Federated learning (FL) is vulnerable to data poisoning attacks due to its distributed nature. Although recent GAN-based data poisoning methods have indicated the potential of using generative AI to generate seemingly legitimate poisoned data, the inherent consistency of GAN outputs can still reveal a sign of data poisoning. In this paper, we propose a diffusion-based data poisoning framework against FL systems, which leverages a Poisoning-Oriented Conditional Diffusion Model (PCDM) to enable fine-grained control over the local generation of poisoned data while ensuring both attack effectiveness and stealthiness. Our PCDM incorporates an adjustable poisoning vector within the global context to precisely control the generation of poisoned data, with theoretical guarantees on attack performance. Furthermore, it employs a novel jumping diffusion strategy for lightweight and efficient poisoned data generation. We conduct the most systematic and broad experimental evaluation for FL poisoning attacks against various defenses, including advanced Byzantine robust aggregation mechanisms, on four open datasets: MNIST, Fashion-MNIST, CIFAR-10, CIFAR-100, and a real-world wireless-specific dataset VRAI. Our results demonstrate that PCDM is less likely to exhibit statistical anomalies compared with the state-of-the-art methods while more effectively degrading global FL performance, which poses a significant risk to data security in FL.

Multi-robot systems are integral to modern logistics, but their capabilities are often limited to tasks executable by individual agents. This paper addresses a critical gap in existing frameworks like Multi-Agent Path Finding (MAPF) and Task Allocation and Path Finding (TAPF), which lack true cooperation for transporting large items that require multiple agents. To this end, we formalise the Cooperative Transportation Task Allocation and Path Finding (CT-TAPF) problem, which integrates team formation, task assignment, and collision-free pathfinding. We present an optimal solver, Cooperative Transportation Task Conflict-Based Search (CT-TCBS), which features a novel Incremental Expansion strategy to tackle the combinatorial explosion inherent in team formation. Recognising the computational cost of optimality, we also develop a family of sub-optimal solvers that employ a global, task-centric perspective, selecting the next task to assign based on a global difficulty metric (Best Task or Worst Task). Our comprehensive empirical evaluation demonstrates three key findings: (1) the incremental expansion strategy significantly outperforms the naive combinatorial approach by successfully pruning the dominant task-allocation search space; (2) we identify a task-conflict expansion dilemma, where sophisticated conflict resolvers effective for large-agent pathfinding subproblems can be detrimental in the integrated CT-TAPF setting; and (3) our proposed sub-optimal solvers establish a new, more efficient frontier on the solution quality-runtime spectrum compared to "nn-" agent-centric baselines. This work provides a foundational framework and a set of effective algorithms for a new, practical class of cooperative multi-agent problems.

We introduce the median uniformity $\mathcal U_{\mathrm m}$, an intrinsic precompact convex uniform structure on a median algebra. It is Hausdorff under natural assumptions, for instance for finite-rank median algebras. In the Hausdorff case, its uniform completion yields the Minimal Median Compactification (MMC). The induced topology $τ_{\mathrm m}$ provides a natural higher-rank analogue of the interval topology on linearly ordered sets and of the shadow topology on rank-one median algebras. When all intervals in the median algebra $X$ are finite, the MMC is the unique proper median compactification of $(X,τ_{\mathrm m})$; in particular, it coincides with the Roller compactification. We apply this uniform framework to continuous actions of a topological group $G$ by median automorphisms. We show that the MMC is a median $G$-compactification. In the finite-rank case, the resulting compact $G$-system is Rosenthal representable and hence dynamically tame.

This is the second part of a series of papers proving the nonlinear stability of a one-parameter family of continuous self-similar $C^{1,α}$ naked singularity solutions, with $0<α\ll1$, to the spherically symmetric Einstein-scalar field equations. These solutions were constructed by Christodoulou and are known to be unstable under sufficiently rough perturbations due to the blue-shift instability mechanism. In complete contrast to the previous instability results, we establish the linearized stability for those naked singularity spacetimes under perturbations of the same regularity as the background, revealing the central role of regularity in determining the strength of the blue-shift instability mechanism, and showing that it is not triggered at the regularity level of the background spacetime. The linear analysis carried out in this paper provides the foundation for the nonlinear stability result established in the companion paper [W. Zheng, Nonlinear stability of the continuous self-similar naked singularities for the Einstein-scalar field equations I: main results]. Together with that companion paper, this yields the nonlinear stability of these continuously self-similar naked singularities.

