We study the Tracy-Widom (TW) distribution $f_β(a)$ in the limit of large Dyson index $β\to +\infty$. This distribution describes the fluctuations of the rescaled largest eigenvalue $a_1$ of the Gaussian (alias Hermite) ensemble (G$β$E) of (infinitely) large random matrices. We show that, at large $β$, its probability density function takes the large deviation form $f_β(a) \sim e^{-βΦ(a)}$. While the typical deviation of $a_1$ around its mean is Gaussian of variance $O(1/β)$, this large deviation form describes the probability of rare events with deviation $O(1)$, and governs the behavior of the higher cumulants. We obtain the rate function $Φ(a)$ as a solution of a Painlevé II equation. We derive explicit formula for its large argument behavior, and for the lowest cumulants, up to order 4. We compute $Φ(a)$ numerically for all $a$ and compare with exact numerical computations of the TW distribution at finite $β$. These results are obtained by applying saddle-point approximations to an associated problem of energy levels $E=-a$, for a random quantum Hamiltonian defined by the stochastic Airy operator (SAO). We employ two complementary approaches: (i) we use the optimal fluctuation method to find the most likely realization of the noise in the SAO, conditioned on its ground-state energy being $E$ (ii) we apply the weak-noise theory to the representation of the TW distribution in terms of a Ricatti diffusion process associated to the SAO. We extend our results to the full Airy point process $a_1>a_2>\dots$ which describes all edge eigenvalues of the G$β$E, and correspond to (minus) the higher energy levels of the SAO, obtaining large deviation forms for the marginal distribution of $a_i$, the joint distributions, and the gap distributions.

This survey paper presents a comprehensive examination of Spiking Neural Network (SNN) architecture search (SNNaS) from a unique hardware/software co-design perspective. SNNs, inspired by biological neurons, have emerged as a promising approach to neuromorphic computing. They offer significant advantages in terms of power efficiency and real-time resource-constrained processing, making them ideal for edge computing and IoT applications. However, designing optimal SNN architectures poses significant challenges, due to their inherent complexity (e.g., with respect to training) and the interplay between hardware constraints and SNN models. We begin by providing an overview of SNNs, emphasizing their operational principles and key distinctions from traditional artificial neural networks (ANNs). We then provide a brief overview of the state of the art in NAS for ANNs, highlighting the challenges of directly applying these approaches to SNNs. We then survey the state of the art in SNN-specific NAS approaches. Finally, we conclude with insights into future research directions for SNN research, emphasizing the potential of hardware/software co-design in unlocking the full capabilities of SNNs. This survey aims to serve as a valuable resource for researchers and practitioners in the field, offering a holistic view of SNNaS and underscoring the importance of a co-design approach to harness the true potential of neuromorphic computing.

We present an analysis on the convergence properties of the so-called geometric heat flow equation for computing geodesics (extremal curves) on Riemannian manifolds. Computing geodesics numerically in real time has become an important capability across several fields, including control and motion planning. The geometric heat flow equation involves solving a parabolic partial differential equation whose solution is a geodesic. In practice, solving this PDE numerically can be done efficiently, and tends to be more numerically stable and exhibit a better rate of convergence compared to numerical optimization. We prove that the geometric heat flow equation is exponentially stable in $L_2$ if the curvature of the Riemannian manifold does not exceed a positive bound and that asymptotic convergence in $L_2$ is always guaranteed. We also present a pseudospectral method that leverages Chebyshev polynomials to accurately compute geodesics in only a few milliseconds for non-contrived manifolds. Our analysis was verified with our custom pseudospectral method by computing geodesics on common non-Euclidean surfaces, and in feedback for a contraction-based controller with a non-flat metric for a nonlinear system.

