arXiv subjects

George Pappas

Publications and source records attributed to George Pappas.

At least 55 records · Page 3Linked to original sources

arXiv2023

Is a black hole shadow a reliable test of the no-hair theorem?

Capturing the image of the shadow cast by the event horizon of an illuminated black hole is, at the most basic level, an experiment of extreme light deflection in a strongly curved spacetime. As such, the properties of an imaged shadow can be used to probe the general relativistic Kerr nature of astrophysical black holes. As an example of this prospect, it is commonly asserted that a shadow can test the validity of the theory's famous `no hair theorem' for the black hole's mass and spin multipole moments. In this paper, we assess this statement by calculating the shadow's equatorial radius in spacetimes with an arbitrary multipolar structure and within a slow rotation approximation. We find that when moments higher than the quadrupole are taken into account, the shadow acquires a high degree of degeneracy as a function of the deviation from the Kerr multipole moments. The results of our analysis suggest that dark objects with strongly non-Kerr multipolar structure could nevertheless produce a Kerr-like shadow with its characteristic quasi-circular shape.

gr-qc↗

arXiv2022

Risk Verification of Stochastic Systems with Neural Network Controllers

Motivated by the fragility of neural network (NN) controllers in safety-critical applications, we present a data-driven framework for verifying the risk of stochastic dynamical systems with NN controllers. Given a stochastic control system, an NN controller, and a specification equipped with a notion of trace robustness (e.g., constraint functions or signal temporal logic), we collect trajectories from the system that may or may not satisfy the specification. In particular, each of the trajectories produces a robustness value that indicates how well (severely) the specification is satisfied (violated). We then compute risk metrics over these robustness values to estimate the risk that the NN controller will not satisfy the specification. We are further interested in quantifying the difference in risk between two systems, and we show how the risk estimated from a nominal system can provide an upper bound the risk of a perturbed version of the system. In particular, the tightness of this bound depends on the closeness of the systems in terms of the closeness of their system trajectories. For Lipschitz continuous and incrementally input-to-state stable systems, we show how to exactly quantify system closeness with varying degrees of conservatism, while we estimate system closeness for more general systems from data in our experiments. We demonstrate our risk verification approach on two case studies, an underwater vehicle and an F1/10 autonomous car.

eess.SY↗

arXiv2022

Resilient Consensus via Voronoi Communication Graphs

Consensus algorithms form the foundation for many distributed algorithms by enabling multiple robots to converge to consistent estimates of global variables using only local communication. However, standard consensus protocols can be easily led astray by non-cooperative team members. As such, the study of resilient forms of consensus is necessary for designing resilient distributed algorithms. W-MSR consensus is one such resilient consensus algorithm that allows for resilient consensus with only local knowledge of the communication graph and no a priori model for the data being shared. However, the verification that a given communication graph meets the strict graph connectivity requirement makes W-MSR difficult to use in practice. In this paper, we show that a commonly used communication graph structure in robotics literature, the communication graph built based on the Voronoi tessellation, automatically results in a sufficiently connected graph to reject a single non-cooperative team member. Further, we show how this graph can be enhanced to reject two non-cooperative team members and provide a roadmap for modifications for further resilience. This contribution will allow for the easy application of resilient consensus to algorithms that already rely on Voronoi-based communication such as distributed coverage and exploration algorithms.

cs.RO↗

arXiv2022

Adaptive Sampling of Latent Phenomena using Heterogeneous Robot Teams (ASLaP-HR)

In this paper, we present an online adaptive planning strategy for a team of robots with heterogeneous sensors to sample from a latent spatial field using a learned model for decision making. Current robotic sampling methods seek to gather information about an observable spatial field. However, many applications, such as environmental monitoring and precision agriculture, involve phenomena that are not directly observable or are costly to measure, called latent phenomena. In our approach, we seek to reason about the latent phenomenon in real-time by effectively sampling the observable spatial fields using a team of robots with heterogeneous sensors, where each robot has a distinct sensor to measure a different observable field. The information gain is estimated using a learned model that maps from the observable spatial fields to the latent phenomenon. This model captures aleatoric uncertainty in the relationship to allow for information theoretic measures. Additionally, we explicitly consider the correlations among the observable spatial fields, capturing the relationship between sensor types whose observations are not independent. We show it is possible to learn these correlations, and investigate the impact of the learned correlation models on the performance of our sampling approach. Through our qualitative and quantitative results, we illustrate that empirically learned correlations improve the overall sampling efficiency of the team. We simulate our approach using a data set of sensor measurements collected on Lac Hertel, in Quebec, which we make publicly available.

