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Aaron Brown

Publications and source records attributed to Aaron Brown.

At least 19 recordsLinked to original sources
arXiv2026

First Light with the Dark100 Array of PANOSETI Telescopes at Palomar Observatory

Dark100 is the first phase of an extensive array of Panoramic SETI (PANOSETI) telescopes at Palomar Observatory, California. PANOSETI telescopes are small, 0.5-m Fresnel lens telescopes instrumented with 1024-pixel silicon photomultiplier (SiPM) cameras. The telescopes were originally designed to search for ultra-fast optical transients, but they also function as cost-effective imaging atmospheric Cherenkov telescopes (IACTs). Dark100 will use seven of these widely separated IACTs to map the ultra-high-energy (UHE) gamma-ray sources on the Galactic Plane at high resolution. Dark100 will also leverage the IACT technique to search for evidence of ultra-heavy dark matter in a mass range that extends beyond 100 TeV. Deployment of the first four telescopes and enclosures was completed in December 2025, and commissioning of the next three is scheduled to finish by the end of 2026. The array has so far collected more than 100 hours of 3-telescope data on sources including the Crab Nebula and Markarian 421. Here we present the current status of Dark100.

astro-ph.IM↗
arXiv2026

Absolute continuity of invariant measures for random diffeomorphisms

We develop criteria showing that invariant measures for random walks generated by diffeomorphisms of manifolds are in the Lebesgue class. Our assumptions are first, that there is a uniform expansion gap in the Lyapunov spectrum of the random walk, and second, that the conditionals of the invariant measure along the appropriate (partial) stable manifolds are in the Lebesgue class.

math.DS↗
arXiv2026

Thermodynamic Formalism Out of Equilibrium Part I: Pressure Out of Equilibrium, and Azuma Inequality and Gibbs Processes

We study the thermodynamic formalism of topological Markov shifts where the potential varies by a random walk on an exterior system. We define the {\em pressure out of equilibrium} which is associated to such a family of potentials, and prove a corresponding variational principle. We present an application to random dynamical systems. In particular, we study an open condition for random dynamical systems where the randomness is driven by a Gibbs process, and prove hyperbolicity estimates via an Azuma inequality which were previously only known in the i.i.d. setting.

math.DS↗
arXiv2026

Image-Based Whole-Heart Cardiac Flow Simulations in Health and Congenital Heart Disease

Intracardiac flow patterns are shaped by the coupled motion of the cardiac chambers and heart valves and provide important information about cardiac function. However, clinical flow imaging remains limited by exam times, noise, resolution, and incomplete details of the three-dimensional flow. Computational fluid dynamics (CFD) can potentially provide detailed flow quantification and predictive insight into treatment outcomes, but clinical translation requires frameworks that reproduce patient-specific measurements while balancing physiological realism, computational cost, and modeling effort. Herein, we present an image-based, patient-specific computational framework for simulating whole-heart intracardiac hemodynamics that balances physiological fidelity with computational efficiency. The framework first employs machine learning-based segmentation and mesh propagation to reconstruct moving cardiac anatomies from time-resolved images. CFD simulations are then performed to resolve blood flow in deforming domains, while resistive immersed surfaces (RIS) are used to model all four cardiac valves with physiologically realistic opening and closing dynamics. The framework was applied to model hemodynamics in a healthy adult and a pediatric patient with complex congenital heart disease (CHD). In the healthy case, the simulations reproduced physiologic pressure-volume behavior, valve timing, and ventricular vortex formation. In the CHD case, simulated chamber and vessel pressures showed agreement with cardiac catheterization measurements. Simulated flow fields were qualitatively consistent with 4D-Flow MRI, while providing higher-resolution visualization of flow structures that were partially obscured by imaging artifacts. Comparison between the healthy and CHD cases further revealed altered diastolic flow organization and elevated normalized viscous dissipation in the CHD heart.

eess.IV↗
arXiv2026

Lyapunov spectrum rigidity and simultaneous linearization for random Anosov diffeomorphisms

In this paper we study the Lyapunov spectrum rigidity for random walks of expanding maps on unit circle $\mathbb{S}^1$ and Anosov diffeomorphisms on $d$-torus $\mathbb{T}^d$. Let $ν$ be a probability supported on the set of expanding maps on $\mathbb{S}^1$ or a neighborhood of a generic Anosov automorphisms on $\mathbb{T}^d$. If the Lyapunov spectrum of the $ν$-stationary SRB-measure coincides with the Lyapunov spectrum of the algebraic action, then we can simultaneously linearize $ν$ almost every system to an affine action. Moreover, we prove the positive Lyapunov exponent rigidity for random walks of irreducible positive matrices acting on $\mathbb{T}^2$.

