Journal articles: 'Ternary computing'

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A. Obiniyi, Afolayan, Ezugwu E. Absalom, and Kwanashie Adako. "Arithmetic Logic Design with ColorCoded Ternary for Ternary Computing." International Journal of Computer Applications 26, no. 11 (July 31, 2011): 31–37. http://dx.doi.org/10.5120/3162-2929.

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Orbach, Ron, Sivan Lilienthal, Michael Klein, R. D. Levine, Francoise Remacle, and Itamar Willner. "Ternary DNA computing using 3 × 3 multiplication matrices." Chemical Science 6, no. 2 (2015): 1288–92. http://dx.doi.org/10.1039/c4sc02930e.

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Ternary computing, beyond Boolean logic, is anticipated to enhance computational complexity. DNA-based ternary computing is demonstrated by the assembly of a 3 × 3 multiplication table, and the parallel operation of three 3 × 3 multiplication matrices is highlighted.

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Cambou, Bertrand, Paul Flikkema, James Palmer, Donald Telesca, and Christopher Philabaum. "Can Ternary Computing Improve Information Assurance?" Cryptography 2, no. 1 (March 2, 2018): 6. http://dx.doi.org/10.3390/cryptography2010006.

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Kim, Sunmean, Yesung Kang, Seunghan Baek, Youngchang Choi, and Seokhyeong Kang. "Low-Power Ternary Multiplication Using Approximate Computing." IEEE Transactions on Circuits and Systems II: Express Briefs 68, no. 8 (August 2021): 2947–51. http://dx.doi.org/10.1109/tcsii.2021.3068971.

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Buchade, Amar, and Rajesh Ingle. "Ternary Tree Based Approach For Accessing the Resources By Overlapping Members in Cloud Computing." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 6 (December 1, 2017): 3593. http://dx.doi.org/10.11591/ijece.v7i6.pp3593-3601.

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<p>In cloud computing, immediate access of resources is important due to cost incurred to customer by pay per use model of cloud computing. Usually resource is protected by using cryptography technique. The resource may be shared by multiple members in group. There can be overlapping members to access the multiple resources. Group key management is important to form the group key to access the resource. Group key formation time is crucial for immediate access of protected resource in cloud computing. Thus ternary tree based approach is proposed to form the key for overlapping members accessing resources. Membership event such as join and leave also considered. Through the analysis, it is found that computational overhead is reduced by 23% if ternary key trees are combined than independent ternary key trees. It is also observed that combined ternary key tree outperforms the combined binary key tree approach for group key formation by considering overlapping members. Security requirement analysis of group membership for key formation is also provided in the paper.</p>

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Monfared, Asma Taheri, and Majid Haghparast. "Design of New Quantum/Reversible Ternary Subtractor Circuits." Journal of Circuits, Systems and Computers 25, no. 02 (December 23, 2015): 1650014. http://dx.doi.org/10.1142/s0218126616500146.

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Ternary quantum circuits play a significant role in future quantum computing technology because they have many advantages over binary quantum circuits. Subtraction is considered as being one of the key arithmetic operations; hence, subtractors are very essential for the construction of various computational units of quantum computers and other complex computational systems. In this paper, we have proposed the realization of a quantum reversible ternary half-subtractor circuit using a generalized ternary gate, a ternary Toffoli gate, and a ternary C2NOT gate. Based on the realization of the ternary half-subtractor, we proposed the realization of a ternary full-subtractor.

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Zheng, Wei-Min, Qing-Wei Chai, Jie Zhang, and Xingsi Xue. "Ternary compound ontology matching for cognitive green computing." Mathematical Biosciences and Engineering 18, no. 4 (2021): 4860–70. http://dx.doi.org/10.3934/mbe.2021247.

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Clementini, E., and R. Billen. "Modeling and computing ternary projective relations between regions." IEEE Transactions on Knowledge and Data Engineering 18, no. 6 (June 2006): 799–814. http://dx.doi.org/10.1109/tkde.2006.102.

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Tabrizchi, Sepehr, Atiyeh Panahi, Fazel Sharifi, Hamid Mahmoodi, and Abdel-Hameed A. Badawy. "Energy-Efficient Ternary Multipliers Using CNT Transistors." Electronics 9, no. 4 (April 14, 2020): 643. http://dx.doi.org/10.3390/electronics9040643.