cs.RO↗

arXiv2022

Chaotic photon orbits and shadows of a non-Kerr object described by the Hartle-Thorne spacetime

The data from the event horizon telescope have provided a novel view of the vicinity of the horizon of a black hole (BH), by imaging the region around the light-ring. They have also raised hopes for measuring in the near future, features of the image (or the shadow) related to higher order effects of photons traveling in these regions, such as the appearance of higher order bright rings. While the prospect of measuring these fine features of Kerr BHs is very interesting in itself, there are some even more intriguing prospects for observing novel features of possible non-Kerr objects, in the case that the subjects of our images are not the BH solutions of GR. In the hope of sufficient resolution being available in the future, we explore in this work the structure and properties of null geodesics around a Hartle-Thorne spacetime that includes a deformation from the Kerr spacetime characterised by the quadrupole deformation $δq$. These spacetimes have been found to exhibit a bifurcation of the equatorial light-ring to two off-equatorial light-rings in a range of $δq$s and spin parameters. In addition to this, there is a range of parameters where both the equatorial and the off-equatorial light-rings are present. This results in the formation of a pocket that can trap photons. We investigate the properties of these trapped orbits and find that chaotic behaviour emerges. Some of these chaotic orbits are additionally found to be "sticky" and get trapped close to periodic orbits for long times. We also explore how these novel features affect the shadow and find that the off-equatorial light-rings produce distinctive features that deform its circular shape, while the chaotic behaviour associated to the pocket creates features with fractal structure. These results are shown to be quite general, extending to higher order Hartle-Thorne spacetimes.

gr-qc↗

arXiv2021

Can supermassive black hole shadows test the Kerr metric?

The unprecedented image of the M87* supermassive black hole has sparked some controversy over its usefulness as a test of the general relativistic Kerr metric. The criticism is mainly related to the black hole's quasi-circular shadow and advocates that its radius depends not only on the black hole's true spacetime properties but also on the poorly known physics of the illuminating accretion flow. In this paper we take a sober view of the problem and argue that our ability to probe gravity with a black hole shadow is only partially impaired by the matter degrees of freedom and the number of non-Kerr parameters used in the model. As we show here, a more intriguing situation arises from the mass scaling of the dimensional coupling constants that typically appear in non-GR theories of gravity. Existing limits from gravitational wave observations imply that supermassive systems like the M87* black hole would suffer a suppression of all non-GR deviation parameters in their metric, making the spacetime and the produced shadow virtually Kerr. Therefore, a supermassive black hole shadow is likely to probe only those extensions of General Relativity which are endowed with dimensionless coupling constants or other special cases with a screening mechanism for black holes or certain types of spontaneous scalarisation.

gr-qc↗

arXiv2021

Exploiting Heterogeneity in Robust Federated Best-Arm Identification

We study a federated variant of the best-arm identification problem in stochastic multi-armed bandits: a set of clients, each of whom can sample only a subset of the arms, collaborate via a server to identify the best arm (i.e., the arm with the highest mean reward) with prescribed confidence. For this problem, we propose Fed-SEL, a simple communication-efficient algorithm that builds on successive elimination techniques and involves local sampling steps at the clients. To study the performance of Fed-SEL, we introduce a notion of arm-heterogeneity that captures the level of dissimilarity between distributions of arms corresponding to different clients. Interestingly, our analysis reveals the benefits of arm-heterogeneity in reducing both the sample- and communication-complexity of Fed-SEL. As a special case of our analysis, we show that for certain heterogeneous problem instances, Fed-SEL outputs the best-arm after just one round of communication. Our findings have the following key implication: unlike federated supervised learning where recent work has shown that statistical heterogeneity can lead to poor performance, one can provably reap the benefits of both local computation and heterogeneity for federated best-arm identification. As our final contribution, we develop variants of Fed-SEL, both for federated and peer-to-peer settings, that are robust to the presence of Byzantine clients, and hence suitable for deployment in harsh, adversarial environments.

