAS in Rubin ugrizy bands, with a typical precision of about 70 mas, and briefly describe the reason this is coarser than our measured static source astrometric precision of about 3 mas in Rubin images. We measure grizy magnitudes of 3I/ATLAS photometry at about 0.01 mag precision, detecting no short-term photometric variability above 0.01 mag. We derive an estimated near-nucleus dust-to-nucleus scattering cross-section ratio of eta >= 13 on UT 2025 July 2 based on Rubin photometry and an upper limit nucleus size computed from Hubble Space Telescope observations. We find Rubin colors of g - r = (0.657 +/- 0.013) mag, r - i = (0.235 +/- 0.018) mag, i - z = (0.147 +/- 0.042) mag, z - y = (0.047 +/- 0.052) mag. These data represent the earliest observations of this object by a large (>=8-meter class) telescope and illustrate the type of measurements (and discoveries) Rubin's Legacy Survey of Space and Time (LSST) will begin to provide after it begins in early 2026.

We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By comparing the finite-horizon game with its ergodic counterpart, we establish exponential convergence estimates between the solutions of the finite-horizon generalized Riccati system and the associated algebraic system arising in the ergodic setting. Building on these results, we prove the convergence of the time-averaged value function and derive a turnpike property for the equilibrium pairs of each player. Importantly, our approach avoids reliance on the mean field game limiting model, allowing for a fully uniform analysis with respect to the number of players $N$. As a result, we further establish a uniform turnpike property for the equilibrium pairs between the finite-horizon and ergodic games with $N$ players. Numerical experiments are also provided to illustrate and support the theoretical results.

We investigate the rate of convergence toward the Boolean extreme value distribution, which is the universal limiting law for the normalized spectral maximum of Boolean independent and identically distributed positive operators, under the von Mises condition.

Solving partial differential equations of highly featured problems represents a formidable challenge, where reaching high precision across multiple length scales can require a prohibitive amount of computer memory or computing time. However, the solutions to physics problems typically have structures operating on different length scales, and as a result exhibit a high degree of compressibility. Here, we use the quantics tensor train representation to build a solver for the time-dependent Gross-Pitaevskii equation. We demonstrate that the quantics approach generalizes well to the presence of the non-linear term in the equation. We show that we can resolve phenomena across length scales separated by seven orders of magnitude in one dimension within one hour on a single core in a laptop, greatly surpassing the capabilities of more naive methods. We illustrate our methodology with various modulated optical trap potentials presenting features at vastly different length scales, including solutions to the Gross-Pitaevskii equation on two-dimensional grids above a trillion points ($2^{20} \times 2^{20}$). This quantum-inspired methodology can be readily extended to other partial differential equations combining spatial and temporal evolutions, providing a powerful method to solve highly featured differential equations at unprecedented length scales.

We analyze the three-body decays of the long-lived neutral kaon $K_L \to ππa$, where $a$ is an axion-like particle (ALP), and compare them to the two-body decay $K_L \to π^0 a$. While the latter requires both flavor violation (FV) and $CP$ violation (CPV), the former can proceed via FV alone, allowing the ratio of decay rates to serve as a probe of CPV of the underlying UV theory. We emphasize the importance of weak-interaction-induced contributions, often neglected in recent calculations. We explore both minimal and non-minimal flavor-violating scenarios, and identify classes of models where ALP production from neutral three-body decays is comparable to - or even dominates over - the two-body decay, despite its reduced phase space. Finally, we discuss the phenomenological implications of our results and show how these decays can provide complementary probes of ALP couplings beyond those accessible via charged kaon channels.

Radiative effects of aerosol-cloud interactions constitute the most uncertain climate forcing of the Earth system, making it important to understand how they may change with climate. We conduct 3-day-long large-eddy simulations of a stratocumulus-to-cumulus transition along an airmass-following trajectory over the Northeast Pacific Ocean. By perturbing boundary layer aerosol concentrations, we simulate aerosol-cloud interactions in both present-day and doubled-CO2 conditions. Aerosol-induced cloud changes, including the Twomey effect and adjustments of cloud fraction and liquid water path, are inhibited in a doubled-CO2 climate. Decomposing the aerosol-induced cloud radiative effect change ($Δ$CRE) reveals that aerosol-induced cloud fraction changes dominate $Δ$CRE. Overall, doubling CO2 attenuates aerosol-induced $Δ$CRE (i.e., cooling) by >30% in our simulations. Our results also show that low cloud feedbacks are sensitive to the background aerosol concentration, highlighting the interplay between climate forcings and feedbacks. These results may aid in predicting the cooling potential of marine cloud brightening in a changing climate.