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In recent decades, power consumption has become an essential factor in attracting the attention of integrated circuit (IC) designers. Multiple-valued logic (MVL) and approximate computing are some techniques that could be applied to integrated circuits to make power-efficient systems. By utilizing MVL-based circuits instead of binary logic, the information conveyed by digital signals increases, and this reduces the required interconnections and power consumption. On the other hand, approximate computing is a class of arithmetic computing used in systems where the accuracy of the computation can be traded-off for lower energy consumption. In this paper, we propose novel designs for exact and inexact ternary multipliers based on carbon-nanotube field-effect transistors (CNFETs). The unique characteristics of CNFETs make them a desirable alternative to MOSFETs. The simulations are conducted using Synopsys HSPICE. The proposed design is compared against existing ternary multipliers. The results show that the proposed exact multiplier reduces the energy consumption by up to 6 times, while the best inexact design improves energy efficiency by up to 35 time compared to the latest state-of-the-art methods. Using the imprecise multipliers for image processing provides evidence that these proposed designs are a low-power system with an acceptable error.

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Peng, Xian Wu, Xiao Ping Fan, and Jian Xun Liu. "Performing Balanced Ternary Logic and Arithmetic Operations with Spiking Neural P Systems with Anti-Spikes." Advanced Materials Research 505 (April 2012): 378–85. http://dx.doi.org/10.4028/www.scientific.net/amr.505.378.

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Spiking neural P systems are a class of distributed and parallel computing models inspired by P systems and spiking neural networks.Spiking neural P system with anti-spikes can encode the balanced ternary three digits in a natural way using three states called anti-spikes, no-input and spikes. In this paper we use this variant of SN P system to simulate universal balanced ternary logic gates including AND,OR and NOT gate and to perform some basic balanced ternary arithmetic operations like addition and subtraction on balanced ternary integers. This paper provides an applicational answer to an open problem formulated by L.Pan and Gh. Păun.

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Blanchet-Sadri, F., Andrew Lohr, and Shane Scott. "Computing the partial word avoidability indices of ternary patterns." Journal of Discrete Algorithms 23 (November 2013): 119–42. http://dx.doi.org/10.1016/j.jda.2013.06.009.

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Pečar, P., A. Ramšak, N. Zimic, M. Mraz, and I. Lebar Bajec. "Adiabatic pipelining: a key to ternary computing with quantum dots." Nanotechnology 19, no. 49 (November 18, 2008): 495401. http://dx.doi.org/10.1088/0957-4484/19/49/495401.

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Guo, Qing, Xiaochen Guo, Yuxin Bai, Ravi Patel, Engin Ipek, and Eby G. Friedman. "Resistive Ternary Content Addressable Memory Systems for Data-Intensive Computing." IEEE Micro 35, no. 5 (September 2015): 62–71. http://dx.doi.org/10.1109/mm.2015.89.

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Li, Yuhang, Xin Dong, Sai Qian Zhang, Haoli Bai, Yuanpeng Chen, and Wei Wang. "RTN: Reparameterized Ternary Network." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4780–87. http://dx.doi.org/10.1609/aaai.v34i04.5912.

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To deploy deep neural networks on resource-limited devices, quantization has been widely explored. In this work, we study the extremely low-bit networks which have tremendous speed-up, memory saving with quantized activation and weights. We first bring up three omitted issues in extremely low-bit networks: the squashing range of quantized values; the gradient vanishing during backpropagation and the unexploited hardware acceleration of ternary networks. By reparameterizing quantized activation and weights vector with full precision scale and offset for fixed ternary vector, we decouple the range and magnitude from direction to extenuate above problems. Learnable scale and offset can automatically adjust the range of quantized values and sparsity without gradient vanishing. A novel encoding and computation pattern are designed to support efficient computing for our reparameterized ternary network (RTN). Experiments on ResNet-18 for ImageNet demonstrate that the proposed RTN finds a much better efficiency between bitwidth and accuracy and achieves up to 26.76% relative accuracy improvement compared with state-of-the-art methods. Moreover, we validate the proposed computation pattern on Field Programmable Gate Arrays (FPGA), and it brings 46.46 × and 89.17 × savings on power and area compared with the full precision convolution.

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CHEN, XUE, GUANGDA HU, and XIAOMING SUN. "THE COMPLEXITY OF WORD CIRCUITS." Discrete Mathematics, Algorithms and Applications 02, no. 04 (December 2010): 483–92. http://dx.doi.org/10.1142/s1793830910000826.

