Theoretical Engineering and Satellite Comlink of a PTVD-SHAM System

This paper focuses on super helical memory system's design, 'Engineering, Architectural and Satellite Communications' as a theoretical approach of an invention-model to 'store time-data'. The current release entails three concepts: 1- an in-depth theoretical physics engineering of the chip including its, 2- architectural concept based on VLSI methods, and 3- the time-data versus data-time algorithm. The 'Parallel Time Varying & Data Super-helical Access Memory' (PTVD-SHAM), possesses a waterfall effect in its architecture dealing with the process of voltage output-switch into diverse logic and quantum states described as 'Boolean logic & image-logic', respectively. Quantum dot computational methods are explained by utilizing coiled carbon nanotubes (CCNTs) and CNT field effect transistors (CNFETs) in the chip's architecture. Quantum confinement, categorized quantum well substrate, and B-field flux involvements are discussed in theory. Multi-access of coherent sequences of 'qubit addressing' in any magnitude, gained as pre-defined, here e.g., the 'big O notation' asymptotically confined into singularity while possessing a magnitude of 'infinity' for the orientation of array displacement. Gaussian curvature of k(k<0) is debated in aim of specifying the 2D electron gas characteristics, data storage system for defining short and long time cycles for different CCNT diameters where space-time continuum is folded by chance for the particle. Precise pre/post data timing for, e.g., seismic waves before earthquake mantle-reach event occurrence, including time varying self-clocking devices in diverse geographic locations for radar systems is illustrated in the Subsections of the paper. The theoretical fabrication process, electromigration between chip's components is discussed as well.Comment: 50 pages, 10 figures (3 multi-figures), 2 tables. v.1: 1 postulate entailing hypothetical ideas, design and model on future technological advances of PTVD-SHAM. The results of the previous paper [arXiv:0707.1151v6], are extended in order to prove some introductory conjectures in theoretical engineering advanced to architectural analysi

Improvements on the k-center problem for uncertain data

In real applications, there are situations where we need to model some problems based on uncertain data. This leads us to define an uncertain model for some classical geometric optimization problems and propose algorithms to solve them. In this paper, we study the $k$-center problem, for uncertain input. In our setting, each uncertain point $P_i$ is located independently from other points in one of several possible locations $\{P_{i,1},\dots, P_{i,z_i}\}$ in a metric space with metric $d$, with specified probabilities and the goal is to compute $k$-centers $\{c_1,\dots, c_k\}$ that minimize the following expected cost $$Ecost(c_1,\dots, c_k)=\sum_{R\in \Omega} prob(R)\max_{i=1,\dots, n}\min_{j=1,\dots k} d(\hat{P}_i,c_j)$$ here $\Omega$ is the probability space of all realizations $$R=\{\hat{P}_1,\dots, \hat{P}_n\}$$ of given uncertain points and $$prob(R)=\prod_{i=1}^n prob(\hat{P}_i).$$ In restricted assigned version of this problem, an assignment $A:\{P_1,\dots, P_n\}\rightarrow \{c_1,\dots, c_k\}$ is given for any choice of centers and the goal is to minimize $$Ecost_A(c_1,\dots, c_k)=\sum_{R\in \Omega} prob(R)\max_{i=1,\dots, n} d(\hat{P}_i,A(P_i)).$$ In unrestricted version, the assignment is not specified and the goal is to compute $k$ centers $\{c_1,\dots, c_k\}$ and an assignment $A$ that minimize the above expected cost. We give several improved constant approximation factor algorithms for the assigned versions of this problem in a Euclidean space and in a general metric space. Our results significantly improve the results of \cite{guh} and generalize the results of \cite{wang} to any dimension. Our approach is to replace a certain center point for each uncertain point and study the properties of these certain points. The proposed algorithms are efficient and simple to implement