Materials with a Kagome lattice are intensely studied because they host exotic states that combine strong correlations and topology. Recently, critical current oscillations were observed in an unstructured flake of CsV3Sb5 . In this work, we show that the origin of these oscillations is a network of Josephson junctions intrinsic to the flake that emerges below its critical temperature. Under radio-frequency radiation, we observe quantized Shapiro steps. The sensitivity of the step height to the contact placement indicates a complex network of junctions. By performing interference studies along multiple field directions, we demonstrate that the interference effects are a result of small junctions and filamentary supercurrent flow. Upon nanostructuring the flake, prominent features of the interference pattern are preserved, illustrating the localized nature of these junctions and their stability to thermal cycles. These results pave the way for determining the exact nature of superconductivity in the AV3Sb5 family.

Despite many years of research, the quest to identify neural correlates of perceptual consciousness (NCC) remains unresolved. One major obstacle lies in methodological limitations: most studies rely on non-invasive neural measures with limited spatial or temporal resolution making it difficult to disentangle proper NCCs from concurrent cognitive processes. Additionally, the relatively low sensitivity of non-invasive neural measures limits the interpretation of null findings in studies targeting proper NCCs. In this review, we discuss how human intracranial recordings can advance the search for NCCs, by offering high spatiotemporal resolution, improved signal sensitivity, and broad cortical and subcortical coverage. We review studies that have examined NCCs at the level of single neurons and populations of neurons, and evaluate their implications on the debates between cognitive and sensory theories of consciousness. Finally, we highlight the limits of current intracranial human recordings and propose future directions based on emerging technologies and novel experimental paradigms.

An invex function generalizes a convex function in the sense that every stationary point is a global minimizer. Recently, invex functions and their subclasses have attracted attention in signal processing and machine learning. However, verifying invexity is often difficult because its definition involves an unknown function called a kernel function. This paper studies kernel functions associated with invex functions, which have received relatively limited attention in the literature. In particular, we develop several methods for constructing explicit kernel functions and establish a characterization of pseudoconvexity in terms of kernel functions. These results provide constructive tools for proving invexity of new functions and for clarifying their structural properties. We also present examples of nonsmooth, non-pseudoconvex invex functions arising in signal processing.

Large Language Models (LLMs) open new possibilities for constructing realistic and interpretable macroeconomic simulations. We present SimCity, a multi-agent framework that leverages LLMs to model an interpretable macroeconomic system with heterogeneous agents and rich interactions. Unlike classical equilibrium models that limit heterogeneity for tractability, or traditional agent-based models (ABMs) that rely on hand-crafted decision rules, SimCity enables flexible, adaptive behavior with transparent natural-language reasoning. Within SimCity, four core agent types (households, firms, a central bank, and a government) deliberate and participate in a frictional labor market, a heterogeneous goods market, and a financial market. Furthermore, a Vision-Language Model (VLM) determines the geographic placement of new firms and renders a mapped virtual city, allowing us to study both macroeconomic regularities and urban expansion dynamics within a unified environment. To evaluate the framework, we compile a checklist of canonical macroeconomic phenomena, including price elasticity of demand, Engel's Law, Okun's Law, the Phillips Curve, and the Beveridge Curve, and show that SimCity naturally reproduces these empirical patterns while remaining robust across simulation runs.

This paper addresses the challenge of synthesizing safety-critical controllers for high-order nonlinear systems, where constructing valid Control Barrier Functions (CBFs) remains computationally intractable. Leveraging layered control, we design CBFs in reduced-order models (RoMs) while regulating full-order models' (FoMs) dynamics at the same time. Traditional Lyapunov tracking functions are required to decrease monotonically, and systematic synthesis methods for such functions exist only for fully-actuated systems. To overcome this limitation, we introduce Recurrent Tracking Functions (RTFs), which replace the monotonic decay requirement with a weaker finite-time recurrence condition. This relaxation permits transient deviations of tracking errors while ensuring safety. By integrating CBFs for RoMs with RTFs, we construct recurrent CBFs (RCBFs) whose zero-superlevel set is control $τ$-recurrent, and guarantee safety for all initial states in such a set when RTFs are satisfied. We establish theoretical safety guarantees and validate the approach through a proof-of-concept numerical experiment, demonstrating RTFs' effectiveness and the safety of FoMs.