We propose a general quantum Hamiltonian formalism of a renormalization group (RG) flow with an emphasis on generalized symmetry by interpreting the elementary relationship between homomorphism, quotient ring, and projection. In our formalism, the noninvertible nature of the ideal of a fusion ring realizing the generalized symmetry of an ultraviolet (UV) theory plays a fundamental role in determining condensation rules between anyons, resulting in the infrared (IR) theories. Our algebraic method applies to the domain wall problem in $2+1$ dimensional topologically ordered systems and the corresponding classification of $1+1$ dimensional gapped phase, for example. An ideal decomposition of a fusion ring provides a straightforward but strong constraint on the gapped phase with noninvertible symmetry and its symmetry-breaking (or emergent symmetry) patterns. Moreover, even in several specific homomorphisms connected under massless RG flows, less familiar homomorphisms appear, and we conjecture that they correspond to partially solvable models in recent literature. Our work demonstrates the fundamental significance of the abstract algebraic structure, ideal, for the RG in physics.

We present a covariant framework for analyzing the interactions and decay rates of axion-like particles (ALPs) that couple to both gluons and quarks. We identify combinations of couplings that are invariant under quark-field redefinitions, and use them to obtain physical expressions for the prominent decay rates of such ALPs, which are compared with previous calculations for scenarios where ALPs couple exclusively to quarks or to gluons. Our framework can be used to obtain ALP decay rates for arbitrary ALP couplings to gluons and quarks across a broad range of ALP masses.

We study a geometric version of the dimension growth conjecture. While it is closely related in spirit to themes arising in geometric Manin's conjecture, it applies in greater generality and provides more uniform bounds. For an irreducible projective variety $X$ defined over $\mathbb{C}(t)$, the set $X(b)$ of $\mathbb{C}(t)$-rational points on $X$ of degree less than $b$ has a natural structure of an algebraic variety over $\mathbb{C}$. We study the dimension and irreducibility of $X(b)$ when $X$ has degree $d \ge 2$, and obtain a geometric analogue of the classical dimension growth conjecture, namely that $\dim X(b) \le b\dim X $ for every $b \ge 1$. In particular, when $X$ is defined over $\mathbb{C}$, this provides uniform bounds on the dimension of the space of degree $b$ rational curves on $X$. We also develop a geometric version of Heath-Brown's $p$-adic determinant method for varieties defined over $\mathbb{C}(t)$. This allows us to show that as soon as $d \ge 6$, the number of irreducible components of $X(b)$ of dimension $b\dim X$ is bounded by a polynomial in $d$ which is independent of $b$. As a further application, we obtain an analogue of the Bombieri--Pila theorem for affine curves, as well as a corresponding result for projective curves.

For the Iwahori-Hecke algebras of type $A$, James and Mathas proved a theorem which relates $v$-decomposition numbers for different values of $e$, by adding empty runners to the James' abacus display. This result is often referred to as the empty runner removal theorem. In this paper, we extend this theorem to the Ariki-Koike algebras, establishing a similar relationship for the $v$-decomposition numbers.

We report the experimental observation of two distinct Berry phases ($+\frac{2π}{3}$ and $-\frac{2π}{3}$) generated on the surface of a Möbius cavity resonator at microwave frequencies supporting the TE$_{1,0,n}$ mode family. This resonator consists of a twisted, mirror-asymmetric prism with a cross-section of the triangular $D_3$ symmetry group, bent around on itself to form a ring. This geometric class supports resonant modes with nonzero electromagnetic helicity (i.e. nonzero $\vec{E}\cdot\vec{B}$ product) at microwave frequencies. There exist modes with three-fold rotational symmetry as well as those that exhibit no rotational symmetry. The latter result in an accumulated Berry phase whilst the former do not, which is determined from the measured frequency shift of the modes when compared to a mirror-symmetric resonator of otherwise equivalent geometry.