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A word circuit [1] is a directed acyclic graph in which each edge holds a w-bit word (i.e., some x ∈ {0, 1}w) and each node is a gate computing some binary function g : {0, 1}w × {0, 1}w → {0, 1}w. The following problem was studied in [1]: How many binary gates are needed to compute a ternary function f : ({0, 1}w)3 → {0, 1}w. They proved that (2 + o(1))2w binary gates are enough for any ternary function, and there exists a ternary function which requires word circuits of size (1 - o(1))2w. One of the open problems in [1] is to get these bounds tight within a low order term. In this paper we solved this problem by constructing new word circuits for ternary functions of size (1 + o(1))2w. We investigate the problem in a general setting: How many k-input word gates are needed for computing an n-input word function f : ({0, 1}w)n → {0, 1}w (here n ≥ k). We show that for any fixed n, (1 - o(1))2(n - k)w basic gates are necessary and (1 + o(1))2(n - k)w gates are sufficient (assume w is sufficiently large). Since word circuit is a natural generalization of boolean circuit, we also consider the case when w is a constant and the number of inputs n is sufficiently large. We show that [Formula: see text] basic gates are necessary and sufficient in this case.

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Clementini, Eliseo, Roland Billen, and Marco Santic. "Errata Corrige on "Modeling and Computing Ternary Projective Relations between Regions"." IEEE Transactions on Knowledge and Data Engineering 25, no. 5 (May 2013): 1196–98. http://dx.doi.org/10.1109/tkde.2011.239.

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Zheng, Le, Sangho Shin, and Sung-Mo Steve Kang. "Memristor-based ternary content addressable memory (mTCAM) for data-intensive computing." Semiconductor Science and Technology 29, no. 10 (September 18, 2014): 104010. http://dx.doi.org/10.1088/0268-1242/29/10/104010.

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Bocharov, Alex, Shawn X. Cui, Martin Roetteler, and Krysta M. Svore. "Improved quantum ternary arithmetic." Quantum Information and Computation 16, no. 9&10 (July 2016): 862–84. http://dx.doi.org/10.26421/qic16.9-10-8.

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Qutrit (or ternary) structures arise naturally in many quantum systems, notably in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of circuits for two families of ternary quantum adders. The main distinction from the binary adders is a richer ternary carry which leads potentially to higher resource counts in universal ternary bases. Our ternary ripple adder circuit has a circuit depth of O(n) and uses only 1 ancilla, making it more efficient in both, circuit depth and width, when compared with previous constructions. Our ternary carry lookahead circuit has a circuit depth of only O(log n), while using O(n) ancillas. Our approach works on two levels of abstraction: at the first level, descriptions of arithmetic circuits are given in terms of gates sequences that use various types of non-Clifford reflections. At the second level, we break down these reflections further by deriving them either from the two-qutrit Clifford gates and the non-Clifford gate C(X) : |i, ji 7→ |i, j + δi,2 mod 3i or from the two-qutrit Clifford gates and the non-Clifford gate P9 = diag(e −2π i/9 , 1, e 2π i/9 ). The two choices of elementary gate sets correspond to two possible mappings onto two different prospective quantum computing architectures which we call the metaplectic and the supermetaplectic basis, respectively. Finally, we develop a method to factor diagonal unitaries using multi-variate polynomials over the ternary finite field which allows to characterize classes of gates that can be implemented exactly over the supermetaplectic basis.

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Xu, Zhiwei, Xuebin Chi, and Nong Xiao. "High-performance computing environment: a review of twenty years of experiments in China." National Science Review 3, no. 1 (January 20, 2016): 36–48. http://dx.doi.org/10.1093/nsr/nww001.

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Abstract A high-performance computing environment, also known as a supercomputing environment, e-Science environment or cyberinfrastructure, is a crucial system that connects users’ applications to supercomputers, and provides usability, efficiency, sharing, and collaboration capabilities. This review presents important lessons drawn from China's nationwide efforts to build and use a high-performance computing environment over the past 20 years (1995–2015), including three observations and two open problems. We present evidence that such an environment helps to grow China's nationwide supercomputing ecosystem by orders of magnitude, where a loosely coupled architecture accommodates diversity. An important open problem is why technology for global networked supercomputing has not yet become as widespread as the Internet or Web. In the next 20 years, high-performance computing environments will need to provide zettaflops computing capability and 10 000 times better energy efficiency, and support seamless human-cyber-physical ternary computing.