Quantum mechanics enables information-processing advantages even at the level of a single qubit. A paradigmatic example is the 2$\to$1 random access code (RAC), where a qubit outperforms a classical bit in retrieving encoded information. In the standard form, however, this quantum advantage is restricted to a single receiver, since decoding measurements inevitably destroy the encoded information. Contrary to this, we address how long the information encoded in a single qubit remains accessible even after multiple decoding, each with a quantum advantage. Introducing preparation distinguishability as an operational resource associated with the sender, we show that its interplay with measurement incompatibility on the receiver's side can mitigate measurement-induced disturbance, thereby enabling an arbitrarily long sequence of receivers to each retain a quantum advantage. Our results show that, even under repeated measurements, the information encoded in a qubit need not be entirely exhausted, revealing a stronger communication feature than previously recognised.

In the seventies, V. G. Drinfeld proved that a moduli problem of deformations by quasi-isogenies of certain $p$-divisible groups with extra actions is representable by an explicit semi-stable model of the $p$-adic symmetric space. This theorem, known as \emph{Drinfeld's representability theorem}, has been one of the cornerstones of geometric aspects in $p$-adic Hodge theory. The purpose of these notes is twofold. On the one hand we give a new and more transparent proof of Drinfeld's representability theorem; on the other hand, we give a detailed presentation of Drinfeld's moduli space and the formal model of the $p$-adic symmetric space.

The experimental determination of eutectic points is a long-established and widely used technique, but it is generally only practical for systems with relatively low melting points. Many modern, promising materials, however, are ultra-refractory, with melting points exceeding 3000 K. For these systems, conventional melting experiments become prohibitively expensive and technically challenging. Advanced AI modeling can serve as a powerful precursor to guide successful experimentation in such cases. This work proposes a novel criterion for determining the eutectic point concentration in ultra-refractory alloys. The approach is verified using the Ti-B-C system - the most thoroughly studied three-component refractory system to date. The core of the algorithm is a machine-learning interatomic potential, based on a neural network, which achieves accuracy comparable to ab initio methods. Crucially, the algorithm operates effectively in the liquid phase, eliminating the need for information about the solid alloy's crystalline structure to estimate eutectic points.

We study downward deviations of the maximum local time of the discrete-time simple random walk on $\mathbb{Z}^d$, $d\ge 3$. In our previous paper \cite{li2026ldmaxlocal}, the corresponding upper bound was established, while the matching lower bound was left open. In the present paper, we prove this lower bound and hence obtain the sharp asymptotic formula for the downward-deviation probability. To provide a discrete-time analogue of the jump-chain/holding-time structure used in the continuous-time argument, we introduce a new random structure which we name as {\it loop-pruned random walk} and the associated loop-pruning decomposition, which is also of independent interest.

The cosmic distance-duality relation (CDDR), expressed as $ D_L/D_A(1+z)^{-2}=1 $, is a fundamental relation in cosmology connecting luminosity distance ($ D_L $) and angular diameter distance ($ D_A $). Any departure from this relation would indicate new physics such as photon non-conservation, cosmic opacity, or non-metric gravity. We perform a stringent, model-independent test of the CDDR using a matched sample of 38 galaxy clusters from the Bonamente et al. compilation and Type Ia supernovae from the Pantheon+ sample. Employing the matched-pair technique, we simultaneously constrain the CDDR-violation parameter $ η$ and a possible redshift evolution of the SNe Ia absolute magnitude, parameterized as $ M_B(z)=M_0 + \varepsilon z $. We assess the robustness against matching tolerance and further supplement the analysis with DESI 2024 BAO measurements. Our results yield $ η= 0.050^{+0.348}_{-0.307} $ and $ \varepsilon = -0.184^{+0.724}_{-0.574} $ (68% CL), showing no statistically significant evidence for CDDR violation or SNe Ia evolution. The conclusions remain unchanged with stricter matching criteria and the inclusion of DESI BAO data. We also derive a cosmology-independent calibration of $ M_0 = -19.460^{+0.126}_{-0.124} $ mag. The standard cosmological model remains robust under this model-independent scrutiny.