Place-based epidemiology studies often rely on circular buffers to define ``exposure'' to spatially distributed risk factors, where the buffer radius represents a threshold beyond which exposure does not influence the outcome of interest. This approach is popular due to its simplicity and alignment with public health policies. However, buffer radii are often chosen relatively arbitrarily and assumed constant across the spatial domain. This may result in suboptimal statistical inference if these modeling choices are incorrect. To address this, we develop SVBR (Spatially-Varying Buffer Radii), a flexible hierarchical Bayesian spatial change points approach that treats buffer radii as unknown parameters and allows both radii and exposure effects to vary spatially. Through simulations, we find that SVBR improves estimation and inference for key model parameters compared to traditional methods. We also apply SVBR to study healthcare access in Madagascar, finding that proximity to healthcare facilities generally increases antenatal care usage, with clear spatial variation in this relationship. By relaxing rigid assumptions about buffer characteristics, our method offers a flexible, data-driven approach to accurately defining exposure and quantifying its impact. The newly developed methods are available in the R package EpiBuffer.

We study the identification of continuous-time vector fields from irregularly sampled trajectories. We introduce spectral flow learning, which learns in a windowed flow space using a lag-linear label operator that aggregates lagged Koopman actions. We provide finite-sample, high-probability (FS-HP) guarantees for the class of variable-step linear multistep methods (vLMM). The FS-HP rates are constructed using spectral regularization with qualification-controlled filters for flow predictors under standard source and filter assumptions. A multistep observability inequality links flow error to vector-field error and yields two-term bounds that combine a statistical rate with an explicit discretization bias from vLMM theory. Simulations on a controlled mass-spring system corroborate the theory and clarify conditioning, step-sample tradeoffs, and practical implications.

There is considerable current interest in applications of generalised Lie algebras graded by an abelian group $Γ$ with a commutative factor $ω$. This calls for a systematic development of the theory of such algebraic structures. We treat the representation theory and invariant theory of the $Γ$-graded general linear Lie $ω$-algebra $\mathfrak{gl}(V(Γ, ω))$, where $V(Γ, ω)$ is any finite dimensional $Γ$-graded vector space. Generalised Howe dualities over symmetric $(Γ, ω)$-algebras are established, from which we derive the first and second fundamental theorems of invariant theory, and a generalised Schur-Weyl duality. The unitarisable $\mathfrak{gl}(V(Γ, ω))$-modules for two ``compact'' $\ast$-structures are classified, and it is shown that the tensor powers of $V(Γ, ω)$ and their duals are unitarisable for the two compact $\ast$-structures respectively. A Hopf $(Γ, ω)$-algebra is constructed, which gives rise to a group functor corresponding to the general linear group in the $Γ$-graded setting. Using this Hopf $(Γ, ω)$-algebra, we realise simple tensor modules and their dual modules by mimicking the classic Borel-Weil theorem. We also analyse in some detail the case with $Γ={\mathbb Z}^{\dim{V(Γ, ω)}}$ and $ω$ depending on a complex parameter $q\ne 0$, where $\mathfrak{gl}(V(Γ, ω))$ shares common features with the quantum general linear (super)group, but is better behaved especially when $q$ is a root of unity.

The moduli space $\mathcal{A}_g$ of principally polarised abelian varieties of dimension $g$, defined over an algebraically closed field of characteristic $p >0$, is studied through various stratifications. The two most prominent ones are the Newton stratification, based on the isogeny class of the $p$-divisible group of an abelian variety, and the Ekedahl-Oort stratification, defined by the isomorphism class of its $p$-torsion group scheme. In general, it is not known how the strata of these two intersect. In this paper we completely determine which of these intersections are non-empty in dimension five. As a consequence, we give an explicit description of the induced Ekedahl-Oort stratification on the supersingular locus $\mathcal{S}_{5}$.

