On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of $\sim 1.7\,{\rm{s}}$ with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of ${40}_{-8}^{+8}$ Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 $\,{M}_{\odot }$. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at $\sim 40\,{\rm{Mpc}}$) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient's position $\sim 9$ and $\sim 16$ days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta.

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Multi-messenger observations of a binary neutron star merger

This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms.Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises.Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation

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Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms

We summarize our current knowledge of neutron-star masses and radii. Recent instrumentation and computational advances have resulted in a rapid increase in the discovery rate and precise timing of radio pulsars in binaries in the past few years, leading to a large number of mass measurements. These discoveries show that the neutron-star mass distribution is much wider than previously thought, with three known pulsars now firmly in the 1.9–2.0-M⊙ mass range. For radii, large, high-quality data sets from X-ray satellites as well as significant progress in theoretical modeling led to considerable progress in the measurements, placing them in the 10–11.5-km range and shrinking their uncertainties, owing to a better understanding of the sources of systematic errors. The combination of the massive-neutron-star discoveries, the tighter radius measurements, and improved laboratory constraints of the properties of dense matter has already made a substantial impact on our understanding of the composition and bulk p...

Masses, Radii, and the Equation of State of Neutron Stars

Gamma-ray bursts (GRBs) display a bimodal duration distribution with a separation between the short- and long-duration bursts at about 2 s. The progenitors of long GRBs have been identified as massive stars based on their association with Type Ic core-collapse supernovae (SNe), their exclusive location in star-forming galaxies, and their strong correlation with bright UV regions within their host galaxies. Short GRBs have long been suspected on theoretical grounds to arise from compact object binary mergers (neutron star–neutron star or neutron star–black hole). The discovery of short GRB afterglows in 2005 provided the first insight into their energy scale and environments, as well as established a cosmological origin, a mix of host-galaxy types, and an absence of associated SNe. In this review, I summarize nearly a decade of short GRB afterglow and host-galaxy observations and use this information to shed light on the nature and properties of their progenitors, the energy scale and collimation of the relativistic outflow, and the properties of the circumburst environments. The preponderance of the evidence points to compact object binary progenitors, although some open questions remain. On the basis of this association, observations of short GRBs and their afterglows can shed light on the on- and off-axis electromagnetic counterparts of gravitational wave sources from the Advanced LIGO/Virgo experiments.

Short-Duration Gamma-Ray Bursts

Modelling the electromagnetic emission of kilonovae enables the mass, velocity and composition (with some heavy elements) of the ejecta from a neutron-star merger to be derived from the observations. Merging neutron stars are potential sources of gravitational waves and have long been predicted to produce jets of material as part of a low-luminosity transient known as a 'kilonova'. There is growing evidence that neutron-star mergers also give rise to short, hard gamma-ray bursts. A group of papers in this issue report observations of a transient associated with the gravitational-wave event GW170817—a signature of two neutron stars merging and a gamma-ray flash—that was detected in August 2017. The observed gamma-ray, X-ray, optical and infrared radiation signatures support the predictions of an outflow of matter from double neutron-star mergers and present a clear origin for gamma-ray bursts. Previous predictions differ over whether the jet material would combine to form light or heavy elements. These papers now show that the early part of the outflow was associated with lighter elements whereas the later observations can be explained by heavier elements, the origins of which have been uncertain. However, one paper (by Stephen Smartt and colleagues) argues that only light elements are needed for the entire event. Additionally, Eleonora Troja and colleagues report X-ray observations and radio emissions that suggest that the 'kilonova' jet was observed off-axis, which could explain why gamma-ray-burst detections are seen as dim. The cosmic origin of elements heavier than iron has long been uncertain. Theoretical modelling1,2,3,4,5,6,7 shows that the matter that is expelled in the violent merger of two neutron stars can assemble into heavy elements such as gold and platinum in a process known as rapid neutron capture (r-process) nucleosynthesis. The radioactive decay of isotopes of the heavy elements is predicted8,9,10,11,12 to power a distinctive thermal glow (a ‘kilonova’). The discovery of an electromagnetic counterpart to the gravitational-wave source13 GW170817 represents the first opportunity to detect and scrutinize a sample of freshly synthesized r-process elements14,15,16,17,18. Here we report models that predict the electromagnetic emission of kilonovae in detail and enable the mass, velocity and composition of ejecta to be derived from observations. We compare the models to the optical and infrared radiation associated with the GW170817 event to argue that the observed source is a kilonova. We infer the presence of two distinct components of ejecta, one composed primarily of light (atomic mass number less than 140) and one of heavy (atomic mass number greater than 140) r-process elements. The ejected mass and a merger rate inferred from GW170817 imply that such mergers are a dominant mode of r-process production in the Universe.

Origin of the heavy elements in binary neutron-star mergers from a gravitational-wave event

This article addresses an important routing problem that arises in surveillance applications involving two heterogeneous vehicles. As the addressed routing problem is NP-Hard, we develop an approximation algorithm and heuristics to solve the problem. Our approach involves solving the routing problem in two main steps: Partitioning and Sequencing. Partitioning involves finding a distinct set of targets to be visited by each vehicle. Sequencing provides the order in which each vehicle must visit the subset of targets assigned to it. The problem of partitioning is tackled by solving a linear program (LP) obtained by relaxing some of the constraints of an integer programming model for the problem. We consider two LP models for partitioning. The first LP model is obtained by mainly relaxing both the integrality and degree constraints, whereas the second model relaxes mainly the integrality constraints. Once the targets are partitioned, the sequencing problem can be solved either by Hoogeveen's algorithm or by the Lin–Kernighan heuristic to yield an approximately optimal solution. Computational results show that the algorithms based on the second LP model, on an average, provided better (closer to the optimum) solutions as compared with those based on the first LP model. We also observed that for both the LP models, the average quality of solutions given by the heuristics were found to be within 4% of the optimum, whereas the average quality of solutions obtained from the approximation algorithms were within 8–20% of the optimum depending on the problem size. Copyright © 2011 John Wiley & Sons, Ltd.

