Three-dimensional lattice logic circuits, Part I: Fundamentals

Fundamentals of regular three-dimensional (3D) lattice circuits are introduced. Lattice circuits represent an important class of regular circuits that allow for local interconnections, predictable timing, fault localization, and self-repair. In addition, three-dimensional lattice circuits can be potentially well suited for future 3D technologies, such as nanotechnologies, where the intrinsic physical delay of the irregular and lengthy interconnections limits the device performance. Although the current technology does not offer a menu for the immediate physical implementation of the proposed three-dimensional circuits, this paper deals with three-dimensional logic circuit design from a fundamental and foundational level for a rather new possible future directions in designing digital logic circuits.

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Three-dimensional lattice logic circuits, Part II: Formal methods

Facta universitatis - series Electronics and Energetics ◽

10.2298/fuee0501015a ◽

2005 ◽

Vol 18 (1) ◽

pp. 15-28 ◽

Cited By ~ 3

Author(s):

Anas Al-Rabadi

Keyword(s):

Formal Methods ◽

Fault Localization ◽

Three Dimensional ◽

Logic Circuits ◽

Design Methods ◽

Algebraic Methods ◽

Automatic Design ◽

Important Class ◽

Dimensional Lattice ◽

Future Technologies

This paper introduces formal algebraic methods for the design of three-dimensional (3D) lattice circuits that were discussed in the first part of my article. New regular 3D logic circuits are introduced, where the application of ternary decompositions into regular three-dimensional lattice circuits is shown. Lattice circuits represent an important class of regular logic circuits that allow for local interconnections, predictable timing fast fault localization, and self-repair. The introduced design methods can be used for the automatic design of logic circuits in 3D for applications and future technologies that require such topologies.

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Memristive Circuit Design of Five-Person Voter Based on Memristor Ratioed Logic

Journal of Nanoelectronics and Optoelectronics ◽

10.1166/jno.2020.2895 ◽

2020 ◽

Vol 15 (12) ◽

pp. 1482-1493

Author(s):

Junwei Sun ◽

Qinfei Yang ◽

Yanfeng Wang

Keyword(s):

Energy Consumption ◽

Circuit Design ◽

Simple Structure ◽

Electronic Device ◽

Logic Circuits ◽

Logic Circuit ◽

Low Power Consumption ◽

Electronic Components ◽

Complex Circuits ◽

Easy Integration

Conventional CMOS-based logic circuits are approaching their limits when it comes to speed and energy consumption, so the development of new electronic components becomes critical. Memristor is a nano-structured special electronic device with the advantages of simple structure, low power consumption and easy integration. This invention supplys a new method for developing complex logic circuits. This article mainly presents the design of a five-person voter circuit. The OR/AND logic can be accomplished by varying the polarity of two parallel memristors. On the basis of the two logic circuits, adder and comparator are constructed. Further, based on the adder and comparator, a five-person voter is implemented. The correctness and rationality of the five-person voter based on MRL are confirmed via logistical analysis and simulation. Compared with the traditional logic circuits, the logic circuit designed in this paper has advantages in area cost. The realization of the five-person voter circuit further proves that the logic circuit based on memristor can be cascaded. The research results are expected to build more complex circuits, which may provide a reference for the design of other practical circuits.

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Three-dimensional lattice logic circuits, Part III: Solving 3D volume congestion problem

Facta universitatis - series Electronics and Energetics ◽

10.2298/fuee0501029a ◽

2005 ◽

Vol 18 (1) ◽

pp. 29-43 ◽

Cited By ~ 1

Author(s):

Anas Al-Rabadi

Keyword(s):

Three Dimensional ◽

Logic Circuits ◽

Two Dimensional ◽

Regular Lattice ◽

3D Design ◽

Dimensional Lattice ◽

Multiple Valued Logic ◽

Multi Stage ◽

3D Volume ◽

Logic Functions

This part is a continuation of the first and second parts of my paper. In a previous work, symmetry indices have been related to regular logic circuits for the realization of logic functions. In this paper, a more general treatment that produces 3D regular lattice circuits using operations on symmetry indices is presented. A new decomposition called the Iterative Symmetry Indices Decomposition (ISID) is implemented for the 3D design of lattice circuits. The synthesis of regular two-dimensional circuits using ISID has been introduced previously, and the synthesis of area-specific circuits using ISID has been demonstrated. The new multiple-valued ISID algorithm can have several applications such as: (1) multi-stage decompositions of multiple valued logic functions for various lattice circuit layout optimizations, and (2) the new method is useful for the synthesis of ternary functions using three-dimensional regular lattice circuits whenever volume-specific layout constraints have to be satisfied.

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DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732391004140 ◽

1991 ◽

Vol 06 (39) ◽

pp. 3591-3600 ◽

Cited By ~ 40

Author(s):

HIROSI OOGURI ◽

NAOKI SASAKURA

Keyword(s):

Gauge Theory ◽

Moduli Space ◽

Three Dimensional ◽

Two Dimensional ◽

Analogue Model ◽

Gauge Invariant ◽

Invariant Functions ◽

Dimensional Lattice ◽

Chern Simons ◽

Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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Restoring isotropy in a three-dimensional lattice model: The Ising universality class

Physical Review B ◽

10.1103/physrevb.104.014426 ◽

2021 ◽

Vol 104 (1) ◽

Author(s):

Martin Hasenbusch

Keyword(s):

Lattice Model ◽

Three Dimensional ◽

Universality Class ◽

Dimensional Lattice

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The Role of Pre-Clinical 3-Dimensional Models of Osteosarcoma

International Journal of Molecular Sciences ◽

10.3390/ijms21155499 ◽

2020 ◽

Vol 21 (15) ◽

pp. 5499

Author(s):

Hannah L. Smith ◽

Stephen A. Beers ◽

Juliet C. Gray ◽

Janos M. Kanczler

Keyword(s):

Three Dimensional ◽

Chorioallantoic Membrane ◽

3D Models ◽

In Ovo ◽

Future Directions ◽

3 Dimensional ◽

In Vivo Animal Models

Treatment for osteosarcoma (OS) has been largely unchanged for several decades, with typical therapies being a mixture of chemotherapy and surgery. Although therapeutic targets and products against cancer are being continually developed, only a limited number have proved therapeutically active in OS. Thus, the understanding of the OS microenvironment and its interactions are becoming more important in developing new therapies. Three-dimensional (3D) models are important tools in increasing our understanding of complex mechanisms and interactions, such as in OS. In this review, in vivo animal models, in vitro 3D models and in ovo chorioallantoic membrane (CAM) models, are evaluated and discussed as to their contribution in understanding the progressive nature of OS, and cancer research. We aim to provide insight and prospective future directions into the potential translation of 3D models in OS.

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