cs.LG↗

arXiv2021

Autoencoder-driven Spiral Representation Learning for Gravitational Wave Surrogate Modelling

Recently, artificial neural networks have been gaining momentum in the field of gravitational wave astronomy, for example in surrogate modelling of computationally expensive waveform models for binary black hole inspiral and merger. Surrogate modelling yields fast and accurate approximations of gravitational waves and neural networks have been used in the final step of interpolating the coefficients of the surrogate model for arbitrary waveforms outside the training sample. We investigate the existence of underlying structures in the empirical interpolation coefficients using autoencoders. We demonstrate that when the coefficient space is compressed to only two dimensions, a spiral structure appears, wherein the spiral angle is linearly related to the mass ratio. Based on this finding, we design a spiral module with learnable parameters, that is used as the first layer in a neural network, which learns to map the input space to the coefficients. The spiral module is evaluated on multiple neural network architectures and consistently achieves better speed-accuracy trade-off than baseline models. A thorough experimental study is conducted and the final result is a surrogate model which can evaluate millions of input parameters in a single forward pass in under 1ms on a desktop GPU, while the mismatch between the corresponding generated waveforms and the ground-truth waveforms is better than the compared baseline methods. We anticipate the existence of analogous underlying structures and corresponding computational gains also in the case of spinning black hole binaries.

cs.LG↗

arXiv2021

The surface of rapidly-rotating neutron stars: implications to neutron star parameter estimation

The Neutron star Interior Composition Explorer (NICER) is currently observing the x-ray pulse profiles emitted by hot spots on the surface of rotating neutron stars allowing for an inference of their radii with unprecedented precision. A critical ingredient in the pulse profile model is an analytical formula for the oblate shape of the star. These formulas require a fitting over a large ensemble of neutron star solutions, which cover a wide set of equations of state, stellar compactnesses and rotational frequencies. However, this procedure introduces a source of systematic error, as (i) the fits do not describe perfectly the surface of all stars in the ensemble and (ii) neutron stars are described by a single equation of state, whose influence on the surface shape is averaged out during the fitting procedure. Here we perform a first study of this systematic error, finding evidence that it is subdominant relative to the statistical error in the radius inference by NICER. We also find evidence that the formula currently used by NICER can be used in the inference of the radii of rapidly rotating stars, outside of the formula's domain of validity. Moreover, we employ an accurate enthalpy-based method to locate the surface of numerical solutions of rapidly rotating neutron stars and a new highly accurate formula to describe their surfaces. These results can be used in applications that require an accurate description of oblate surfaces of rapidly rotating neutron stars.

astro-ph.HE↗

arXiv2021

A Temporal Logic-Based Hierarchical Network Connectivity Controller

In this paper, we consider networks of static sensors with integrated sensing and communication capabilities. The goal of the sensors is to propagate their collected information to every other agent in the network and possibly a human operator. Such a task requires constant communication among all agents which may result in collisions and congestion in wireless communication. To mitigate this issue, we impose locally non-interfering connectivity constraints that must be respected by every agent. We show that these constraints along with the requirement of propagating information in the network can be captured by a Linear Temporal Logic (LTL) framework. Existing temporal logic control synthesis algorithms can be used to design correct-by-construction communication schedules that satisfy the considered LTL formula. Nevertheless, such approaches are centralized and scale poorly with the size of the network. We propose a hierarchical LTL-based algorithm that designs communication schedules that determine which agents should communicate while maximizing network usage. We show that the proposed algorithm is complete and demonstrate its efficiency and scalability through analysis and numerical experiments.

eess.SY↗

arXiv2021

Fair Robust Assignment using Redundancy

We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, which we cast as the optimization of worst-case task costs under a cardinality constraint. Solving this problem optimally is NP-hard. We exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. In supermodular redundant assignment, the use of additional agents always improves task costs. Therefore, we provide a solution set that is $α$ times larger than the cardinality constraint. This constraint relaxation enables our approach to achieve a super-optimal cost by using a sub-optimal assignment size. We derive the sub-optimality bound on this cardinality relaxation, $α$. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.

