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48

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489

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## Publications

Publications (48)

We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations (ODEs) or partial differential equation (PDEs) can be challenging to solve on classical computers due to high d...

We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on propagating waves through the graph. However, instead of using a fast Fourier transform (FFT) computation at every node,...

We exploit the relationship between the stochastic Koopman operator and the Kolmogorov backward equation to construct importance sampling schemes for stochastic differential equations. Specifically, we propose using eigenfunctions of the stochastic Koopman operator to approximate the Doob transform for an observable of interest (e.g., associated wi...

We discuss approaches to computing eigenfunctions of the Ornstein--Uhlenbeck (OU) operator in more than two dimensions. While the spectrum of the OU operator and theoretical properties of its eigenfunctions have been well characterized in previous research, the practical computation of general eigenfunctions has not been resolved. We review special...

The secure command & control (C&C) of mobile agents arises in various settings including unmanned aerial vehicles, single pilot operations in commercial settings, and mobile robots to name a few. As more and more of these applications get integrated into aerospace and defense use cases, the security of the communication channel between the ground s...

In this paper, we present Talaria, a novel permissioned blockchain simulator that supports numerous protocols and use cases, most notably in supply chain management. Talaria extends the capability of BlockSim, an existing blockchain simulator, to include permissioned blockchains and serves as a foundation for further private blockchain assessment....

We exploit the relationship between the stochastic Koopman operator and the Kolmogorov backward equation to construct importance sampling schemes for stochastic differential equations. Specifically, we propose using eigenfunctions of the stochastic Koopman operator to approximate the Doob transform for an observable of interest (e.g., associated wi...

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety of physical systems. These methods have also been employed to build surrogate models for accelerating inverse u...

The secure command and control (C&C) of mobile agents arises in various settings including unmanned aerial vehicles, single pilot operations in commercial settings, and mobile robots to name a few. As more and more of these applications get integrated into aerospace and defense use cases, the security of the communication channel between the ground...

This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems have fallen under the purview of computer science and discrete optimization. However, over the past few years,...

This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems have fallen under the purview of computer science and discrete optimization. However, over the past few years,...

Given a Boolean formula ϕ(x) in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly e clauses, for all values of e. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (M...

In this paper, we consider the problem of learning Boolean formulae from examples obtained by actively querying an oracle that can label these examples as either positive or negative. This problem has received attention in both machine learning as well as formal methods communities, and it has been shown to have exponential worst-case complexity in...

We propose a novel passive learning approach, TeLex, to infer signal temporal logic (STL) formulas that characterize the behavior of a dynamical system using only observed signal traces of the system. First, we present a template-driven learning approach that requires two inputs: a set of observed traces and a template STL formula. The unknown para...

Given a Boolean formula $\phi(x)$ in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly $e$ clauses, for all values of $e$. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfia...

In this work, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the discrete optimization problem into continuous spaces. We explore multiple embedding techniques -- namely, the construction of dynamical flows on the manifold of orthogonal matrices and associated Procrustes approximations of the TSP cost...

We introduce a new measure of complexity (called spectral complexity ) for directed graphs. We start with splitting of the directed graph into its recurrent and nonrecurrent parts. We define the spectral complexity metric in terms of the spectrum of the recurrence matrix (associated with the reccurent part of the graph) and the Wasserstein distance...

We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. We define the spectral complexity metric in terms of the spectrum of the recurrence matrix associated with the recurrent part of the graph and the Wasserstein distance....

We propose a novel passive learning approach, TeLEx, to infer signal temporal logic formulas that characterize the behavior of a dynamical system using only observed signal traces of the system. The approach requires two inputs: a set of observed traces and a template Signal Temporal Logic (STL) formula. The unknown parameters in the template can i...

In this paper, we consider the problem of learning Boolean formulae from examples obtained by actively querying an oracle that can label these examplesz as either positive or negative. This problem has received attention in both machine learning as well as formal methods communities, and it has been shown to have exponential worst-case complexity i...

Can a dynamical system paint masterpieces such as Da Vinci's Mona Lisa or
Monet's Water Lilies? Moreover, can this dynamical system be chaotic in the
sense that although the trajectories are sensitive to initial conditions, the
same painting is created every time? Setting aside the creative aspect of
painting a picture, in this work, we develop a n...

In this paper, we propose a heuristic for the graph isomorphism problem that
is based on the eigendecomposition of the adjacency matrices. It is well known,
that the eigenvalues of the adjacency matrices of isomorphic graphs need to be
identical. However, two graphs $ G_A $ and $ G_B $ can be isospectral but
non-isomorphic. If the graphs possess re...

We consider a planning and control problem in which a large number of moving targets must be intercepted by a single agent as quickly as possible. The agent maintains estimates of the instantaneous position and velocity of all targets, and decides which target to pursue next by predicting their future positions. Decision-making is driven by the rep...