Unstructured-mesh ocean models are increasingly used for coastal applications due to their ability to represent complex geometries and apply local grid refinement where needed. However, their broader use has been hindered by their high computational cost, particularly for models based on the Discontinuous Galerkin finite element (DG-FE) method, which involves significantly more degrees of freedom than traditional finite volume or continuous finite element approaches. The rapid emergence of GPU-based high-performance computing architectures now offers a pathway to address this limitation, as DG-FE formulations are inherently well suited to massively parallel, element-wise computations. Here, we present a full 3D DG-FE ocean model implementation optimized for both single- and multi-GPU systems, with support for both NVIDIA and AMD architectures. We detail the computational strategies employed to achieve high performance, including memory layout optimization, kernel-level parallelization, and matrix-free solvers for key vertical processes. Benchmark results demonstrate that a single HPC-grade GPU (e.g. NVIDIA A100) delivers performance equivalent to approximately 1500 CPU cores, while replacing a 128-core CPU node with a 4xA100 GPU node yields a speedup of around 50x. Weak-scaling efficiency is maintained up to 1024 GPUs. We further demonstrate the model's capabilities on a real-world application in the Great Barrier Reef, achieving a spatial resolution five times finer than the most accurate existing model while maintaining a physical-to-numerical time ratio of 100. These results highlight how GPU-accelerated DG-FE methods can dramatically advance the capabilities of unstructured-mesh ocean modeling, enabling ultra-high-resolution coastal simulations that were previously infeasible.

Recent advances in data collection technologies have led to the emergence of massive spatial datasets, with measurements obtained at millions of spatial locations. Geostatistical models typically employ Gaussian processes (GPs) to capture spatial dependence, but standard GP fitting becomes prohibitive at such scales. A promising solution is optimal subsampling, where a subset of locations is selected that optimizes a criterion. In this study, we propose a randomized exchange algorithm for subsampling (REX-SUB) which efficiently selects small subsamples that minimize prediction errors in the fitted spatial GP models. To further improve computational efficiency, we embed a scalable Vecchia approximation to the GP's joint likelihood, which takes advantage of sparsity in the precision matrix to enable fast inference on the selected subsamples. Through a simulation study and an application to a remotely sensed precipitable water dataset, we show that REX-SUB yields lower mean squared prediction errors and interval scores compared to competing subsampling strategies.

Order finding is the core subroutine of Shor's algorithm. On NISQ hardware, phase estimation output distributions are often distorted by noise, making correct order recovery difficult. We study recoverability in noisy order finding: given a measured precision-register distribution, when does standard classical post-processing still return the true order? We analyze 680 distributions from IBM quantum systems across problem instances and circuit settings. For each distribution, we apply continued-fraction post-processing with modular verification and define recoverability as whether the recovered order equals the true one. We characterize each distribution using four features: autocorrelation peak strength, normalized entropy, dominant verified mass fraction, and verified margin fraction. We evaluate these quantities using marginal feature comparisons, single-feature AUROC analysis, and multivariate tree-based classifiers. We use random-forest permutation importance to assess which quantities contribute distinct predictive information once the other features are known. To make classification behavior interpretable, we train a decision tree that exposes threshold rules for recoverable and non-recoverable distributions. We find that recoverability is strongly associated with residual comb-like structure in the measured distribution and the way verified probability mass is organized across candidate denominators. The dominant verified mass fraction is the strongest single-feature indicator of recoverability, and tree-based analysis shows it also provides the primary split in an interpretable threshold description. Some highly distorted distributions remain recoverable when one verified denominator dominates the post-processing mass, while some visibly structured distributions fail because classical post-processing favors an incorrect verified denominator.