cs.RO↗

arXiv2020

Kernel Mean Embedding of Distributions: A Review and Beyond

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing kernel Hilbert space (RKHS) in which the whole arsenal of kernel methods can be extended to probability measures. It can be viewed as a generalization of the original "feature map" common to support vector machines (SVMs) and other kernel methods. While initially closely associated with the latter, it has meanwhile found application in fields ranging from kernel machines and probabilistic modeling to statistical inference, causal discovery, and deep learning. The goal of this survey is to give a comprehensive review of existing work and recent advances in this research area, and to discuss the most challenging issues and open problems that could lead to new research directions. The survey begins with a brief introduction to the RKHS and positive definite kernels which forms the backbone of this survey, followed by a thorough discussion of the Hilbert space embedding of marginal distributions, theoretical guarantees, and a review of its applications. The embedding of distributions enables us to apply RKHS methods to probability measures which prompts a wide range of applications such as kernel two-sample testing, independent testing, and learning on distributional data. Next, we discuss the Hilbert space embedding for conditional distributions, give theoretical insights, and review some applications. The conditional mean embedding enables us to perform sum, product, and Bayes' rules---which are ubiquitous in graphical model, probabilistic inference, and reinforcement learning---in a non-parametric way. We then discuss relationships between this framework and other related areas. Lastly, we give some suggestions on future research directions.

stat.ML↗

arXiv2020

Stochastic Motion Planning under Partial Observability for Mobile Robots with Continuous Range Measurements

In this paper, we address the problem of stochastic motion planning under partial observability, more specifically, how to navigate a mobile robot equipped with continuous range sensors such as LIDAR. In contrast to many existing robotic motion planning methods, we explicitly consider the uncertainty of the robot state by modeling the system as a POMDP. Recent work on general purpose POMDP solvers is typically limited to discrete observation spaces, and does not readily apply to the proposed problem due to the continuous measurements from LIDAR. In this work, we build upon an existing Monte Carlo Tree Search method, POMCP, and propose a new algorithm POMCP++. Our algorithm can handle continuous observation spaces with a novel measurement selection strategy. The POMCP++ algorithm overcomes over-optimism in the value estimation of a rollout policy by removing the implicit perfect state assumption at the rollout phase. We validate POMCP++ in theory by proving it is a Monte Carlo Tree Search algorithm. Through comparisons with other methods that can also be applied to the proposed problem, we show that POMCP++ yields significantly higher success rate and total reward.

cs.RO↗

arXiv2020

A new method to constrain neutron star structure from quasi-periodic oscillations

We develop a new method to measure neutron star parameters and derive constraints on the equation of state of dense matter by fitting the frequencies of simultaneous Quasi Periodic Oscillation modes observed in the X-ray flux of accreting neutron stars in low mass X-ray binaries. To this aim we calculate the fundamental frequencies of geodesic motion around rotating neutron stars based on an accurate general-relativistic approximation for their external spacetime. Once the fundamental frequencies are related to the observed frequencies through a QPO model, they can be fit to the data to obtain estimates of the three parameters describing the spacetime, namely the neutron star mass, angular momentum and quadrupole moment. From these parameters we derive information on the neutron star structure and equation of state. We present a proof of principle of our method applied to pairs of kHz QPO frequencies observed from three systems (4U1608-52, 4U0614+09 and 4U1728-34). We identify the kHz QPOs with the azimuthal and the periastron precession frequencies of matter orbiting the neutron star, and via our Bayesian inference technique we derive constraints on the neutrons stars' masses and radii. This method is applicable to other geodesic-frequency-based QPO models.

astro-ph.HE↗

arXiv2020

Online Learning of the Kalman Filter with Logarithmic Regret

In this paper, we consider the problem of predicting observations generated online by an unknown, partially observed linear system, which is driven by stochastic noise. For such systems the optimal predictor in the mean square sense is the celebrated Kalman filter, which can be explicitly computed when the system model is known. When the system model is unknown, we have to learn how to predict observations online based on finite data, suffering possibly a non-zero regret with respect to the Kalman filter's prediction. We show that it is possible to achieve a regret of the order of $\mathrm{poly}\log(N)$ with high probability, where $N$ is the number of observations collected. Our work is the first to provide logarithmic regret guarantees for the widely used Kalman filter. This is achieved using an online least-squares algorithm, which exploits the approximately linear relation between future observations and past observations. The regret analysis is based on the stability properties of the Kalman filter, recent statistical tools for finite sample analysis of system identification, and classical results for the analysis of least-squares algorithms for time series. Our regret analysis can also be applied for state prediction of the hidden state, in the case of unknown noise statistics but known state-space basis. A fundamental technical contribution is that our bounds hold even for the class of non-explosive systems, which includes the class of marginally stable systems, which was an open problem for the case of online prediction under stochastic noise.

