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Sandip Roy

Publications and source records attributed to Sandip Roy.

At least 55 records · Page 3Linked to original sources

Compressive Representations of Weather Scenes for Strategic Air Traffic Flow Management

Terse representation of high-dimensional weather scene data is explored, in support of strategic air traffic flow management objectives. Specifically, we consider whether aviation-relevant weather scenes are compressible, in the sense that each scene admits a possibly-different sparse representation in a basis of interest. Here, compression of weather scenes extracted from METAR data (including temperature, flight categories, and visibility profiles for the contiguous United States) is examined, for the graph-spectral basis. The scenes are found to be compressible, with 75-95% of the scene content captured using 0.5-4% of the basis vectors. Further, the dominant basis vectors for each scene are seen to identify time-varying spatial characteristics of the weather, and reconstruction from the compressed representation is demonstrated. Finally, potential uses of the compressive representations in strategic TFM design are briefly scoped.

cs.CV↗

Distinguishing Aerial Intruders from Trajectory Data: A Model-Based Hypothesis-Testing Approach

Motivated by security needs in unmanned aerial system (UAS) operations, an algorithm for identifying airspace intruders (e.g., birds vs. drones) is developed. The algorithm is structured to use sensed intruder velocity data from Internet-of-Things platforms together with limited knowledge of physical models. The identification problem is posed as a statistical hypothesis testing or detection problem, wherein inertial feedback-controlled objects subject to stochastic actuation must be distinguished by speed data. The maximum a posteriori probability detector is obtained, and then is simplified to an explicit computation based on two points in the sample autocorrelation of the data. The simplified form allows computationally-friendly implementation of the algorithm, and simplified learning from archived data. Also, the total probability of error of the detector is computed and characterized. Simulations based on synthesized data are presented to illustrate and supplement the formal analyses.

eess.SY↗

Compressibility of Network Opinion and Spread States in the Laplacian-Eigenvector Basis

Opinion-evolution and spread processes on networks (e.g., infectious disease spread, opinion formation in social networks) are not only high dimensional but also volatile and multiscale in nature. In this study, we explore whether snapshot data from these processes can admit terse representations. Specifically, using three case studies, we explore whether the data are compressible in the Laplacian-eigenvector basis, in the sense that each snapshot can be approximated well using a (possibly different) small set of basis vectors. The first case study is concerned with a linear consensus model that is subject to a stochastic input at an unknown location; both empirical and formal analyses are used to characterize compressibility. Second, compressibility of state snapshots for a stochastic voter model is assessed via an empirical study. Finally, compressibility is studied for state-level daily COVID-19 positivity-rate data. The three case studies indicate that state snapshots from opinion-evolution and spread processes allow terse representations, which nevertheless capture their rich propagative dynamics.

eess.SY↗

Sign Patterns of Inverse Doubly-Nonnegative Matrices

The sign patterns of inverse doubly-nonnegative matrices are examined. A necessary and sufficient condition is developed for a sign matrix to correspond to an inverse doubly-nonnegative matrix. In addition, for a doubly-nonnegative matrix whose graph is a tree, the inverse is shown to have a unique sign pattern, which can be expressed in terms of a two-coloring of the graph.

eess.SY↗

Cyber-Physical Queueing-Network Model for Risk Management in Next-Generation Emergency Response Systems

Queueing-network models are developed for enhanced and next-generation 911 (E911 and NG911) systems, which capture both their cyber-components (communications, data-processing) and physical-world-elements (call takers, vehicle dispatch). The models encompass both the call-processing and dispatch functions of 911, and can represent the interdependencies between multiple PSAPs enabled by NG911. An instantiation of the model for a future NG911 system for Charlotte, North Carolina, is developed and used to assess performance metrics. Representation of cyber-threats (e.g. Distributed Denial-of-Service attacks) within the queueing-network model is undertaken. Based on these representations, the model is used for analysis of holistic threat impacts, as a step toward risk and vulnerability assessment for future emergency response systems.

eess.SY↗

Network Theoretic Analysis of Maximum a Posteriori Detectors for Optimal Input Detection

This paper considers maximum-a-posteriori (MAP) and linear discriminant based MAP detectors to detect changes in the mean and covariance of a stochastic input, driving specific network nodes, using noisy measurements from sensors non-collocated with the input nodes. We explicitly characterize both detectors' performance in terms of the network edge weights and input and sensor nodes' location. In the asymptotic measurement regime, when the input and measurement noise are jointly Gaussian, we show that the detectors' performance can be studied using the input to output gain of the system's transfer function matrix. Using this result, we obtain conditions for which the detection performance associated with the sensors on a given network cut is better (or worse) than that of the sensors associated with the subnetwork induced by the cut and not containing the input nodes. Our results also provide structural insights into the sensor placement from a detection-theoretic viewpoint. We validate our theoretical findings via multiple numerical examples.