Foundation model (FM)-based AI agents are rapidly gaining adoption across diverse domains, but their inherent non-determinism and non-reproducibility pose testing and quality assurance challenges. While recent benchmarks provide task-level evaluations, there is limited understanding of how developers verify the internal correctness of these agents during development. To address this gap, we conduct the first large-scale empirical study of testing practices in the AI agent ecosystem, analyzing 39 open-source agent frameworks and 439 agentic applications. We identify ten distinct testing patterns and find that novel, agent-specific methods like DeepEval are seldom used (around 1%), while traditional patterns like negative and membership testing are widely adapted to manage FM uncertainty. By mapping these patterns to canonical architectural components of agent frameworks and agentic applications, we uncover a fundamental inversion of testing effort: deterministic components like Resource Artifacts (tools) and Coordination Artifacts (workflows) consume over 70% of testing effort, while the FM-based Plan Body receives less than 5%. Crucially, this reveals a critical blind spot, as the Trigger component (prompts) remains neglected, appearing in around 1% of all tests. Our findings offer the first empirical testing baseline in FM-based agent frameworks and agentic applications, revealing a rational but incomplete adaptation to non-determinism. To address it, framework developers should improve support for novel testing methods, application developers must adopt prompt regression testing, and researchers should explore barriers to adoption. Strengthening these practices is vital for building more robust and dependable AI agents.

Online social networks offer a valuable lens to analyze both individual and collective phenomena. Researchers often use simulators to explore controlled scenarios, and the integration of Large Language Models (LLMs) makes these simulations more realistic by enabling agents to understand and generate natural language content. In this work, we investigate the behavior of LLM-based agents in a simulated microblogging social network. We initialize agents with realistic profiles calibrated on real-world online conversations from the 2022 Italian political election and extend an existing simulator by introducing mechanisms for opinion modeling. We examine how LLM agents simulate online conversations, interact with others, and evolve their opinions under different scenarios. Our results show that LLM agents generate coherent content, form connections, and build a realistic social network structure. However, their generated content displays less heterogeneity in tone and toxicity compared to real data. We also find that LLM-based opinion dynamics evolve over time in ways similar to traditional mathematical models. Varying parameter configurations produces no significant changes, indicating that simulations require more careful cognitive modeling at initialization to replicate human behavior more faithfully. Overall, we demonstrate the potential of LLMs for simulating user behavior in social environments, while also identifying key challenges in capturing heterogeneity and complex dynamics.

Understanding the formation and evolution of the cosmic web of galaxies is a fundamental goal of cosmology, using various tracers of the cosmic large-scale structure at an ever wider range of redshifts. Our principal aim is to advance the mapping of the cosmic web at high redshifts using observational and synthetic catalogues of quasars (QSOs), which offer a powerful probe of structure formation and the validity of the concordance cosmological model. In this analysis, we selected 708,483 QSOs at $0.8<z<2.2$ from the Quaia data set, allowing a reconstruction of the matter density field using 24,372 deg$^2$ sky area with a well-understood selection function, and thus going beyond previous studies. Using the REVOLVER method, we created catalogues of voids and clusters based on the estimation of the local density at QSO positions with Voronoi tessellation. We tested the consistency of Quaia data and 50 mock catalogues, including various parameters of the voids and clusters in data subsets, and also measurements of the density profiles of these cosmic super-structures at $100 h^{-1}$Mpc scales. We identified 12,842 voids and 41,111 clusters in the distribution of Quaia QSOs. The agreement between data and mocks is at a level of 5-10%, considering void and cluster radii, average inner density, and density profiles. In particular, we tested the role of survey mask proximity effects in the void and cluster detection, which albeit present, are consistent in simulations and observations. The largest voids and clusters reach $R_{eff} \approx 250 h^{-1}$Mpc and $150 h^{-1}$Mpc, respectively, but without evidence for ultra-large cosmic structures exceeding the dimensions of the largest structures in the mocks. As an important deliverable, we share our density field estimation, void catalogues, and cluster catalogues with the public, allowing various additional cross-correlation probes at high-z.