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Rani, P. Mercy Nesa, and Kamalika Datta. "Improved Ternary Reversible Logic Synthesis Using Group Theoretic Approach." Journal of Circuits, Systems and Computers 29, no. 12 (February 19, 2020): 2050192. http://dx.doi.org/10.1142/s0218126620501923.

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Quantum computation relies on exploiting quantum mechanical phenomena, and has received significant attention in recent years. Higher-dimensional quantum systems increase the density of encoded information per computing element (e.g., qutrit for three-level system), resulting in less resource overhead. For instance, 63% reduction in the number of qutrits is possible for ternary quantum systems as compared to the corresponding binary systems. The proposed work exploits this fact to synthesize ternary reversible circuits employing a cycle-based technique. The method starts from the ternary reversible specification of a given function in the form of a permutation. The permutation cycles are factored into simpler three-cycles and two-cycles, which are then mapped to ternary reversible gates. Different gate libraries are used to synthesize three-cycles and two-cycles, respectively. A gate decomposition approach is also proposed to synthesize a quantum gate netlist in terms of elementary ternary quantum gates, viz. Muthukrishnan–Stroud gate and shift gate. Synthesis results on benchmark functions indicate that the proposed method results in 27% and 6% improvements in quantum cost and gate count, respectively, over existing works in the literature.

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Mohammaden, Amr, Mohammed Fouda, Ihsen Alouani, Lobna A. Said, and Ahmed Radwan. "CNTFET-Based Ternary Multiply-and-Accumulate Unit." Electronics 11, no. 9 (April 30, 2022): 1455. http://dx.doi.org/10.3390/electronics11091455.

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Multiply-Accumulate (MAC) is one of the most commonly used operations in modern computing systems due to its use in matrix multiplication, signal processing, and in new applications such as machine learning and deep neural networks. Ternary number system offers higher information processing within the same number of digits when compared to binary systems. In this paper, a MAC is proposed using a CNTFET-based ternary logic number. Specifically, we build a 5-trit multiplier and 10-trit adder as building blocks of two ternary MAC unit designs. The first is a basic MAC which has two methods to implement, serial and pipeline. The second is an improved MAC design that optimizes the number of transistors, offers higher performance and lower power consumption. The designed MAC unit can operate up to 300MHz. Finally, a comparative study in terms of power, delay, and area variations is conducted under different supply voltages and temperature levels.

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KANE, BEN. "REPRESENTATIONS OF INTEGERS BY TERNARY QUADRATIC FORMS." International Journal of Number Theory 06, no. 01 (February 2010): 127–58. http://dx.doi.org/10.1142/s1793042110002831.

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We investigate the representation of integers by quadratic forms whose theta series lie in Kohnen's plus space [Formula: see text], where p is a prime. Conditional upon certain GRH hypotheses, we show effectively that every sufficiently large discriminant with bounded divisibility by p is represented by the form, up to local conditions. We give an algorithm for explicitly calculating the bounds. For small p, we then use a computer to find the full list of all discriminants not represented by the form. Finally, conditional upon GRH for L-functions of weight 2 newforms, we give an algorithm for computing the implied constant of the Ramanujan–Petersson conjecture for weight 3/2 cusp forms of level 4N in Kohnen's plus space with N odd and squarefree.

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Prakash, Shiroman. "Magic state distillation with the ternary Golay code." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (September 2020): 20200187. http://dx.doi.org/10.1098/rspa.2020.0187.

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The ternary Golay code—one of the first and most beautiful classical error-correcting codes discovered—naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distil the ‘most magic’ qutrit state—an eigenstate of the qutrit Fourier transform known as the strange state —with cubic error suppression and a remarkably high threshold. It also distils the ‘second-most magic’ qutrit state, the Norell state, with quadratic error suppression and an equally high threshold to depolarizing noise.

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Shcherbakova, Nataliya, Ivonne Rodriguez-Donis, Jens Abildskov, and Vincent Gerbaud. "A novel method for detecting and computing univolatility curves in ternary mixtures." Chemical Engineering Science 173 (December 2017): 21–36. http://dx.doi.org/10.1016/j.ces.2017.07.007.

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Zhang, Jin, Zhiting Lin, Xiulong Wu, Chunyu Peng, Wenjuan Lu, Qiang Zhao, and Junning Chen. "An 8T SRAM Array with Configurable Word Lines for In-Memory Computing Operation." Electronics 10, no. 3 (January 27, 2021): 300. http://dx.doi.org/10.3390/electronics10030300.