math.OC↗

On the Complexity and Approximability of Optimal Sensor Selection and Attack for Kalman Filtering

Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design-time) to minimize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomial-time constant-factor approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity (or supermodularity) of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering. We then study the problem of attacking (i.e., removing) a set of installed sensors, under predefined attack budget constraints, to maximize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter. Again, we show that there is no polynomial-time constant-factor approximation algorithm for this problem, and show specifically that greedy algorithms can perform arbitrarily poorly.

math.OC↗

Resilient Sensor Placement for Kalman Filtering in Networked Systems: Complexity and Algorithms

Given a linear dynamical system affected by noise, we study the problem of optimally placing sensors (at design-time) subject to a sensor placement budget constraint in order to minimize the trace of the steady-state error covariance of the corresponding Kalman filter. While this problem is NP-hard in general, we consider the underlying graph associated with the system dynamics matrix, and focus on the case when there is a single input at one of the nodes in the graph. We provide an optimal strategy (computed in polynomial-time) to place the sensors over the network. Next, we consider the problem of attacking (i.e., removing) the placed sensors under a sensor attack budget constraint in order to maximize the trace of the steady-state error covariance of the resulting Kalman filter. Using the insights obtained for the sensor placement problem, we provide an optimal strategy (computed in polynomial-time) to attack the placed sensors. Finally, we consider the scenario where a system designer places the sensors under a sensor placement budget constraint, and an adversary then attacks the placed sensors subject to a sensor attack budget constraint. The resilient sensor placement problem is to find a sensor placement strategy to minimize the trace of the steady-state error covariance of the Kalman filter corresponding to the sensors that survive the attack. We show that this problem is NP-hard, and provide a pseudo-polynomial-time algorithm to solve it.

math.OC↗

Precision Mass and Density Measurement of Individual Optically Levitated Microspheres

We report an $\textit{in situ}$ mass measurement of approximately-$4.7{\text -}μ$m-diameter, optically levitated microspheres with an electrostatic co-levitation technique. The mass of a trapped, charged microsphere is measured by holding its axial (vertical) position fixed with an optical feedback force, under the influence of a known electrostatic force. A mass measurement with $1.8\%$ systematic uncertainty is obtained by extrapolating to the electrostatic force required to support the microsphere against gravity in the absence of optical power. In three cases, the microspheres are recovered from the trap on a polymer-coated silicon beam and imaged with an electron microscope to measure their radii. The simultaneous precision characterization of the mass and radius of individual microspheres implies a density of $1.55\pm0.08~$g/cm$^3$. The ability to recover individual microspheres from an optical trap opens the door to further diagnostics.

physics.ins-det↗

Electrically Driven, Optically Levitated Microscopic Rotors

We report on the electrically driven rotation of $2.4~μ$m-radius, optically levitated dielectric microspheres. Electric fields are used to apply torques to a microsphere's permanent electric dipole moment, while angular displacement is measured by detecting the change in polarization state of light transmitted through the microsphere (MS). This technique enables greater control than previously achieved with purely optical means because the direction and magnitude of the electric torque can be set arbitrarily. We measure the spin-down of a microsphere released from a rotating electric field, the harmonic motion of the dipole relative to the instantaneous direction of the field, and the phase lag between the driving electric field and the dipole moment of the MS due to drag from residual gas. We also observe the gyroscopic precession of the MS when the axis of rotation of the driving field and the angular momentum of the microsphere are orthogonal. These observations are in quantitative agreement with the equation of motion. The control offered by the electrical drive enables precise measurements of microsphere properties and torque as well as a method for addressing the direction of angular momentum for an optically levitated particle.

physics.optics↗

Small-Signal Stability Analysis for Droop-Controlled Inverter-based Microgrids with Losses and Filtering

An islanded microgrid supplied by multiple distributed energy resources (DERs) often employs droop-control mechanisms for power sharing. Because microgrids do not include inertial elements, and low pass filtering of noisy measurements introduces lags in control, droop-like controllers may pose significant stability concerns. This paper aims to understand the effects of droop-control on the small-signal stability and transient response of the microgrid. Towards this goal, we present a compendium of results on the small-signal stability of droop-controlled inverter-based microgrids with heterogeneous loads, which distinguishes: (1) lossless vs. lossy networks; (2) droop mechanisms with and without filters, and (3) mesh vs. radial network topologies. Small-signal and transient characteristics are also studied using multiple simulation studies on IEEE test systems

eess.SY↗

Averager-copier-voter models for hybrid opinion dynamics in complex networks

A hybrid model for opinion dynamics in complex multi-agent networks is introduced, wherein some continuous-valued agents average neighbors' opinions to update their own, while other discrete-valued agents use stochastic copying and voting protocols. A statistical and graph-theoretic analysis of the model is undertaken, and consensus is shown to be achieved whenever the network matrix is ergodic. Also, the time required for consensus is characterized, in terms of the network's graph and the distribution of agents of different types.

