arXiv subjects

Khalid Khan

Publications and source records attributed to Khalid Khan.

10 recordsLinked to original sources

arXiv2024

Self-Supervised Path Planning in UAV-aided Wireless Networks based on Active Inference

This paper presents a novel self-supervised path-planning method for UAV-aided networks. First, we employed an optimizer to solve training examples offline and then used the resulting solutions as demonstrations from which the UAV can learn the world model to understand the environment and implicitly discover the optimizer's policy. UAV equipped with the world model can make real-time autonomous decisions and engage in online planning using active inference. During planning, UAV can score different policies based on the expected surprise, allowing it to choose among alternative futures. Additionally, UAV can anticipate the outcomes of its actions using the world model and assess the expected surprise in a self-supervised manner. Our method enables quicker adaptation to new situations and better performance than traditional RL, leading to broader generalizability.

cs.RO↗

arXiv2023

Global quantum discord and von Neumann entropy in multipartite two-level atomic systems

We have computed the global quantum discord and von Neumann entropy of multipartite two-level atomic systems interacting with a single-mode Fock field. We use Tavis-Cumming model. We have explored how quantum correlations and quantum entanglement evolve with time in such systems. The quantum system is prepared initially in a mixed state and different parameters are varied to see how they affect the information processing in the system. The dynamical character of the global quantum discord and von Neumann entropy show an interplay between classical and non-classical correlations. Photons in this model play an important role to assist the global quantum discord and von Neumann entropy and we observed that the effects of the field on the global quantum discord and von Neumann entropy reside in the time evolution of the system indicating that both atom and field states have become entangled. The global quantum discord is assisted in a non-linear fashion with the number of photons in the system. The global quantum discord and von Neumann entropy show linear behavior with each other in the dynamics of the system. The effects of intrinsic decoherence on the dynamics of the global quantum discord and von Neumann entropy are also studied. We have extrapolated the results for a large photon number on the system. We have studied the effect of the change in the size of the system on the maximum value of global quantum discord and von Neumann entropy and we have estimated the scaling coefficients for this behavior.

quant-ph↗

arXiv2020

Algorithms and Identities for B$\acute{e}$zier curves via Post Quantum Blossom

In this paper, a new analogue of blossom based on post quantum calculus is introduced. The post quantum blossom has been adapted for developing identities and algorithms for Bernstein bases and B$\acute{e}$zier curves. By applying the post quantum blossom, various new identities and formulae expressing the monomials in terms of the post quantun Bernstein basis functions and a post quantun variant of Marsden's identity are investigated. For each post quantum B$\acute{e}$zier curves of degree $m,$ a collection of $m!$ new, affine invariant, recursive evaluation algorithms are derived.

cs.GR↗

arXiv2017

Quantum renormalization group of XY model in two dimensions

We investigate entanglement and quantum phase transition (QPT) in a two-dimensional Heisenberg anisotropic spin-1/2 XY model, using quantum renormalization group method (QRG) on a square lattice of $N\times N$ sites. The entanglement through geometric average of concurrences is calculated after each step of the QRG. We show that the concurrence achieves a non zero value at the critical point more rapidly as compared to one-dimensional case. The relationship between the entanglement and the quantum phase transition is studied. The evolution of entanglement develops two saturated values corresponding to two different phases. We compute the first derivative of the concurrence, which is found to be discontinuous at the critical point $γ=0$, and indicates a second-order phase transition in the spin system. Further, the scaling behaviour of the system is investigated by computing the first derivative of the concurrence in terms of the system size.

quant-ph↗

arXiv2016

Spatial dependence of entanglement renormalization in $XY$ model

In this article a comparative study of the renormalization of entanglement in one, two and three dimensional space and its relation with quantum phase transition (QPT) near the critical point is presented by implementing the Quantum Renormalization Group (QRG) technique. Adopting the Kadanoff's block approach, numerical results for the concurrence are obtained for the spin -1/2 $XY$ model in all the spatial dimensions. The results show similar qualitative behavior as we move from the lower to the higher dimensions in space but the number of iterations reduces for achieving the QPT in the thermodynamic limit. We find that in the two dimensional and three dimensional spin -1/2 $XY$ model, maximum values of the concurrence reduce by the factor of $1/n$ $(n=2,3)$ with reference to the maximum value of one dimensional case. Moreover, we study the scaling behavior and the entanglement exponent. We compare the results for one, two and three dimensional cases and illustrate how the system evolves near the critical point.