Humid heat stress and heatwaves pose significant risks for living organisms, from humans and wildlife to insects. These threats have wide-ranging health, ecological, and socio-economic impacts that are expected to worsen with climate change. How large-scale climate modes drive the week-to-month variability of humid heat remains poorly understood at the global scale. This limitation hinders the development of accurate forecasts necessary for risk-management measures, notably in the heavily populated and ecologically fragile regions of the tropics and subtropics. With forecast lead times up to several weeks, the Madden-Julian Oscillation (MJO), a global-scale intraseasonal tropical atmospheric disturbance circumnavigating earth in around 30-60 days, provides considerable predictability for weather conditions, and meteorological and oceanic extremes. Here we show that the MJO, and the associated boreal summer intraseasonal oscillation (BSISO), have a significant influence on humid heat and heatwaves over much of the tropics and subtropics across all seasons, both over terrestrial and marine regions. Humid heatwave likelihood can double or halve, depending on the MJO phase, in large areas of the Earth. The MJO/BSISO's influence on wet-bulb temperature is primarily via specific humidity rather than dry-bulb temperature anomalies. In the subtropics and other regions where we typically do not find a strong signal of the convection, we find that intraseasonal anomalies of specific humidity and dry-bulb temperature are influenced by horizontal advection in the planetary boundary layer. Particularly in the subtropics where advection of the climatological moisture and temperature gradient by MJO-related anomalous winds is an important term.

We demonstrate a logical neutral atom architecture that integrates atom motion with in-place entanglement to achieve lower overheads than entangling-zone approaches. Using a 114-qubit device, we perform three proof-of-principle logical-qubit experiments. First, we implement a pre-compiled, non-scalable variant of Shor's algorithm, observing improved logical-over-physical performance, including with loss correction and leakage detection, achieving up to a 2x reduction in TVD. Second, we construct constant-depth logical CX ladders; on current hardware these execute with serial entangling operations, yet still yield 2-4x lower error for 8 and 12 logical qubits. Third, we prepare the [[16,4,4]] code and perform single-round decoding with post-processed error correction, achieving 8x improvement on logical vs physical. These results demonstrate how combining motion with in-place entanglement offers lower overhead than entangling-zone approaches.

To select suitable filters for a task or to improve existing filters, a deep understanding of their inner workings is vital. Diffusion echoes, which are space-adaptive impulse responses, are useful to visualise the effect of nonlinear diffusion filters. However, they have received little attention in the literature. There may be two reasons for this: Firstly, the concept was introduced specifically for diffusion filters, which might appear too limited. Secondly, diffusion echoes have large storage requirements, which restricts their practicality. This work addresses both problems. We introduce the filter echo as a generalisation of the diffusion echo and use it for applications beyond adaptive smoothing, such as image inpainting, osmosis, and variational optic flow computation. We provide a framework to visualise and inspect echoes from various filters with different applications. Furthermore, we propose a compression approach for filter echoes, which reduces storage requirements by a factor of 20 to 100.

In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective function consists of two components: one is a smooth convex function, and the other is a non-smooth convex function. We establish the strong convergence of the proposed method, provided that the smooth convex function is Lipschitz continuous. We also prove that the expected value of the error between the estimated gradient and the actual gradient converges to zero. Furthermore, we get an \( O(\sqrt{1/k}) \) convergence rate for our method. Finally, the effectiveness of the proposed method is validated through numerical experiments on Logistic regression and Lasso regression.

In practical least squares realization problems, partial information about the pole locations of the dynamical model may be known a priori. Existing techniques for incorporating this prior knowledge, such as prefiltering the given data, are typically heuristic and lack theoretical guarantees. We extend our previously developed globally optimal estimation approach to accommodate fixed poles in the least squares realization problem. In particular, we reformulate the problem as a (rectangular) multiparameter eigenvalue problem, the eigenvalues of which characterize all local and global minimizers of the constrained estimation problem. We present numerical examples to demonstrate the effectiveness of the proposed method and experimentally validate the paper's central hypothesis: incorporating a priori information on the poles enhances the estimation results.