eess.SY↗

Controllability-Gramian Submatrices for a Network Consensus Model

Principal submatrices of the controllability Gramian and their inverses are examined, for a network-consensus model with inputs at a subset of network nodes. Specifically, several properties of the Gramian submatrices and their inverses -- including dominant eigenvalues and eigenvectors, diagonal entries, and sign patterns -- are characterized by exploiting the special doubly-nonnegative structure of the matrices. In addition, majorizations for these properties are obtained in terms of cutsets in the network's graph, based on the diffusive form of the model. The asymptotic (long time horizon) structure of the controllability Gramian is also analyzed. The results on the Gramian are used to study metrics for target control of the network-consensus model.

eess.SY↗

Three-dimensional force-field microscopy with optically levitated microspheres

We report on the use of 4.7-$μ$m-diameter, optically levitated, charged microspheres to image the three-dimensional force field produced by charge distributions on an Au-coated, microfabricated Si beam in vacuum. An upward-propagating, single-beam optical trap, combined with an interferometric imaging technique, provides optimal access to the microspheres for microscopy. In this demonstration, the Au-coated surface of the Si beam can be brought as close as ${\sim}10~μ$m from the center of the microsphere while forces are simultaneously measured along all three orthogonal axes, fully mapping the vector force field over a total volume of ${\sim}10^6~μ$m$^3$. We report a force sensitivity of $(2.5 \pm 1.0) \times 10^{-17}~{\rm N / \sqrt{Hz}}$, in each of the three degrees of freedom, with a linear response to up to ${\sim}10^{-13}~{\rm N}$. While we discuss the case of mapping static electric fields using charged microspheres, it is expected that the technique can be extended to other force fields, using microspheres with different properties.

physics.ins-det↗

Comments Regarding `On the Identifiability of the Influence Model for Stochastic Spatiotemporal Spread Processes'

The identifiability analysis of a networked Markov chain model known as the influence model, as described in a recent contribution to Arxiv, is examined. Two errors in the identifiability analysis -- one related to the unidentifiability of the partially-observed influence model, the second related to an omission of an additional recurrence criterion for identifiability -- are noted. In addition, some concerns about the formulation of the identifiability problem and the proposed estimation approach are noted.

eess.SY↗

Cyber Threat Impact Analysis to Air Traffic Flows Through Dynamic Queue Networks

Air traffic control increasingly depends on information and communication technology (ICT) to manage traffic flow through highly congested and increasingly interdependent airspace regions. While these systems are critical to ensuring the efficiency and safety of our airspace, they are also increasingly vulnerable to cyber threats that could potentially lead to reduction in capacity and/or reorganization of traffic flows. In this paper, we model various cyber threats to air traffic control systems, and analyze how these attacks could impact the flow of aircraft through the airspace. To perform this analysis, we consider a model for wide-area air traffic based on a dynamic queuing network model. Then we introduce three different attacks (Route Denial of Service, Route Selection Tampering, and Sector Denial of Service) to the air traffic control system, and explore how these attacks manipulate the sector flows by evaluating the queue backlogs for each sector's outflows. Furthermore, we then explore graph-level vulnerability metrics to identify the sectors that are most vulnerable to various flow manipulations, and compare them to case-study simulations of the various attacks. The results suggest that Route Denial of Service attacks have a significant impact on the target sector and lead to the largest degradation to the overall air traffic flows. Furthermore, the impact of Sector Denial of Service attack impacts are primarily confined to the target sector, while the Route Selection Tampering impacts are mostly confined to certain aircraft.

eess.SY↗

Modal Barriers to Controllability in Networks with Linearly-Coupled Homogeneous Subsystems

The controllability of networks comprising homogeneous multi-input multi-output linear subsystems with linear couplings among them is examined, from a modal perspective. The eigenvalues of the network model are classified into two groups: 1) network-invariant modes, which have very high multiplicity regardless of the network's topology; and 2) special-repeat modes, which are repeated for only particular network topologies and have bounded multiplicity. Characterizations of both types of modes are obtained, in part by drawing on decentralized-fixed-mode and generalized-eigenvalue concepts. We demonstrate that network-invariant modes necessarily prevent controllability unless a sufficient fraction of the subsystems are actuated, both in the network as a whole and in any weakly-connected partition. In contrast, the multiplicities of special-repeat modes have no influence on controllability. Our analysis highlights a distinction between built networks where subsystem interfaces may be unavoidable barriers to controllability, and multi-agent systems where protocols can be designed to ensure controllability.

eess.SY↗