We present a study of LLM integration in final-year undergraduate astronomy education, examining how students develop AI literacy through structured guidance and documentation requirements. We developed AstroTutor, a domain-specific astronomy tutoring system enhanced with curated arXiv content, and deployed it alongside general-purpose LLMs in the course. Students documented their AI usage through homework reflections and post-course surveys. We analyzed student evolution in AI interaction strategies and conducted experimental comparisons of LLM-assisted versus traditional grading methods. LLM grading showed strong correlation with human evaluation while providing more detailed and consistent feedback. We also piloted LLM-facilitated interview-based examinations as a scalable alternative to traditional assessments, demonstrating potential for individualized evaluation that addresses common testing limitations. Students experienced decreased rather than increased reliance on LLMs over the semester, developing critical evaluation skills and strategic tool selection. They evolved from basic assistance-seeking to verification workflows, with documentation requirements fostering metacognitive awareness. Students developed effective prompting strategies, contextual enrichment techniques, and cross-verification practices. Our findings suggest that structured LLM integration with transparency requirements and domain-specific tools can enhance astronomy education while building essential AI literacy skills. We provide implementation guidelines for educators and make our AstroTutor repository freely available.

Entanglement distribution is a crucial problem in quantum information science, owing to the essential role that entanglement plays in enabling advanced quantum protocols, including quantum teleportation and quantum cryptography. We investigate strategies for distributing quantum entanglement between two distant parties through noisy quantum channels. Specifically, we compare two configurations: one where the entanglement source is placed at the midpoint of the communication line, and another where it is located at one end. For certain families of qubit channels we show analytically that the midpoint strategy is optimal. Based on extensive numerical analysis, we conjecture that this strategy is generally optimal for all qubit channels. Focusing on the midpoint configuration, we develop semidefinite programming (SDP) techniques to assess whether entanglement can be successfully distributed through the network, and to quantify the amount of entanglement that can be distributed in the process. In many relevant cases the SDP formulation reliably captures the maximal amount of entanglement which can be distributed, if entanglement is quantified using the negativity. We analyze several channel models and demonstrate that, for various combinations of amplitude damping and depolarizing noise, entanglement distribution is only possible with weakly entangled input states. Excessive entanglement in the input state can hinder the channel's ability to establish entanglement. Our findings have implications for optimizing entanglement distribution in realistic quantum communication networks.

We present the complete one-loop matching of the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model Effective Field Theory (SMEFT), considering the most general case for the MSSM with conserved $R$-parity, which has 124 free parameters. The matching is performed with the Matchete package, which integrates out all superpartners at once with non-degenerate masses, while also retaining the most general flavor structure. Our results include all correlations among the different SMEFT Wilson coefficients that are governed by supersymmetry and thus provide a basis for future systematic and global studies of the MSSM parameter space employing EFT methods. A detailed discussion is provided on the treatment of the Higgs sector and electroweak symmetry breaking, along with the reduction of redundant operators in the EFT Lagrangian to the Warsaw basis. Furthermore, we validate against existing results in the literature and present a minimal phenomenological example. As an alternative low-energy scenario, we also provide the complete one-loop matching of the MSSM onto the two-Higgs-doublet-model EFT, where the second Higgs doublet is retained in the infrared spectrum. Extensive auxiliary material, including the code utilized for the matching, is available on GitHub.

We prove that an extremal metric on a polarised smooth complex projective variety exists if it is $\mathbb{G}$-uniformly $K$-stable relative to the extremal torus over models, extending a result due to Chi Li for constant scalar curvature Kähler metrics.

We study the stability of multiple almost circular concentrated vortices in a fluid evolving according to the two-dimensional Euler equations. We show that, for general configurations, they must remain concentrated on time-scales much longer than previously known as long as they remain separated. We further prove a new stability estimate for the logarithmic interaction energy as part of the proof.