We introduce NeedForHeat DataGear: an open hardware and open software data collection system designed to accelerate the residential heating transition. NeedForHeat DataGear collects time series monitoring data in homes that have not yet undergone a heating transition, enabling assessment of real-life thermal characteristics, heating system efficiency, and residents' comfort needs. This paper outlines its architecture and functionalities, emphasizing its modularity, adaptability, and cost-effectiveness for field data acquisition. Unlike conventional domestic monitoring solutions focused on home automation, direct feedback, or post-installation heat pump monitoring, it prioritizes time series data we deemed essential to evaluate the current situation in existing homes before the heating transition. Designed for seamless deployment across diverse households, NeedForHeat DataGear combines openness, security, and privacy with a low-cost, user-friendly approach, making it a valuable tool for researchers, energy professionals, and energy coaches.

Dynamic multilayer networks are frequently used to describe the structure and temporal evolution of multiple relationships among common entities, with applications in fields such as sociology, economics, and neuroscience. However, exploration of analytical methods for these complex data structures remains limited. We propose a functional tensor-based model for dynamic multilayer networks, with the key feature of capturing the shared structure among common vertices across all layers, while simultaneously accommodating smoothly varying temporal dynamics and layer-specific heterogeneity. The proposed model and its embeddings can be applied to various downstream network inference tasks, including dimensionality reduction, vertex community detection, analysis of network evolution periodicity, visualization of dynamic network evolution patterns, and evaluation of inter-layer similarity. We provide an estimation algorithm based on functional tensor Tucker decomposition and the reproducing kernel Hilbert space framework, with an effective initialization strategy to improve computational efficiency. The estimation procedure can be extended to address more generalized functional tensor problems, as well as to handle missing data or unaligned observations. We validate our method on simulated data and two real-world cases: the dynamic Citi Bike trip network and an international food trade dynamic multilayer network, with each layer corresponding to a different product.

Recent fully non-linear simulations of ultracompact spherically symmetric boson stars have presented evidence for their long-term stability. All observed dynamics could be mainly attributed to the fundamental radial mode. In this work, we additionally decompose some of the data in spherical harmonics, providing a first step towards the characterization of non-spherical modes present.

We introduce new algorithms and provide example constructions of stabilizer models for the gapped boundaries, domain walls, and $0D$ defects of Abelian composite-dimensional twisted quantum doubles. Using the physically intuitive concept of condensation, our algorithm explicitly describes how to construct the boundary and domain-wall stabilizers starting from the bulk model. This extends the utility of Pauli stabilizer models in describing non-translationally invariant topological orders with gapped boundaries. To highlight this utility, we provide a series of examples, including a new family of quantum error-correcting codes where the double of $\mathbb{Z}_4$ is coupled to instances of the double semion (DS) phase. We discuss the codes' utility in the burgeoning area of quantum error correction with an emphasis on the interplay between deconfined anyons, logical operators, error rates, and decoding. We also augment our construction, built using algorithmic tools to describe the properties of explicit stabilizer layouts at the microscopic lattice-level, with dimensional counting arguments and macroscopic-level constructions building on pants decompositions. The latter outlines how such codes' representation and design can be automated. Our results are validated by a series of error-correcting threshold calculations comparing our code's performance with standard surface codes. To do so, we introduce a composite dimensional belief propagation decoder with ordered statistics that utilizes combination sweeps. Going beyond our worked-out examples, we expect our explicit step-by-step algorithms to pave the path for new higher-dimensional codes to be discovered and implemented in near-term architectures that take advantage of various hardware's distinct strengths.

The description of the entanglement dynamics of monitored noninteracting fermions, including the existence of measurement-induced phase transitions (MIPTs), is a challenging problem with conflicting results in the literature. The mapping of the problem onto a non-linear sigma model (NLSM) indicates that relatively large lattice sizes are required to determine the nature of the entanglement entropy (EE) in the thermodynamics limit. Here we address this problem numerically for monitored noninteracting fermions with $U(1)$ symmetry. The use of graphics processing unit (GPU) techniques, even with outdated hardware, makes it possible to reach much larger lattice sizes ($L = 16384$ and $160\times160$ in one (1d) and two (2d) dimensions respectively) than in previous studies which enables us to characterize quantitatively the entanglement dynamics. In 1d, we show that in order to confirm the absence of a MIPT, for both projective and homodyne measurements, predicted by the NLSM it is necessary to reach $L \sim 10000$. In 2d, also as predicted by the NLSM, we observe for both protocols a MIPT at finite monitoring rate characterized by a scale invariant mutual information. The critical monitoring strength depends on the protocol while the critical exponent $ν\approx 1.3$ governing the approach to the MIPT is similar in both cases. These features are not correctly predicted by the NLSM. Our results paves the way for a fully quantitative description of the entanglement dynamics of monitoring quantum systems.