Perovskite quantum dots (pQDs) are promising materials for optoelectronic and photocatalytic applications due to their unique optical properties. To enhance charge carrier extraction or injection donor/acceptor molecules can be tethered to the pQD. These molecules must strongly bind to the ionic surfaces of pQDs without compromising colloidal stability. These we achieve by using multifunctional ligands containing a quaternary ammonium binding group for strong pQDs surface attachment, a long tail group for colloidal stability, and a functional group near the pQD surface. Such pQDs with ferrocene-functionalized ligands show fast photoexcited hole transfer with near-unity efficiency. Density functional theory calculations reveal how ferrocene's molecular structure reorganizes following hole transfer, affecting its charge separation efficiency. This approach can also be extended to in photoexcited electron and energy transfer processes with pQDs. Therefore, this strategy offers a blueprint for creating efficient QD-molecular hybrids for applications like photocatalysis.

We develop a stochastic integration theory for predictable integrands with respect to a Lévy basis. Our approach is based on decoupling inequalities for tangent sequences and reduces the construction of the stochastic integral essentially to the deterministic integration theory for infinitely divisible random measures developed by Rajput and Rosiński. We characterise the corresponding class of integrable predictable processes in terms of the semimartingale characteristics associated with the driving random measure and show that the resulting space of integrands possesses a natural Musielak-Orlicz type structure equipped with an F-norm. Furthermore, we establish continuity properties of the integral operator and a stochastic version of Lebesgue's dominated convergence theorem.

Designing the objective function in Model Predictive Control (MPC) is challenging when performance assessment criteria are available only from human judgment. We adopt a preference-based learning (PbL) approach to learn the MPC objective function from preferences over trajectory pairs. However, the real-world application of PbL is often restricted by the significant cost or limited availability of human preference queries. To address this, Active Learning (AL) strategies seek to improve sampling efficiency, reducing the labeling effort required to obtain a well-performing classifier. We present two AL strategies for learning the MPC objective function from human preferences over pairwise system trajectories: a pool-based strategy that selects trajectory pairs that are both uncertain under the current surrogate and diverse relative to previously labeled comparisons, and a query-synthesis strategy that incorporates new trajectories using the current surrogate-driven MPC. Numerical results show that the proposed strategies yield closed-loop behaviors that align more with the expressed preference using fewer number of queries compared to a random sampling approach.

Antibody-based therapeutics-including antibody-drug conjugates (ADCs), bispecific antibodies, and novel formats-are reshaping oncology, yet key determinants of efficacy, safety, and manufacturability frequently emerge after conjugation and formulation. We argue that computational biophysics provides an underexploited framework to address this gap by connecting molecular interactions to biological outcomes. We highlight how molecular dynamics, coarse-grained simulations, and free energy calculations reveal how conjugation site, linker chemistry, and drug-antibody ratio reshape conformational landscapes. We emphasize structural coupling between antibody, linker, and payload, with implications for antigen binding, internalization, and developability. We propose that integrating physics-based modeling into development pipelines-alongside experimental validation-can reduce empirical iteration and de-risk translation. As force fields, and hybrid physics-machine-learning methods improve, this field is poised to become a central driver of next-generation ADC design.

Modeling data lineage in relational databases remains a challenging problem, particularly in scenarios involving incomplete or missing dependencies between database objects. In this paper, we propose a novel ontology for relational database data lineage, designed to provide a richer and more expressive semantic representation supporting discovering the lineage links by means of knowledge graphs (KGs). Building upon our previous work on KG-based lineage discovery, the proposed ontology extends the earlier model with additional concepts capturing structural, semantic, and transformation-level characteristics of relational data. These extensions enable more precise encoding of lineage evidence. To evaluate the impact of the proposed ontology, we conduct a comparative study using a KG-based inductive link prediction framework. Specifically, we assess the performance of a graph neural network model based on path embeddings under two settings: using the original baseline ontology and the newly proposed one. Experimental results demonstrate that the application of the enriched semantic model leads to improvements in lineage link prediction performance, as measured by AUC and Hits@10 metrics.