Polynomial chaos is a powerful technique for propagating uncertainty through
ordinary and partial differential equations. Random variables are expanded in
terms of orthogonal polynomials and differential equations are derived for the
expansion coefficients. Here we study the structure and dynamics of these
differential equations when the original s...

Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with stringent assumptions on smoothness (such as polynomial chaos and Quasi-Monte Carlo). In this work, we develop a f...

Structure learning of Bayesian networks is an important problem that arises
in numerous machine learning applications. In this work, we present a novel
approach for learning the structure of Bayesian networks using the solution of
an appropriately constructed traveling salesman problem. In our approach, one
computes an optimal ordering (partially o...

The emergence of cloud computing has enabled an incredible growth in
available hardware resources at very low costs. These resources are being
increasingly utilized by corporations for scalable analysis of "big data"
problems. In this work, we explore the possibility of using commodity hardware
such as Amazon EC2 for performing large scale scientif...

Uncertainty quantification (UQ) techniques are frequently used to ascertain
output variability in systems with parametric uncertainty. Traditional
algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or
fast with stringent assumptions on smoothness (such as polynomial chaos and
Quasi-Monte Carlo). In this work, we develop a f...

In this paper we address the problem of uncertainty management for robust
design, and verification of large dynamic networks whose performance is
affected by an equally large number of uncertain parameters. Many such networks
(e.g. power, thermal and communication networks) are often composed of weakly
interacting subnetworks. We propose intrusive...

Development of robust dynamical systems and networks such as autonomous
aircraft systems capable of accomplishing complex missions faces challenges due
to the dynamically evolving uncertainties coming from model uncertainties,
necessity to operate in a hostile cluttered urban environment, and the
distributed and dynamic nature of the communication...

We propose a novel distributed algorithm to compute eigenvectors and eigenvalues of the graph Laplacian matrix L. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of L. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based ap...

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication...

Micromechanical oscillators often display rich dynamics due to nonlinearities in their response, actuation, and detection.
This paper investigates the complicated response of a forced micromechanical oscillator. In particular, we investigate a thermally
induced transition in the resonant response of a forced micromechanical oscillator with optical...

The study of high-dimensional differential equations is challenging and
difficult due to the analytical and computational intractability. Here, we
improve the speed of waveform relaxation (WR), a method to simulate
high-dimensional differential-algebraic equations. This new method termed
adaptive waveform relaxation (AWR) is tested on a communicati...

We propose a novel distributed algorithm to cluster graphs. The algorithm
recovers the solution obtained from spectral clustering without the need for
expensive eigenvalue/vector computations. We prove that, by propagating waves
through the graph, a local fast Fourier transform yields the local component of
every eigenvector of the Laplacian matrix...

(CO)1−x(Ar)x mixtures physisorbed on graphite experimentally display a novel phenomenon of increasing phase-transition temperature (stabilizing the system) with increasing Ar impurity concentration or uncertainty [ H. Wiechert and K.-D. Kortmann Surf. Sci. 441 65 (1999)]. We develop a two-dimensional Ising-type model that accurately captures the ph...

In this paper we develop new methods for computing k−dimensional invariant man- ifolds of delayed systems for k ≥ 2. Our current implementation is built for k = 2 only, but the numerical and algorithmic challenges encountered in this case will be also present for any k > 1. For small delays, we consider methods for approximating delay differential...

Synchronized micromechanical oscillators have potential for applications in signal processing, neural computing, sensing, and other fields. This paper explores the conditions under which coupled nonlinear limit cycle microoscillators can synchronize. As an example of the modeling approach and to be able to obtain results for a system that has been...

We present an investigation into the response of a cantilever microbeam with a plate attached to its tip to mechanical shock. This structural configuration is found in numerous MEMS devices, such as gas sensors and capacitive accelerometers. To ensure reliable operation of these devices, their performance under mechanical shock has to be analyzed....

The small size and low damping of MEMS oscillators give rise to phenomena that are not observed routinely at the macroscopic scale. In this work we document and explain an experimentally observed transition in the response of a doubly clamped micromechanical oscillator with pretension. The transition from softening to hardening is repeatedly observ...

Coupled micromechanical oscillators vibrating in synchrony have the potential for novel applications such as filters, neurocomputers and generators of clock signals in computer processors. In this work we analyze a feasible approach for constructing coupled micromechanical oscillators that synchronize. For this purpose we consider dome shaped micro...

The present paper addresses the problem of spin recovery of an aircraft as a nonlinear inverse dynamics problem of determining the control inputs that need to be applied to transfer the aircraft from a spin state to a level trim flight condition. A stable, oscillatory, flat, left spin state is first identified from a standard bifurcation analysis o...

This article uses the logistic map as an example to illustrate the vagaries that afflict a chaotic attractor in the course
of its progress along a path of varying parameter. Several critical junctures, called crises, are encountered, where the chaotic
attractor either goes boom or bust!