In this paper, we study the asymptotic behaviour of plane partitions distributed according to a $q^{\text{Volume}}$-weighted Muttalib--Borodin ensemble and its associated discrete point process. We establish a Large Deviation Principle for the process, explicitly characterizing the rate function. A defining feature of our model is the emergence of a strict upper bound on the macroscopic particle density, which translates the asymptotic analysis into a non-trivial constrained minimization problem. Through a rigorous Riemann--Hilbert analysis, we derive exact, closed-form formulas for the limit shape of the partitions across all parameter regimes. To the best of our knowledge, this represents the first time a constrained Riemann--Hilbert problem has been formulated and analytically solved for a bi-orthogonal ensemble. Our analysis allows to track the system through a macroscopic phase transition, computing the minimizer in both the subcritical and supercritical regimes. As a byproduct of our analysis, we obtain an explicit expression for the arctic curve that separates the ``frozen'' and ``liquid'' regions of the limit shape. Furthermore, we reveal that the equilibrium measure exhibits a continuously varying exponent at the hard edge departing from the universal fixed exponents typically observed in classical random matrix theory.

Scalable and controlled doping of two-dimensional transition metal dichalcogenides is essential for tuning their electronic and optoelectronic properties. In this work, we demonstrate a robust approach for substitution of vanadium in tungsten diselenide (WSe$_2$) via the selenization of pre-deposited V$_2$O$_5$/WO$_3$ thin films. By adjusting the thickness of the vanadium oxide layer, the V concentration in W$_{1-x}$V$_x$Se$_2$ is systematically varied. Electrical measurements on field-effect transistors reveal a substantial enhancement in hole conduction, with drain current increasing by nearly three orders of magnitude compared to undoped WSe$_2$. Temperature-dependent electrical resistivity indicates a clear insulator-to-metal transition with increasing V content, likely due to band structure modifications. Concurrently, the photoconductive gain decreases, suggesting enhanced recombination and charge screening effects. These results establish vanadium doping via selenization of V$_2$O$_5$/WO$_3$ films as a scalable strategy for modulating the transport and photoresponse of WSe$_2$, offering promising implications for wafer-scale optoelectronic device integration.

We establish a symmetry principle for asymptotically cylindrical steady gradient Ricci solitons (GRSs) and asymptotically conical expanding GRSs with homogeneous links. Using this, we show that the Bryant steady soliton is the unique asymptotically cylindrical steady GRS that has a round spherical link and satisfies a particular quantitative rigidity condition. A similar characterization is proved for Bryant's expanding solitons. Finally, we establish a global symmetry result for GRSs which exhibit the aforementioned asymptotics with quotient-Berger sphere asymptotic links.

This paper describes the developed setup and characterization approach for full two-port calibrated S-parameter measurements at cryogenic temperatures, together with a complete uncertainty budget. The system developed at the Istituto Nazionale di Ricerca Metrologica (INRiM, Italy), exploits the Short-Open-Load-Reciprocal technique to realize error-corrected cryogenic measurements within a single cooling cycle. The system operates down to mK temperatures over the 4-12 GHz band in coaxial line. Calibration standards are referenced to SI-traceable room-temperature measurements, while a numerical approach is used to evaluate the response shift of the artifacts upon cooling and to derive an additional cryogenic uncertainty contribution for the measurement uncertainty budget. Moreover, relevant measurement uncertainty contributions are evaluated according to internationally agreed procedures, and a comprehensive uncertainty budget is presented. Test measurements on a 20 dB attenuator are shown as an example. An attenuation of 20.70 +/- 0.08 dB (95% confidence interval) was obtained at 6 GHz. Full SI-traceable verification at mK temperatures remains an open challenge; however, an initial calibration verification is also presented.

Estimations of trigger efficiencies are essential to modern particle physics analyses. A data-driven method provides a framework in which to estimate these efficiencies from the properties of reconstructed candidates, described in this paper. This paper also presents the design, implementation and performance of a software package, TriggerCalib, which provides a first centralised implementation of these calculations and can be seamlessly employed in physics analyses. Additionally, the estimation of statistical and systematic uncertainties is discussed.