Perfectoid spaces have become a crucial tool in $p$-adic geometry, serving as a bridge between adic spaces in characteristic $0$ and those in characteristic $p$. In this article, we develop a systematic way to study the structure of perfectoid spaces within the setting of multivariate $p$-adic Hodge theory over a variant of the rings introduced in \cite{Bri}.

We study a size-structured population model in which individual cells grow at a rate determined by a fluctuating internal variable (e.g., gene expression levels). Many previous models of phenotypically heterogeneous populations can be viewed as special cases of this model, and it has previously been observed that the internal variable decouples from cell size under certain conditions. In this work, we generalize these results and connect them to the Feynman-Kac formula, which yields relationships between the lineage dynamics and population distribution in branching processes. To this end, we derive conditions for decoupling, both in the lineage and population ensemble. When decoupling occurs in both ensembles, the size dynamics can be transformed, via a random time change, into a growth-homogeneous process, and expectations can be evaluated through an exponential tilting procedure that follows from the Feynman-Kac formula. We further characterize weaker, ensemble-specific forms of decoupling that hold in either the lineage or the population ensemble, but not both. We provide a more general interpretation of tilted expectations in terms of the mass-weighted phenotype distribution

In this paper we aim to study viability and completeness in finite markets. In order to do that, we characterize the set of equivalent martingale measures of two-period markets as convex combinations of a finite number of martingale measures. We provide an algorithm for finding such measures, that can be applied in other problems of convex geometry, and represents the starting point for a study of such characterizations of convex sets' intersections. We apply these results to the study of a discrete-time version of the Korn-Kreer-Lenssen model, and give an example of the limitations of using discrete-time models to understand continuous-time ones.

We study the asymptotic symmetries of the Nappi-Witten spacetime in four dimensions, a plane wave arising as the Penrose limit of AdS$_2\times S^2$. Imposing suitable boundary conditions at large transverse distance, we uncover a new infinite-dimensional symmetry algebra allowing for non-trivial central extensions. The corresponding phase space encompasses the most general four-dimensional pp-wave metric, including in particular the Penrose limit of Kerr black holes.

Starburst galaxies, like M82, launch kiloparsec-scale galactic outflows that interact with the circumgalactic medium (CGM) in complex ways. Apart from enriching the CGM with metals and energy, these outflows may trigger star formation in the halo -- either by driving shocks into the CGM or transporting cold, star-forming gas. To investigate such processes, we analyze the star formation history (SFH) of the Southern Arcs -- arc-like stellar features located ~5 kpc from M82's star-forming disk along the minor axis -- using Hubble Space Telescope Wide Field Camera 3 photometry. From resolved stellar populations, we derive SFHs over the last ~500 Myr, finding that ~85% of the stellar mass formed between ~150 and ~70 Myr ago, followed by a brief pause, with the remaining ~15% forming since ~30 Myr ago. The two stellar populations are co-spatial on scales of at least ~200 pc. The timing of the ~100 Myr burst aligns with star formation in the M82 disk and the age distribution of its star clusters, suggesting a causal link between the disk starburst and halo star formation. We explore two mechanisms that could explain these observations. In the first, shocks driven by the interaction between hot outflowing gas and cooler CGM material compress dense clouds, triggering collapse and star formation. In the second, stars form directly within massive, cool clouds associated with the outflow. As these clouds move ballistically through the halo, subsequent interactions with tidal debris may trigger additional star formation, producing the observed episodic structure.