math.DS↗
arXiv2026

Developing a Quantitative Resiliency Approach

Resiliency has garnered attention in the management of critical infrastructure as a metric of system performance, but there are significant roadblocks to its implementation in a realistic decision-making framework. Contrasted to risk and reliability, which have robust quantification approaches and undergird many regulatory approaches to system safety (e.g., "risk-informed decision-making"), resiliency is a diffuse, qualitatively-understood characteristic, often treated differently or distinctly. However, in the emerging context of highly-complex, highly-interdependent critical systems, the idea of reliability (as the probability of non-failure) may not be an appropriate metric of system health. As a result, focus is shifting towards resiliency-centered approaches that value the response to failure as much as the avoidance of failure. Supporting this approach requires a robustly-defined, quantitative understanding of resiliency. In this paper, we explore the foundations of reliability and resiliency engineering, and propose an approach to resiliency-informed decision-making bolstered by a quantitative understanding of resiliency.

eess.SY↗
arXiv2025

Absolute continuity of stationary measures for random surface dynamics

We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and past (UEP). Our results can cover random dynamical systems generated by "very dissipative" diffeomorphisms and perturbations of volume preserving surface diffeomorphisms. For example, we can consider a random dynamical system on $\mathbb{T}^2$ generated by perturbations of a pair of non-commuting infinite order toral automorphisms with any arbitrary single diffeomorphism. In this case, we conclude that stationary measures are either atomic or absolutely continuous. We also obtain an orbit classification and equidistribution result.

math.DS↗
arXiv2025

Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method

We obtain measure rigidity results for stationary measures of random walks generated by diffeomorphisms, and for actions of $\operatorname{SL}(2,\mathbb{R})$ on smooth manifolds. Our main technical result, from which the rest of the theorems are derived, applies also to the case of a single diffeomorphism or $1$-parameter flow and establishes extra invariance of a class of measures that we call ``generalized u-Gibbs states''.

math.DS↗
arXiv2025

Positive entropy actions by higher-rank lattices

We study smooth actions by lattices in higher-rank simple Lie groups. Assuming one element of the action acts with positive topological entropy, we prove a number of new rigidity results. For lattices in $\mathrm{SL}(n,\mathbb{R})$ acting on $n$-manifolds, if the action has positive topological entropy we show the lattice must be commensurable with $\mathrm{SL}(n,\mathbb{Z})$. Moreover, such actions admit an absolutely continuous probability measure with positive metric entropy; adapting arguments by Katok and Rodriguez Hertz, we show such actions are measurably conjugate to affine actions on (infra-)tori. In a main technical argument, we study families of probability measures invariant under sub-actions of the induced action by the ambient Lie group on an associated fiber bundle. To control entropy properties of such measures when passing to limits, in the appendix we establish certain upper semicontinuity of fiber entropy under weak-$*$ convergence, adapting classical results of Yomdin and Newhouse.

math.DS↗
arXiv2024

From Ceilings to Walls: Universal Dynamic Perching of Small Aerial Robots on Surfaces with Variable Orientations

This work demonstrates universal dynamic perching capabilities for quadrotors of various sizes and on surfaces with different orientations. By employing a non-dimensionalization framework and deep reinforcement learning, we systematically assessed how robot size and surface orientation affect landing capabilities. We hypothesized that maintaining geometric proportions across different robot scales ensures consistent perching behavior, which was validated in both simulation and experimental tests. Additionally, we investigated the effects of joint stiffness and damping in the landing gear on perching behaviors and performance. While joint stiffness had minimal impact, joint damping ratios influenced landing success under vertical approaching conditions. The study also identified a critical velocity threshold necessary for successful perching, determined by the robot's maneuverability and leg geometry. Overall, this research advances robotic perching capabilities, offering insights into the role of mechanical design and scaling effects, and lays the groundwork for future drone autonomy and operational efficiency in unstructured environments.

cs.RO↗
arXiv2024

Zimmer's conjecture for non-split semisimple Lie groups

We prove many new cases of Zimmer's conjecture for actions by lattices in non-$\mathbb{R}$-split semisimple Lie groups $G$. By prior arguments, Zimmer's conjecture reduces to studying certain probability measures invariant under a minimal parabolic subgroup for the induced $G$-action. Two techniques are introduced to give lower bounds on the dimension of a manifold $M$ admitting a non-isometric action. First, when the Levi component of the stabilizer of the measure has higher-rank simple factors, cocycle superrigidity provides a lower bound on the dimension of $M$. Second, when certain fiberwise coarse Lyapunov distributions are one-dimensional, a measure rigidity argument provides additional invariance of the measure if the associated root spaces are higher-dimensional.

math.DS↗
arXiv2024

Absolute continuity of stationary measures

Let $f$ and $g$ be two volume preserving, Anosov diffeomorphisms on $\mathbb{T}^2$, sharing common stable and unstable cones. In this paper, we find conditions for the existence of (dissipative) neighborhoods of $f$ and $g$, $\mathcal{U}_f$ and $\mathcal{U}_g$, with the following property: for any probability measure $μ$, supported on the union of these neighborhoods, and verifying certain conditions, the unique $μ$-stationary SRB measure is absolutely continuous with respect to the ambient Haar measure. Our proof is inspired in the work of Tsujii for partially hyperbolic endomorphisms [Tsu05]. We also obtain some equidistribution results using the main result of [BRH17].