In past years, several studies have proposed new methods and applications for urban wind simulations. In this article, we present a fast and automatic methodology for reconstructing airflows within urban environments using LiDAR and cadastral data coupled with Computational Fluid Dynamics (CFD) simulations. Our approach integrates meteorological predictions with computational techniques to simulate the complex interactions between wind currents, buildings, vegetation, water zones and terrain morphology within urban environments. Accurate boundary conditions based on meteorological predictions are introduced into a coupled methodology that directly creates the terrain shape inside the simulation environment, simplifying the geometry creation process, which is one of the most prevalent problems in CFD urban simulations. The simulation results are confronted against ground-truth real data obtained from a meteorological station, showing strong agreement with the outcomes generated by the proposed CFD model, with a concordance correlation coefficient up to $ρ_c = 0.985$ for the wind direction and $ρ_c = 0.853$ for the wind speed. The results from these simulations are then used for validating a wind tunnel approach that mimics the interaction between a moving drone and the extracted wind currents, demonstrating a great improvement in computation times when compared to the most straightforward approach that consists in embedding the drone within the full urban landscape. This research contributes to the advancement of urban CFD modeling, and it has significant implications for various applications, providing valuable insights for urban development.

In this paper, we investigate evaporation and accretion of uncharged, non-rotating, spherically symmetric black-holes from the path integral perspective. We show that the effective actions derived using the path integral techniques incorporate both accreting and evaporating configurations, thus presenting a novel methodology to study black-hole accretion and evaporation in $4D$ on the same footing. We specifically focus on evaporating configurations which deviate from the standard thermodynamic modes of black-hole evaporation.

The correlation properties of the nonaffine elastic response in strongly disordered materials are investigated using the theory of correlated random matrices and supported by numerical models. While the nonaffine displacement field itself predominantly exhibits power-law decay, we demonstrate that its spatial derivatives reveal large-scale exponentially decaying correlations. Specifically, the correlation functions of the divergence and (for most deformations) the rotor of the nonaffine field are governed by a heterogeneity length scale $ξ$. This length scale is set by the disorder strength and can become indefinitely large, far exceeding the structural correlation length. A notable exception occurs under volumetric deformation, where the rotor correlations lack the exponential tail with the length scale $ξ$. The theory also predicts that the rotor correlations may have small power-law tails. We directly observe the exponential decay, characterized by $ξ$, in numerical studies of a rigidity percolation model and in molecular dynamics simulations of amorphous polystyrene and the Lennard-Jones glass. The latter example also confirms the existence of the power-law tail in the rotor correlation function at large distances.

The mean compositions of individual components can be tuned to control phase behavior in number-conserving passive mixtures. In this work, we investigate the role of variable average density in a system of infinitely many non-reciprocally interacting scalar densities, within the framework of the multi-species non-reciprocal Cahn-Hilliard (NRCH) model. Rather than focusing on specific parameter choices, we study ensembles of systems where the inter-species interaction coefficients and average densities are sampled from probability distributions. We show that non-reciprocity stabilizes the homogeneous mixed state even in the presence of compositional disorder. Using random matrix theory, we derive a general condition for the onset of spinodal instability, which we verify through simulations. Finally, we illustrate the connection between the statistics of the most unstable eigenvalue and the emergent nonlinear dynamics.

We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property between the smooth term and its proximal term. On the other hand, the ability to efficiently solve the subproblem depends on the compatibility between the nonsmooth term and the proximal term. Selecting an appropriate proximal term by considering both factors simultaneously is generally difficult. We overcome this issue by providing convergence analyses for proximal gradient-type methods with general proximal terms, without requiring global descent property of the smooth term. As a byproduct, new convergence results of the interior gradient methods for conic optimization are also provided.

Scriptwriting has traditionally been text-centric, a modality that only partially conveys the produced audiovisual experience. A formative study with professional writers informed us that connecting textual and audiovisual modalities can aid ideation and iteration, especially for writing dialogues. In this work, we present Script2Screen, an AI-assisted tool that integrates scriptwriting with audiovisual scene creation in a unified, synchronized workflow. Focusing on dialogues in scripts, Script2Screen generates expressive scenes with emotional speeches and animated characters through a novel text-to-audiovisual-scene pipeline. The user interface provides fine-grained controls, allowing writers to fine-tune audiovisual elements such as character gestures, speech emotions, and camera angles. A user study with both novice and professional writers from various domains demonstrated that Script2Screen's interactive audiovisual generation enhances the scriptwriting process, facilitating iterative refinement while complementing, rather than replacing, their creative efforts.