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Approximation Algorithms and Heuristics for a 2-depot, Heterogeneous Hamiltonian Path Problem

One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound for the deviation of such a policy from the optimum via a linear programming approach. The state-space is partitioned and the optimal cost-to-go or value function is approximated by a constant over each partition. By minimizing a non-negative cost function defined on the partitions, one can construct an approximate value function which also happens to be an upper bound for the optimal value function of the original Markov Decision Process (MDP). As a key result, we show that this approximate value function is {\it independent} of the non-negative cost function (or state dependent weights as it is referred to in the literature) and moreover, this is the least upper bound that one can obtain once the partitions are specified. Furthermore, we show that the restricted system of linear inequalities also embeds a family of MDPs of lower dimension, one of which can be used to construct a lower bound on the optimal value function. The construction of the lower bound requires the solution to a combinatorial problem. We apply the linear programming approach to a perimeter surveillance stochastic optimal control problem and obtain numerical results that corroborate the efficacy of the proposed methodology.

Bounding Procedures for Stochastic Dynamic Programs with Application to the Perimeter Patrol Problem

Practical problems require the synthesis of a set of stabilizing controllers that guarantee transient performance specifications such as a bound on the overshoot of its closed loop step response. A majority of these specifications for Linear Time Invariant (LTI) systems can be converted to the requirement of synthesizing a set of stabilizing controllers guaranteeing the non-negative impulse response of an appropriate transfer function whose coefficients are functions of the controller parameters. The main topic of investigation of this paper is to find a bound for the set of control parameters, K, so that a rational, proper transfer function, N (z, K)/D (z, K) has a decaying, non-negative impulse response. For Single Input Single Output (SISO) LTI systems, one may assume that the coefficients of the polynomials N (z, K) and D (z, K) are affine in K. An earlier result by the authors provides an approximation of the set of stabilizing controller parameters in terms of unions of polyhedral sets. In this paper, we provide necessary and sufficient conditions for a rational proper stable transfer function to have a non-negative impulse response. For the synthesis problem, we show that these conditions translate into a sequence of polynomial matrix inequalities in K using Markov-Lucaks' theorem. We propose an outer approximation of the feasible set of matrix inequalities using Lasserre's moment method.

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On the transient control of Linear Time Invariant systems

Brake systems in trucks are crucial for ensuring the safety of vehicles and passengers on the roadways. Most trucks in the US are equipped with S-cam drum brake systems and they are sensitive to maintenance. Brake defects such as leaks are a major cause of accidents involving trucks. Leaks in the air brake systems affect braking performance drastically by decreasing the maximum braking pressure and also increasing the time required to attain the same, thereby resulting in longer stopping distances. In this paper, we present a mathematical model for an air brake system in the presence of leaks with a view towards developing a diagnostic system based on this model in the near future. The model that has been developed builds on earlier research at Texas A&M University in which the pressure evolution in the brake chamber was determined as a function of the brake pedal input in the absence of any leaks in the air brake system. A leak may be characterized by its location and size. Since the connecting pipes are short, the location of the leak does not significantly affect the evolution in the brake pressure as much as its size. We provide a constitutive relationship for the leak and we estimated the associated parameter, namely, the “effective area” of the leak from the experimental data. The supply pressure and effective area of leak comprised the inputs to the model along with the displacement of the brake pedal (treadle valve plunger). We also provide a simple leak detection scheme and estimates of the severity of the leak in terms of the mass flow rate of leaking air based on the input measurements of brake pressure for a full application of the brake pedal and the supply pressure. This scheme can be implemented using a simple look-up table.

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Development of a model for an air brake system with leaks

In this article, we address the problem of synthesizing communication networks for unmanned aerial vehicles (UAVs) in the presence of resource constraints. UAVs can be deployed as backbone nodes in ad hoc networks that can be central to civilian and military applications. The cost of operation of the network depends on the resources that are used such as the total power consumption associated with the network and the number of communication links in the network. The objective of the problem is to synthesize a communication network that maximizes connectivity subject to the cost of operation being within the specified budget for the resources. It is known that algebraic connectivity is a measure of robust connectivity and hence, it is chosen as an objective for optimization. We pose the network synthesis problem as a mixed-integer semidefinite program (MISDP): (1) provide an algorithm for computing optimal solutions using cutting plane methods; (2) develop lower bounds by posing the problem as a binary semidefinite program; and (3) construct feasible solutions using heuristics and estimate their quality. The network synthesis problem is a nondeterministic polynomial--time (NP)-hard problem. We provide some computational results to corroborate the performance of the proposed algorithms.

Swaroop Darbha

Papers

Approximation Algorithms and Heuristics for a 2-depot, Heterogeneous Hamiltonian Path Problem

Bounding Procedures for Stochastic Dynamic Programs with Application to the Perimeter Patrol Problem

On the transient control of Linear Time Invariant systems

Development of a model for an air brake system with leaks

Synthesizing Robust Communication Networks for Unmanned Aerial Vehicles With Resource Constraints