In-play football forecasting models have struggled to match the accuracy of betting exchange prices, which aggregate information from many market participants. We close this gap by combining two extensions to a Weibull accelerated failure time model: calibrating team strength parameters to Betfair Exchange prices at kick-off to capture pre-match market information, and including post-shot expected goals as a time-varying covariate to capture in-play information. The calibration approach, where we jointly fit team-strength parameters to 1X2 and over/under betting markets via squared-error minimisation, applies to any intensity-based goal arrival model and enables stronger in-play forecasting. Evaluated across 140 English Premier League matches at minute intervals, the calibrated model almost matches Betfair's classification accuracy (70.2% versus 70.6%) while retaining interpretable team-level parameters and covariate effects. A comparison with two alternative continuous-time scoring models, both calibrated to the same pre-match odds, confirms that market calibration is the dominant driver of predictive accuracy. A betting simulation against Betfair in-play odds yields a 4.5% return on investment (Sharpe ratio 5.94) over 17,458 bets, suggesting an inefficiency within in-play football markets.

We construct global versions of the analytic Hopf algebras used in the $p$-adic Fourier theory of Amice and Mahler over a general Banach ring, independently of the choice of prime $p$. This is done by generalising Köthe echelon and coechelon spaces to an arbitrary base Banach ring $R$ and proving reflexivity and nuclearity results. We show how to define an analytic Hopf algebra structure on them and investigate their duality theory. The particular case of the Hopf algebra of analytic functions converging on the open unit disk around $1$ and its dual is studied in detail. Amice duality is recovered from this case by base-change to a $p$-adic ring. Most notably, when $R$ is the ring of integers with the trivial norm, we obtain a global analytic version of Amice duality that does not depend on $p$.

Correlative nanoscale surface characterization benefits from simultaneously measuring electronic and structural properties in the same environment, a capability that is essential for modern-day materials science and semiconductor failure analysis. In-situ AFM-SEM measurements facilitated by self-sensing cantilevers offer great potential here; however, they are limited due to their inherent capacitive crosstalk. Here, we demonstrate for the first time the in-situ implementation of single-pass heterodyne Kelvin probe force microscopy inside a scanning electron microscope, using piezo-resistive cantilevers. We overcome the capacitive crosstalk prevalent in piezo-resistive cantilevers by demodulating excitation and detection to simultaneously map surface topography and contact potential difference for correlation with compositional analysis. We systematically compare different operational modes of this heterodyne technique, elucidating their spatial resolution, signal sensitivity, and signal-to-noise ratio. The integrated approach yields exceptional signal quality and reveals how electron beam scan parameters can directly influence surface potential contrast. We demonstrate this correlative analysis workflow on two-dimensional heterostructures and semiconductor circuits. This work establishes a robust and versatile correlative imaging mode for in-situ Kelvin force and topography imaging inside a scanning electron microscope for next-generation semiconductor device analysis and materials science.

In two-dimensional materials where interacting Fermi pockets occur in valleys related by time-reversal symmetry, a spontaneous valley imbalance results in a novel state known as an orbital magnet. Due to the breaking of time-reversal symmetry, this state can be probed in transport experiments by the violation of Onsager relations, most often done through the anomalous Hall effect (AHE). Here we propose that odd-in-field, in-plane linear magnetoconductivity (LMC) is an alternative probe of valley polarization which can occur even when the AHE vanishes. In multilayer structures, the effect originates from in-plane orbital moments and Berry curvatures enabled by interlayer tunneling and dominates over the spin response. After a classification of many recently studied multilayers, we focus on two valley polarized examples: twisted bilayer graphene, where LMC is finite but the AHE vanishes unless additional symmetry breaking from the substrate is present, and rhombohedral graphene multilayers, where LMC and AHE both track valley polarization because they have the same symmetry. Using self-consistent Hartree-Fock and semiclassical transport calculations, we present detailed predictions of LMR for these two examples and analyze the implications for recent experiments.

The main ideas and some of the most important results of the spherically symmetric self-consistent approach and a number of related theoretical algorithms are presented. These methods make it possible to study low-dimensional Heisenberg-type spin models, including frustrated ones, with careful consideration of the theoretic (Mermin-Wagner and Marshall) theorems, as well as the site spin constraint. Thus, the difficulties that may arise in the traditional analysis of low-dimensional magnetic systems are avoided. The approach can also be applied to the spin-pseudospin model, and is also embedded in more complex constructions when considering spin models with free carriers, such as the basic and three-band Hubbard models, t-J and s-d models, and the Kondo lattice.

