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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
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Posts
Future Blog Post
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Blog Post number 4
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Blog Post number 3
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Blog Post number 2
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Blog Post number 1
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publications
Stable and accurate numerical methods for generalized Kirchhoff–Love plates
Published in Journal of Engineering Mathematics, 2021
In this paper, efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff–Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. The generalization stems from the inclusion of additional physics to the classical Kirchhoff–Love model that accounts for bending only. We solve the model equation by discretizing the spatial derivatives using second-order finite-difference schemes, and then advancing the semi-discrete problem in time with either an explicit predictor–corrector or an implicit Newmark-Beta time-stepping algorithm.
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Distributed Nash Equilibrium Seeking over Time-Varying Directed Communication Networks
Published in [Under review] IEEE Transactions on Automatic Control, 2022
We propose a distributed gradient play algorithm for finding a Nash equilibrium (NE) in a class of non-cooperative convex games under partial information. In this algorithm, every agent performs agradient step to minimize its own cost function while sharing and retrieving information locally among its neighbors. The existing methods impose strong assumptions such as balancedness of the mixing matrices and global knowledge of the network communication structure, including Perron-Frobenius eigenvector of the adjacency matrix and other graph connectivity constants. In contrast, our approach relies only on a reasonable and widely-used assumption of row-stochasticity of the mixing matrices. We analyze the algorithm for time-varying directed graphs and prove its convergence to the NE, when the agents’ cost functions are strongly convex and have Lipschitz continuous gradients.
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AB/Push-Pull Method for Distributed Optimization in Time-Varying Directed Networks
Published in [Under review] Optimization Methods and Software, 2022
In this paper, we study the distributed optimization problem for a system of agents embedded in time-varying directed communication networks. Each agent has its own cost function and agents cooperate to determine the global decision that minimizes the summation of all individual cost functions. We consider the so-called push-pull gradient-based algorithm (termed as AB/Push-Pull) which employs both row- and column-stochastic weights simultaneously to track the optimal decision and the gradient of the global cost while ensuring consensus and optimality. We show that the algorithm converges linearly to the optimal solution over a time-varying directed network for a constant stepsize when the agent’s cost function is smooth and strongly convex. The linear convergence of the method has been shown in Saadatniaki et al. (2020), where the multi-step consensus contraction parameters for row- and column- stochastic mixing matrices are not directly related to the underlying graph structure, and the explicit range for the stepsize value is not provided. With respect to Saadatniaki et al. (2020), the novelty of this work is twofold: (1) we establish the one-step consensus contraction for both row- and column-stochastic mixing matrices with the contraction parameters given explicitly in terms of the graph diameter and other graph properties; and (2) we provide explicit upper bounds for the stepsize value in terms of the properties of the cost functions, the mixing matrices, and the graph connectivity structure.
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A Fairness-Aware Attacker-Defender Model for Optimal Edge Network Operation and Protection
Published in [Under review] IEEE Networking Letter, 2022
talks
A stable and accurate algorithm for a generalized Kirchhoff-Love plate model
Published:
In this paper, efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff–Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. The generalization stems from the inclusion of additional physics to the classical Kirchhoff–Love model that accounts for bending only. We solve the model equation by discretizing the spatial derivatives using second-order finite-difference schemes, and then advancing the semi-discrete problem in time with either an explicit predictor–corrector or an implicit Newmark-Beta time-stepping algorithm.
A stable and accurate algorithm for a generalized Kirchhoff-Love plate model
Published:
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A comparative study of physics-informed deep learning models for discovering partial differential equations
Published:
In this work, we study physics-informed deep learning models to identify the general time-dependent nonlinear partial differential equations governing noisy data. We compare the performance of different regression techniques (LASSO, Ridge, TrainSTridge, and elastic net). We propose a different approach by employing pre-train neural networks to reduce the computation time.
Two-stage Robust Edge Service Placement And Sizing Under Uncertainties
Published:
We study the optimal service placement and workload allocation problem under uncertainties from the perspective of a service provider who can procure resources from numerous distributed edge nodes. To tackle this problem, we propose novel two-stage and multi-period robust optimization models which aim to balance between minimizing the operating cost for the provider and improving the experience for its users, considering various uncertainties such as resource demand and edge node failures. We employ and tailor the column-and-constraint generation method to develop iterative algorithms to solve the proposed robust models, which show significant advantages compared to benchmark solutions.
Market-based Mechanisms For Fair And Efficient Resource Allocation In Edge Computing
Published:
Edge computing enables novel Internet of Things applications and drastically enhances user experience. We propose a novel market equilibrium-based framework for allocating geographically distributed heterogeneous edge resources to competing services with diverse preferences in a fair and efficient manner. The proposed solution not only maximizes resource utilization but also gives each service its favorite resource bundle. Furthermore, the equilibrium allocation is Pareto-optimal and satisfies desired fairness properties including sharing incentive, proportionality, and envy-freeness. We also introduce privacy-preserving distributed algorithms for equilibrium computation.
Distributed Nash Equilibrium Seeking over Time-Varying Directed Communication Networks
Published:
We propose a distributed gradient play algorithm for finding a Nash equilibrium (NE) in a class of non-cooperative convex games under partial information. In this algorithm, every agent performs agradient step to minimize its own cost function while sharing and retrieving information locally among its neighbors. The existing methods impose strong assumptions such as balancedness of the mixing matrices and global knowledge of the network communication structure, including Perron-Frobenius eigenvector of the adjacency matrix and other graph connectivity constants. In contrast, our approach relies only on a reasonable and widely-used assumption of row-stochasticity of the mixing matrices. We analyze the algorithm for time-varying directed graphs and prove its convergence to the NE, when the agents’ cost functions are strongly convex and have Lipschitz continuous gradients.
teaching
STAT 214 - Elementary Statistics (TA)
Undergraduate course, Department of Mathematics, University of Louisiana at Lafayette, 2017
Description: Descriptive statistics, elementary hypothesis testing, confidence intervals, introduction to correlation and regression.
STAT 214 - Elementary Statistics (TA)
Undergraduate course, Department of Mathematics, University of Louisiana at Lafayette, 2018
Description: Descriptive statistics, elementary hypothesis testing, confidence intervals, introduction to correlation and regression.
MATH 103 - Applied College Algebra Fundamentals (Instructor)
Undergraduate course, Department of Mathematics, University of Louisiana at Lafayette, 2018
Description: Functions and graphs including linear functions, quadratic and other polynomial functions, exponential and logarithmic functions; zeros of polynomial functions; systems of equations and inequalities.
CSE 539 - Applied Cryptography (TA)
Graduate course, Arizona State University, 2022
Description: This course covers the standard cryptographic notions such as symmetric-key encryption, and discusses how to determine security properties for specific applications and how to combine existing cryptographic tools to realize those properties.