cs.LG↗

arXiv2019

Finite size effects on the light curves of slowly-rotating neutron stars

An important question when studying the light curves produced by hot spots on the surface of rotating neutron stars is, how might the shape of the light curve be affected by relaxing some of the simplifying assumptions that one would adopt on a first treatment of the problem, such as that of a point-like spot. In this work we explore the dependence of light curves on the size and shape of a single hot spot on the surface of slowly-rotating neutron stars. More specifically, we consider two different shapes for the hot spots (circular and annular) and examine the resulting light curves as functions of the opening angle of the hot spot (for both) and width (for the latter). We find that the point-like approximation can describe light curves reasonably well, if the opening angle of the hot spot is less than $\sim 5^\circ$. Furthermore, we find that light curves from annular spots are almost the same as those of the full circular spot if the opening angle is less than $\sim 35^\circ$ independently of the hot spot's width.

astro-ph.HE↗

arXiv2019

On the connection of spacetime separability and spherical photon orbits

The notion of non-equatorial spherical photon orbits is among the very special properties of the Kerr spacetime of rotating black holes and is one that leaves a clear mark on the electromagnetic and gravitational wave signature of these objects. In principle, one could use observations like the shadow a black hole casts when is externally illuminated or the gravitational quasi-normal mode ringdown of merging black holes in order to identify the Kerr metric via its light-ring and spherical photon orbit structure, or perhaps look for the presence of more exotic non-Kerr ultracompact objects. This approach would require some understanding of how circular photon orbits behave in alternative (and far less special) non-Kerr spacetimes. In this letter we explore the connection between the existence of spherical photon orbits and the separability of a general stationary and axisymmetric spacetime. We show that a spacetime cannot be separable if it possesses an equatorial photon ring but at the same time does not admit (in any coordinate system) non-equatorial spherical photon orbits. As a result, the separability-circularity connection could serve as a non-Kerr diagnostic of black hole candidates.

gr-qc↗

arXiv2019

The modification of photon trapping orbits as a diagnostic of non-Kerr spacetimes

Photon circular orbits, an extreme case of light deflection, are among the hallmarks of black holes and are known to play a central role in a variety of phenomena related to these extreme objects. The very existence of such orbits when motion is not confined in the equatorial plane, i.e. spherical orbits, is indeed a special property of the separable Kerr metric and may not occur, for instance, in the spacetime of other more speculative ultracompact objects. In this paper we consider a general stationary-axisymmetric spacetime and examine under what circumstances spherical or more general, variable-radius, `spheroidal' non-equatorial photon orbits may exist with the ultimate goal of using the modifications -- or even loss -- of photon trapping orbits as a telltale of non-Kerr physics. In addressing this issue, we first derive a general necessary condition for the existence of spherical/spheroidal orbits and then go on to study photon trapping orbits in a variety of known non-Kerr metrics (Johannsen, Johanssen-Psaltis, and Hartle-Thorne). The first of these is an example of a separable spacetime which supports Kerr-like spherical photon orbits. A more detailed analysis reveals a deeper connection between the presence of spherical orbits and the separability of a metric (that is, the existence of a third integral of motion). Specifically, a spacetime that does not admit spherical orbits in any coordinates is necessarily non-separable. The other two spacetimes considered here exhibit a clear non-Kerr behaviour by having spherical photon orbits replaced by spheroidal ones. More importantly, subject to the degree of deviation from Kerr, equatorial photon rings give place to non-equatorial ones with an accompanying loss of low-inclination spheroidal orbits. The implications of these results for the electromagnetic and gravitational wave signature of non-Kerr objects are briefly discussed.

gr-qc↗