Search

A novel space shift keying (SSK) multiple–input multiple–output (MIMO) technique based on Steiner triple system is proposed and analyzed in this article. SSK attracted considerable research interest in the past few years driven by the several promised inherent advantages including low error probability, low computational complexity and a very simple hardware implementation with very low cost and power consumption. Yet, the spectral efficiency of SSK increases with a base two logarithm of the number of transmit antennas and high data rates are only viable with a massive and impractical number of transmit antennas. Alternatively, generalized SSK (GSSK) scheme is considered, where a combination of antennas is activated at each time instant. GSSK promises the use of arbitrary number of transmit antennas not necessarily a power of two integer. Also, GSSK can attain high data rate with low number of transmit antennas at the cost of substantial degradation in the error performance. In this study, a Steiner triple system is utilized to propose a tailored SSK scheme with substantial reduction in the required number of transmit antennas, without compromising the error probability. It is shown that the proposed Steiner–SSK (S–SSK) MIMO system achieves almost identical error performance to a conventional SSK system but with nearly 90% reduction in the number of transmit antennas. As well, the average bit error rate (ABER) of S–SSK is shown to outperform GSSK by at least 3dB. It is also reported that a S–SSK system accomplishes significant reduction in hardware cost, power consumption, and computational complexity as compared to conventional SSK scheme. Yet, GSSK is shown to marginally outperforms S–SSK in these metrics as it requires smaller number of transmit antennas per a target spectral efficiency. [ABSTRACT FROM AUTHOR]

This paper introduces Steiner-quadrature space shift keying (QSSK) (S-QSSK), an innovative modulation scheme tailored for multiple–input multiple–output (MIMO) systems. The study compares S-QSSK with existing modulation schemes (S-space shift keying (SSK)(S-SSK), QSSK, generalized quadrature space shift keying (GQSSK)) across various performance metrics, considering diverse channel conditions, transmit antenna numbers, and spectral efficiencies. Theoretical average bit error rate (ABER) analysis, validated by Monte Carlo simulations, establishes a close agreement between analytical and practical results, especially at realistic signal-to-noise-ratio (SNR) values. Additionally, capacity and mutual information formulas shed light on the system's information transmission capabilities. The research delves into the outage probability, power consumption, and computational complexity of S-QSSK MIMO systems. It unveils a promising trade-off, demonstrating that S-QSSK achieves competitive performance in ABER, capacity, and mutual information, positioning it as a practical modulation technique. Importantly, S-QSSK exhibits about a 1 dB ABER performance decrease compared to S-SSK and QSSK, while offering a noteworthy 2 dB improvement over GQSSK. Despite requiring slightly more transmit antennas than GQSSK, S-QSSK demands significantly fewer than both S-SSK and traditional QSSK, particularly when targeting high spectral efficiencies. Moreover, the analysis underscores the advantageous power consumption and favorable computational complexity of S-QSSK relative to other modulation schemes. The proposed S-QSSK MIMO system thus presents itself as an efficient solution, enabling high data rates with fewer transmit antennas, resulting in substantial reductions in power consumption and computational complexity without a significant sacrifice in ABER and mutual information. These attributes make it a compelling choice for various applications, including those requiring efficient massive multiple–input multiple–output (mMIMO) operations. [ABSTRACT FROM AUTHOR]

Discusses the minimal spanning tree. Ways to construct a minimal spanning tree; Comparison between minimal Steiner trees and minimal spanning trees; Kruskal's greedy algorithm for the construction of minimal spanning trees; Good algorithm for finding a minimal Steiner tree spanning the points of regular patterns.

The article presents a mathematical solution to the problems regarding a dinner guests, strolling school girls and handcuffed prisoners. These problems can be generalized into triplets, quartets, sextets and so on. The problems can be considered as combinatorics which is called the block design theory. The problems regarding the dinner guests and schoolgirls can be solved by using the Steiner triple system by arranging the objects in triplets and having each to appear in a group only once.

In this paper, we consider the problem of obtaining graph-theoretic characterizations of controllability for the Laplacian-based leader-follower dynamics. Our developments rely on the notion of graph controllability classes, namely, the classes of essentially controllable, completely uncontrollable, and conditionally controllable graphs. In addition to the topology of the underlying graph, the controllability classes rely on the specification of the control vectors; our particular focus is on the set of binary control vectors. The choice of binary control vectors is naturally adapted to the Laplacian dynamics, as it captures the case when the controller is unable to distinguish between the followers and, moreover, controllability properties are invariant under binary complements. We prove that the class of essentially controllable graphs is a strict subset of the class of asymmetric graphs and provide numerical results that suggests that the ratio of essentially controllable graphs to asymmetric graphs increases as the number of vertices increases. Although graph symmetries play an important role in graph-theoretic characterizations of controllability, we provide an explicit class of asymmetric graphs that are completely uncontrollable, namely the class of block graphs of Steiner triple systems. We prove that for graphs on four and five vertices, a repeated Laplacian eigenvalue is a necessary condition for complete uncontrollability but, however, show through explicit examples that for eight and nine vertices, a repeated eigenvalue is not necessary for complete uncontrollability. For the case of conditional controllability, we give an easily checkable necessary condition that identifies a class of binary control vectors that result in a two-dimensional controllable subspace. Several constructive examples demonstrate our results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study how to obtain Steiner trees appropriately for efficient multicast routing. We first introduce a scheme for generating a new weighted multicast parameter by efficiently combining two independent measures: cost and delay. We call our proposal the Weighted Parameter for Multicast Trees (WPMT) algorithm. The WPMT can be adjusted by the weight ω ∈[0,1]. For instance, if ω approaches 0, then the delay of the multicast tree may be relatively lower than the delay of other trees that are obtained as ω approaches 1. Otherwise, as the weight approaches 1 then the cost of the obtained tree may be relatively lower compared with other trees. A case study shows how to find an appropriate Steiner tree for each ω. The simulation results show that the use of the proposed WPMT produces results similar to the k-minimum Steiner tree algorithm. The WPMT can be applied to several existing multicast problems as we describe. We also propose several multicast algorithms using the WPMT in order to solve well-known multicast problems, and compare the proposed algorithms-based the WPMT with representative algorithms for the well-known problems. [Copyright &y& Elsevier]

The article offers information on the "War of the Weasels," the ongoing creationist attacks on evolutionary (genetic) algorithms, in the May/June 2010 issue of SkepticalInquirer (Thomas 2010). Genetic algorithms (GAs) are computerized simulations of evolution and are used to study evolutionary processes and also to solve difficult engineering or math problems. Topic include Intelligent design (ID) creationists often criticize these algorithms for not generating true novelty.

Focuses the symmetries of the biplane. Permutation and automorphism group of the biplane; Block designs; Distinct element of a difference set; Orbit-Stabilizer theorem; Error-correcting codes; Steiner systems.

The article focuses on creating perfect pangram with wacky words, which is a sentence containing every odd letter exactly once. The author says one of the biggest challenges when constructing a pangram using the Steiner System is finding a word on a set of 7 or 9 letters, which is seen in the case of seven letters like that of ABCDEFG and AYTEROU. He adds the basic triangles of the lattice will be equilateral if the spacing of the letters are chosen correctly.

Reports on mathematicians, Ding-Zhu Du and Frank Hwang's solution to an optimization problem, known as the Steiner ratio conjecture. Background on the Steiner minimum tree (SMT); Problem of finding an SMT; Minimum spanning tree (MST) solution; Comparison between SMT and MST solutions; Transformation of the Steiner ratio conjecture into a minimax problem.