9 papers
Spectral Statistics of the Sample Covariance Matrix for High Dimensional Linear Gaussians
Muhammad Abdullah Naeem, Miroslav Pajic
Performance of ordinary least squares(OLS) method for the \emph{estimation of high dimensional stable state transition matrix} (i.e., spectral radius ) from a single noi…
From Spectral Theorem to Statistical Independence with Application to System Identification
Muhammad Abdullah Naeem, Amir Khazraei, Miroslav Pajic
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profi…
Correction to the Friedmann equation with Sharma-Mittal entropy: A new perspective on cosmology
Muhammad Naeem, Aysha Bibi
As the black hole entropy does not obey the area law on it. The area law, given by , where and , for , , indicates the amoun…
High Dimensional Geometry and Limitations in System Identification
Muhammad Abdullah Naeem, Miroslav Pajic
We study the problem of identification of linear dynamical system from a single trajectory, via excitations of isotropic Gaussian. In stark contrast with previously reported result…
Learning and Concentration for High Dimensional Linear Gaussians: an Invariant Subspace Approach
Muhammad Abdullah Naeem
In this work, we study non-asymptotic bounds on correlation between two time realizations of stable linear systems with isotropic Gaussian noise. Consequently, via sampling from a…
Concentration Phenomenon for Random Dynamical Systems: An Operator Theoretic Approach
Muhammad Abdullah Naeem, Miroslav Pajic
Via operator theoretic methods, we formalize the concentration phenomenon for a given observable `' of a discrete time Markov chain with `' as invariant ergodic measure, po…
Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space
Muhammad Abdullah Naeem, Miroslav Pajic
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concen…
Learning Expected Reward for Switched Linear Control Systems: A Non-Asymptotic View
Muhammad Abdullah Naeem, Miroslav Pajic
In this work, we show existence of invariant ergodic measure for switched linear dynamical systems (SLDSs) under a norm-stability assumption of system dynamics in some unbounded su…
Estimation of Time Delay caused by Point Geometry in Public Transport
Muhammad Naeem, Mehdi Katranji, Guilhem Sanmarty +3
Travel time prediction is a well-renowned topic of research. It is primarily influenced by traffic congestion, road conditions and route geometry. Among them route geometry at any…