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In-memory computing (IMC) has been widely accepted to be an effective method to improve energy efficiency. To realize IMC, operands in static random-access memory (SRAM) are stored in columns, which contradicts SRAM write patterns and requires additional data movement. In this paper, an 8T SRAM array with configurable word lines is proposed, in where the operands are arranged in rows, following the traditional SRAM storage pattern, and therefore additional data movement is not required. The proposed structure supports three different computing modes. In the ternary multiplication mode, the reference voltage generation column is not required. The energy of computing is only 1.273 fJ/bit. In the unsigned multibit multiplication mode, discharge and charging paths are used to enlarge the voltage difference of the least significant bit. In the logic operation mode, different types of operations (e.g., IMP, OR, NOR, XNOR, and XOR) are achieved in a single cycle. The frequency of logic computing is up to 909 MHz.

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Wang, Yuqi, Kun She, Qingbin Luo, Fan Yang, and Chao Zhao. "Symmetric weak ternary quantum homomorphic encryption schemes." Modern Physics Letters B 30, no. 07 (March 20, 2016): 1650076. http://dx.doi.org/10.1142/s0217984916500767.

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Based on a ternary quantum logic circuit, four symmetric weak ternary quantum homomorphic encryption (QHE) schemes were proposed. First, for a one-qutrit rotation gate, a QHE scheme was constructed. Second, in view of the synthesis of a general [Formula: see text] unitary transformation, another one-qutrit QHE scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit QHE scheme about generalized controlled [Formula: see text] (GCX([Formula: see text])) gate was constructed and further generalized to the [Formula: see text]-qutrit unitary matrix case. Finally, the security of these schemes was analyzed in two respects. It can be concluded that the attacker can correctly guess the encryption key with a maximum probability [Formula: see text], thus it can better protect the privacy of users’ data. Moreover, these schemes can be well integrated into the future quantum remote server architecture, and thus the computational security of the users’ private quantum information can be well protected in a distributed computing environment.

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Pajarre, Risto, Pertti Koukkari, Toshihiro Tanaka, and Joonho Lee. "Computing surface tensions of binary and ternary alloy systems with the Gibbsian method." Calphad 30, no. 2 (June 2006): 196–200. http://dx.doi.org/10.1016/j.calphad.2005.08.003.

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Khan, Faheem, Ghulam Mustafa, Aamir Shahzad, Dumitru Baleanu, and Maysaa M. Al-Qurashi. "A Computational Method for Subdivision Depth of Ternary Schemes." Mathematics 8, no. 5 (May 18, 2020): 817. http://dx.doi.org/10.3390/math8050817.

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Subdivision schemes are extensively used in scientific and practical applications to produce continuous shapes in an iterative way. This paper introduces a framework to compute subdivision depths of ternary schemes. We first use subdivision algorithm in terms of convolution to compute the error bounds between two successive polygons produced by refinement procedure of subdivision schemes. Then, a formula for computing bound between the polygon at k-th stage and the limiting polygon is derived. After that, we predict numerically the number of subdivision steps (depths) required for smooth limiting shape based on the demand of user specified error (distance) tolerance. In addition, extensive numerical experiments were carried out to check the numerical outcomes of this new framework. The proposed methods are more efficient than the method proposed by Song et al.

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Yang, Li, Zhezhi He, and Deliang Fan. "Harmonious Coexistence of Structured Weight Pruning and Ternarization for Deep Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6623–30. http://dx.doi.org/10.1609/aaai.v34i04.6138.