In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy compared to traditional matrix methods. Under the star-M tensor framework, tensors can be decomposed in a matrix-mimetic way, including using the star-M SVD. This tensor SVD has optimality guarantees and has shown exceptional performance on specific types of data, but software implementations have been mostly limited to productivity-oriented languages. In this work, we present our development of a shared-memory parallel, high-performance solution designed to efficiently implement the underlying algorithms. This software will enable optimal compression of extensive scientific datasets, paving the way for enhanced data analysis and insights.

Terahertz communication offers vast bandwidth for high-speed transmission in the 6G networks but faces severe blockage challenges in the near-field region due to large antenna arrays. To overcome the limitation that near-field focused beams are susceptible to obstacles, wavefront engineering is leveraged to generate an Airy beam that propagates along a parabolic trajectory to circumvent blockages. In this paper, we consider the reconfigurable holographic surface (RHS) as a potential solution for such precise wavefront engineering owing to its compact radiation element spacing being much smaller than half-wavelength. We reveal that the adjustable effective aperture of the RHS allows the parabolic offset to be located within the antenna aperture, which enhances the freedom in designing Airy beam trajectories. An analog beamforming method, named the holographic Airy beamforming scheme based on amplitude control, is then proposed to generate the curved beam that propagates along the desired trajectory. To maximize the received power of a blocked user, we develop a geometry-based trajectory optimization algorithm. Simulation results validate that, compared to traditional phase-controlled arrays with analog beamforming, the RHS can leverage its adjustable effective aperture to improve the received power of the blocked user by over 10 dB.

The extension of ab-initio methods like density functional theory (DFT) to quantum dot (QD) geometries has enabled researchers to explore relationships between QD surface termination and electronic structure. However, fully utilizing the data from DFT requires novel classification methods for QD orbitals. Here, we identify relationships between QD geometry and electronic structure by transforming real-space QD orbitals into momentum-space using Bloch orbital expansion (BOE), yielding a fuzzy QD band structure. Comparing with bulk band structures, we show that truncated, unpassivated facets in III-V and II-VI QDs produce mid-gap orbitals derived from bulk surface orbitals; an identification challenging in real space. QDs with reconstructed facets, however, feature delocalized orbitals formed by superposition of bulk Bloch orbitals. Moreover, we prepare for the first time atomistic core/shell QD models and by the BOE expansion we can clearly identify the core/shell band alignment not possible in real space. These findings emphasize BOE as a vital tool for connecting computational and experimental insights in nanocrystal research.

The Schmidt arrangement of an imaginary quadratic number field $K$ is the orbit of the extended real line under $\text{PSL}(2, \mathcal{O}_K)$ as Möbius transformations on the extended complex plane. If $K\neq\mathbb{Q}(\sqrt{-3})$, then the resulting set of circles can only intersect tangentially, leading to various classes of integral circle packings, including Apollonian circle packings. When $K=\mathbb{Q}(\sqrt{-3})$, circles can intersect at angles of $\fracπ{3}$ and $\frac{2π}{3}$, making it unclear how to extract circle packings from the arrangement. The goal of this paper is to study a modification of the $\mathbb{Q}(\sqrt{-3})-$Schmidt arrangement called the "Eisenpint Schmidt arrangement" and associated integral "Eisenstein circle packings". In analogy to the study of Apollonian circle packings, we study the number theory of such packings, including associated families of quadratic forms, show the Eisenpint Schmidt arrangement is formed of exactly all primitive Eisenstein circle packings, show strong approximation and classify congruence obstructions, prove a density-one local-global statement, and find quadratic -- but alas no cubic -- reciprocity obstructions. Unexpected aspects of the Eisenstein case include the role of congruence subgroups, the bipartite nature of the packings and reciprocity obstructions, the coefficients of quadratic obstructions, an abundance of extra symmetry, and the need to use "first-odd" quadratic forms.

