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Over the past two decades, the cloud computing paradigm has gradually attracted more popularity due to its efficient resource usage and simple service access model. Virtualization technology is the fundamental element of cloud computing…
We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional $Q$-curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of…
Cloud computing has achieved an unbelievable adoption response rate but still its infancy stage is not over. It is an emerging paradigm and amazingly gaining popularity. The size of the market shared of the applications provided by cloud…
We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions on the sphere which speed up computations by a factor \order{\sqrt{N}} compared to present methods where $N$ is the number of pixels. No…
Simulation of turbulent flows, especially at the edges of clouds in the atmosphere, is an inherently challenging task. Hitherto, the best possible computational method to perform such experiments is the Direct Numerical Simulation (DNS).…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
This is a computational study of bottlenecks on algebraic varieties. The bottlenecks of a smooth variety $X \subseteq \mathbb{C}^n$ are the lines in $\mathbb{C}^n$ which are normal to $X$ at two distinct points. The main result is a…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
Many graph processing algorithms require determination of shortest-path distances between arbitrary numbers of node pairs. Since computation of exact distances between all node-pairs of a large graph, e.g., 10M nodes and up, is…
Cloud computing is a new model of computing which provides scalability, flexibility and on-demand service. Virtualization is one of the main components of the cloud, but unfortunately, this technology suffers from many security…
The theory of vortex motion in a dilute superfluid of inhomogeneous density demands a boundary layer approach, in which different approximation schemes are employed close to and far from the vortex, and their results matched smoothly…
The advent of High Performance Computing (HPC) has provided the computational capacity required for power system operators (SO) to obtain solutions in the least time to highly-complex applications, i.e., Unit Commitment (UC). The UC…
This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer…
We introduce a new approach for the adaptation of the Maximal Internal Envelope method, extended to address the Largest Empty Sphere problem within unstructured 3D point clouds. We explore the identification of the Largest Empty Sphere by…
We study the existence of minimal networks in the unit sphere $\mathbf{S}^d$ and the unit ball $\mathbf{B}^d$ of $\mathbf{R}^d$ endowed with Riemannian metrics close to the standard ones. We employ a finite-dimensional reduction method,…
There is a growing need for low latency for many devices and users. The traditional cloud computing paradigm can not meet this requirement, legitimizing the need for a new paradigm. Edge computing proposes to move computing capacities to…
We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…
So far, various solutions have been proposed for symmetric distribution of load cloud computing environments. In this article, a new solution to the optimal allocation of virtual machines in the cloud data centers is presented to provide a…
We consider an inverse problem for a finite graph $(X,E)$ where we are given a subset of vertices $B\subset X$ and the distances $d_{(X,E)}(b_1,b_2)$ of all vertices $b_1,b_2\in B$. The distance of points $x_1,x_2\in X$ is defined as the…
Cloud infrastructure supports the efficient operation of data pipelines regarding requirements like cost, speed, and resource utilization. We present an integrated view of optimization opportunities for cloud-based data pipelines by…