quant-ph↗

arXiv2016

B$\acute{e}$zier curves based on Lupaş $(p,q)$-analogue of Bernstein polynomials in CAGD

In this paper, we use the blending functions of Lupaş type (rational) $(p,q)$-Bernstein operators based on $(p,q)$-integers for construction of Lupaş $(p,q)$-B$\acute{e}$zier curves (rational curves) and surfaces (rational surfaces) with shape parameters. We study the nature of degree elevation and degree reduction for Lupaş $(p,q)$-B$\acute{e}$zier Bernstein functions. Parametric curves are represented using Lupaş $(p,q)$-Bernstein basis. We introduce affine de Casteljau algorithm for Lupaş type $(p,q)$-Bernstein B$\acute{e}$zier curves. The new curves have some properties similar to $q$-B$\acute{e}$zier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain $(u, v) \in [0, 1] \times [0, 1] $ depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. We get $q$-B$\acute{e}$zier surfaces for $(u, v) \in [0, 1] \times [0, 1] $ when we set the parameter $p_1=p_2=1.$ In comparison to $q$-B$\acute{e}$zier curves and surfaces based on Lupaş $q$-Bernstein polynomials, our generalization gives us more flexibility in controlling the shapes of curves and surfaces. We also show that the $(p,q)$-analogue of Lupaş Bernstein operator sequence $L^{n}_{p_n,q_n}(f,x)$ converges uniformly to $f(x)\in C[0,1]$ if and only if $0 0$ fixed and $p \neq 1,$ the sequence $L^{n}_{p,q}(f,x)$ converges uniformly to $f(x)~ \in C[0,1]$ if and only if $f(x)=ax+b$ for some $a, b \in \mathbb{R}.$

cs.GR↗

arXiv2015

A de Casteljau Algorithm for Bernstein type Polynomials based on (p,q)-integers

In this paper, a de Casteljau algorithm to compute (p,q)-Bernstein Bezier curves based on (p,q)-integers is introduced. We study the nature of degree elevation and degree reduction for (p,q)-Bezier Bernstein functions. The new curves have some properties similar to q-Bezier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u, v) \in [0, 1] \times [0, 1] depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. Furthermore, some fundamental properties for (p,q)-Bernstein Bezier curves are discussed. We get q-Bezier curves and surfaces for (u, v) \in [0, 1] \times [0, 1] when we set the parameter p1 = p2 = 1.

cs.GR↗

arXiv2015

Bezier curves and surfaces based on modified Bernstein polynomials

In this paper, we use the blending functions of Bernstein polynomials with shifted knots for construction of Bezier curves and surfaces. We study the nature of degree elevation and degree reduction for Bezier Bernstein functions with shifted knots. Parametric curves are represented using these modified Bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve. We get Bezier curve defined on [0, 1] when we set the parameter α=βto the value 0. We also present a de Casteljau algorithm to compute Bernstein Bezier curves and surfaces with shifted knots. The new curves have some properties similar to Bezier curves. Furthermore, some fundamental properties for Bernstein Bezier curves and surfaces are discussed.

cs.GR↗

arXiv2015

Performance evaluation of different optimization techniques for coverage and connectivity control in backbone based wireless networks

In this paper, performance evaluation of Newton-Raphson and Conjugate Gradient method has been studied in comparison to Steepest Decent method for coverage and connectivity control in backbone based wireless networks. In order to design such wireless networks, the main challenge is to ensure network requirements such as network coverage and connectivity. To optimize coverage and connectivity, backbone nodes will be repositioned by the use of mobility control based on above mentioned methods. Thus the network get self organized which autonomously achieve energy minimizing configuration. Furthermore by simulation using MATLAB R2010a, methods are compared on the basis of optimized cost, number of iterations and elapsed time i.e. total time taken to execute the algorithm.

cs.NI↗

arXiv2006

Generalized Ideal Gas Equations for Structureful Universe

We have derived generalized ideal gas equations for a structureful universe consisting of all forms of matters. We have assumed a universe that contains superclusters. Superclusters are then made of clusters. Each cluster can be further divided into smaller ones and so on. We have derived an expression for the entropy of such a universe. Our model is rather independent of the geometry of the intermediate clusters. Our calculations are valid for a non-interacting universe within non-relativistic limits. We suggest that structure formation can reduce the expansion rate of the universe.

physics.gen-ph↗