We investigate power series satisfying the exponential concentration property, and show that suitable modifications of hypergeometric series respect this property. As a geometric application, we prove that the quantum period of a Fano manifold possesses the same property, whenever the manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients.

The Milky Way in-situ halo, also known as the Splash, consists of old (Age $>$ 10 Gyr), metal-rich ([Fe/H] $> -0.7$), high-$α$ stars, i.e., thick disk-like chemistry, on halo-like orbits (eccentricity > 0.6). Its origin is linked to stars formed in the disk and dynamically heated by either internal or external agents. In this work, we investigate its low-$α$ counterpart, the low-$α$ Splash, motivated by recent findings of an old thin disk population. We conjecture that any mechanism capable of heating disk stars should affect both of present-day high- and low-$α$ old populations. Using data from the APOGEE DR17 spectroscopic catalog, we identify metal-rich low-$α$ stars with halo-like kinematics similar to those of the classical high-$α$ Splash. We investigate their possible heating mechanisms using the GASTRO suite of simulations, which allows us to explore the effects of star-forming clumps as well as a major merger in the proto-disk of a Milky Way analog galaxy. Our main results show that only clumpy Milky Way models are able to produce Splash populations through scattering by clumps in the early Galaxy, including the low-$α$ counterpart, whereas the model including only the merger and without an early clumpy phase fails to produce these populations. In the models, the low-$α$ Splash corresponds to a subset of the old thin disk that was dynamically heated by the same mechanism responsible for the formation of the high-$α$ Splash.

We study the onset of spatial instabilities in reaction networks where the spatially homogeneous system admits a steady state parameterization. We formulate a sufficient condition -- based on the signs of the constant and leading coefficients of the characteristic polynomial of the linearized Jacobian scaled by the diffusion coefficients -- that guarantees a Turing-like instability to spatially inhomogeneous solutions on appropriately chosen domains $Ω$. We also present a specific condition on the domain size $|Ω|$ required to trigger this instability. As a consequence of employing a monomial parameterization, these conditions take the form of algebraic polynomial inequalities involving only rate constants and diffusion coefficients. We apply these ideas to a network describing the sequential and distributive (de-)phosphorylation of a protein at two binding sites, ultimately deriving a condition involving only the four catalytic constants of the enzymes and the diffusion coefficients of the four enzyme-substrate complexes that guarantees a Turing-like instability.

We study the homological mirror symmetry statement where A-side is the conic bundle Hori--Vafa mirror $\mathcal{Y} = \{uv = f(z)\} \subset \mathbb{C}^2 \times (\mathbb{C}^\ast)^n$ for a Laurent polynomial $f$ in $(\mathbb{C}^\ast)^n$, and B-side is some a toric Calabi--Yau $(n+2)$-fold with a smooth anti-canonical divisor removed $\mathcal{X}^\circ = \mathcal{X} \setminus w^{-1}(-1)$. We show that when $\mathcal{X}$ is the canonical bundle of a toric Fano $n$-orbifold $S$ and $f$ is its Givental superpotential, the strong deformation retraction skeleton $\mathsf{L}$ of $\mathcal{Y}$ in the sense of RSTZ (Ruddat--Sibilla--Treumann--Zaslow in Geom. Topol. 18(3):1343--1395, 2014) has a Weinstein neighborhood $U$, such that the wrapped microlocal sheaf category $μ\mathrm{Sh}^w_{\mathsf{L}}(\mathsf{L}) \cong \mathrm{Coh}(\mathcal{X}^\circ)$. This proves a microlocal categorical version of the SYZ mirror in (Abouzaid--Auroux--Katzarkov in Publ. math. IHÉS 123(1):199--282, 2016, Thm. 1.7). We also extend the definition of characteristic cycles for constructible sheaves in cotangent bundles from (Kashiwara--Schapira in Sheaves on Manifolds, Grundlehren math. Wiss. 292, Springer, 1990, Ch. IX) to finite-rank objects in $μ\mathrm{Sh}^w_{\mathsf{L}}(\mathsf{L})$, and describe the characteristic cycles for objects mirror to a coherent sheaf supported on $S$.