math.DS↗
arXiv2024

Liger at W.M. Keck Observatory: imager structural analysis, fabrication, and characterization plan

Liger is an adaptive optics (AO) fed imager and integral field spectrograph (IFS) designed to take advantage of the Keck All-sky Precision Adaptive-optics (KAPA) upgrade to the Keck I telescope. Liger adapts the design of the InfraRed Imaging Spectrograph (IRIS) for the Thirty Meter Telescope (TMT) to Keck by implementing a new imager and re-imaging optics. The performance of the imager is critical as it sequentially feeds the spectrograph and contains essential components such as the pupil wheel, filter wheel, and pupil viewing camera. We present the design and structural analysis of the Liger imager optical assembly including static, modal, and thermal simulations. We present the fabrication as well as the full assembly and characterization plan. The imager will be assembled bench-top in a clean room utilizing a coordinate-measuring machine (CMM) for warm alignment. To ensure optimal performance, the imager will be characterized in a test cryostat before integration with the full Liger instrument. This comprehensive approach to characterization ensures the precision and reliability of the imager, enhancing the observational capabilities of Liger and W.M. Keck Observatory.

astro-ph.IM↗
arXiv2024

Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors

We study actions by lattices in higher-rank (semi)simple Lie groups on compact manifolds. By classifying certain measures invariant under a related higher-rank abelian action (the diagonal action on the suspension space) we deduce a number of new rigidity results related to standard projective actions (i.e. boundary actions) by such groups. Specifically, in low dimensions we show all actions (with infinite image) are conjugate to boundary actions. We also show standard boundary actions (e.g. projective actions on generalized flag varieties) are local rigid and classify all smooth actions that are topological factors of such actions. Finally, for volume-preserving actions in low dimensions (with infinite image) we provide a mechanism to detect the presence of "blow-ups" for the action by studying measures that are $P$-invariant but not $G$-invariant for the suspension action.

math.DS↗
arXiv2024

Zimmer's conjecture for non-uniform lattices: escape of mass and growth of cocycles

We establish finiteness of low-dimensional actions of lattices in higher-rank semisimple Lie groups and establish Zimmer's conjecture for many such groups. This builds on previous work of the authors handling the case of actions by cocompact lattices and of actions by $\Sl(n,\Z)$. While the results are not sharp in all cases, they do dramatically improve all known results. The key difficulty overcome in this paper concerns escape of mass when taking limits of sequences of measures. Due to a need to control Lyapunov exponents for unbounded cocycles when taking such limits, quantitative controls on the concentration of mass at infinity are need and novel techniques are introduced to avoid ``escape of Lyapunov exponent."

math.DS↗
arXiv2023

The development of HISPEC for Keck and MODHIS for TMT: science cases and predicted sensitivities

HISPEC is a new, high-resolution near-infrared spectrograph being designed for the W.M. Keck II telescope. By offering single-shot, R=100,000 between 0.98 - 2.5 um, HISPEC will enable spectroscopy of transiting and non-transiting exoplanets in close orbits, direct high-contrast detection and spectroscopy of spatially separated substellar companions, and exoplanet dynamical mass and orbit measurements using precision radial velocity monitoring calibrated with a suite of state-of-the-art absolute and relative wavelength references. MODHIS is the counterpart to HISPEC for the Thirty Meter Telescope and is being developed in parallel with similar scientific goals. In this proceeding, we provide a brief overview of the current design of both instruments, and the requirements for the two spectrographs as guided by the scientific goals for each. We then outline the current science case for HISPEC and MODHIS, with focuses on the science enabled for exoplanet discovery and characterization. We also provide updated sensitivity curves for both instruments, in terms of both signal-to-noise ratio and predicted radial velocity precision.

astro-ph.IM↗
arXiv2023

PeV Gamma-ray Astronomy With Panoramic Optical SETI Telescopes

The Panoramic Search for Extraterrestrial Intelligence (PANOSETI) experiment is designed to detect pulsed optical signals on nanosecond timescales. PANOSETI is therefore sensitive to Cherenkov radiation generated by extensive air showers, and can be used for gamma-ray astronomy. Each PANOSETI telescope uses a 0.5 m Fresnel lens to focus light onto a 1024 pixel silicon photomultiplier camera that images a 9.9$^\circ\times$9.9$^\circ$ square field of view. Recent detections of PeV gamma-rays from extended sources in the Galactic Plane motivate constructing an array with effective area and angular resolution surpassing current observatories. The PANOSETI telescopes are much smaller and far more affordable than traditional imaging atmospheric Cherenkov telescopes (IACT), making them ideal instruments to construct such an array. We present the results of coincident observations between two PANOSETI telescopes and the gamma-ray observatory VERITAS, along with simulations characterizing the performance of a PANOSETI IACT array.

astro-ph.IM↗