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Deep convolutional neural network (DNN) has demonstrated phenomenal success and been widely used in many computer vision tasks. However, its enormous model size and high computing complexity prohibits its wide deployment into resource limited embedded system, such as FPGA and mGPU. As the two most widely adopted model compression techniques, weight pruning and quantization compress DNN model through introducing weight sparsity (i.e., forcing partial weights as zeros) and quantizing weights into limited bit-width values, respectively. Although there are works attempting to combine the weight pruning and quantization, we still observe disharmony between weight pruning and quantization, especially when more aggressive compression schemes (e.g., Structured pruning and low bit-width quantization) are used. In this work, taking FPGA as the test computing platform and Processing Elements (PE) as the basic parallel computing unit, we first propose a PE-wise structured pruning scheme, which introduces weight sparsification with considering of the architecture of PE. In addition, we integrate it with an optimized weight ternarization approach which quantizes weights into ternary values ({-1,0,+1}), thus converting the dominant convolution operations in DNN from multiplication-and-accumulation (MAC) to addition-only, as well as compressing the original model (from 32-bit floating point to 2-bit ternary representation) by at least 16 times. Then, we investigate and solve the coexistence issue between PE-wise Structured pruning and ternarization, through proposing a Weight Penalty Clipping (WPC) technique with self-adapting threshold. Our experiment shows that the fusion of our proposed techniques can achieve the best state-of-the-art ∼21× PE-wise structured compression rate with merely 1.74%/0.94% (top-1/top-5) accuracy degradation of ResNet-18 on ImageNet dataset.

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Alharbi, Khalid Abdulkhaliq M., Ahmed El-Sayed Ahmed, Maawiya Ould Sidi, Nandalur Ameer Ahammad, Abdullah Mohamed, Mohammed A. El-Shorbagy, Muhammad Bilal, and Riadh Marzouki. "Computational Valuation of Darcy Ternary-Hybrid Nanofluid Flow across an Extending Cylinder with Induction Effects." Micromachines 13, no. 4 (April 9, 2022): 588. http://dx.doi.org/10.3390/mi13040588.

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The flow of an electroconductive incompressible ternary hybrid nanofluid with heat conduction in a boundary layer including metallic nanoparticles (NPs) over an extended cylindrical with magnetic induction effects is reported in this research. The ternary hybrid nanofluid has been synthesized with the dispersion of titanium dioxide, cobalt ferrite, and magnesium oxide NPs in the base fluid water. For a range of economical and biological applications, a computational model is designed to augment the mass and energy conveyance rate and promote the performance and efficiency of thermal energy propagation. The model has been written as a system of partial differential equations. Which are simplified to the system of ordinary differential equations through similarity replacements. The computing approach parametric continuation method is used to further process the resultant first order differential equations. The results are validated with the bvp4c package for accuracy and validity. The outcomes are displayed and analyzed through Figures and Tables. It has been observed that the inverse Prandtl magnetic number and a larger magnetic constant reduce the fluid flow and elevate the energy profile. The variation of ternary hybrid NPs significantly boosts the thermophysical features of the base fluid.

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Bormashenko, Edward. "Generalization of the Landauer Principle for Computing Devices Based on Many-Valued Logic." Entropy 21, no. 12 (November 25, 2019): 1150. http://dx.doi.org/10.3390/e21121150.

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The Landauer principle asserts that “the information is physical”. In its strict meaning, Landauer’s principle states that there is a minimum possible amount of energy required to erase one bit of information, known as the Landauer bound W = k B T l n 2 , where T is the temperature of a thermal reservoir used in the process and k B is Boltzmann’s constant. Modern computers use the binary system in which a number is expressed in the base-2 numeral system. We demonstrate that the Landauer principle remains valid for the physical computing device based on the ternary, and more generally, N-based logic. The energy necessary for erasure of one bit of information (the Landauer bound) W = k B T l n 2 remains untouched for the computing devices exploiting a many-valued logic.

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DENG, JUAN, HUI RAO, and ZHI-YING WEN. "HAUSDORFF MEASURE OF CARTESIAN PRODUCT OF THE TERNARY CANTOR SET." Fractals 20, no. 01 (March 2012): 77–88. http://dx.doi.org/10.1142/s0218348x12500077.

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Computing the Hausdorff measure of C × C, where C is the classical ternary Cantor set, is a long standing difficult problem. It is well-known that for a self-similar set, calculating the Hausdorff measure is equivalent to determining its optimal sets. This paper studies optimal sets of C × C: their diameters, measures, symmetries and the shapes. For this purpose, we introduce several devices: the repulsive principle, a bipartite graph G and a W-function. We show that the diameter of the optimal set B is between 1.2993 and 1.3082. Two symmetry properties of B are proved. Finally, we show that the shape of B is very close to a disk. We conjecture that an optimal set might be a disk.

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Chen, Qi-Lai, Gang Liu, Ming-Hua Tang, Xin-Hui Chen, Yue-Jun Zhang, Xue-Jun Zheng, and Run-Wei Li. "A univariate ternary logic and three-valued multiplier implemented in a nano-columnar crystalline zinc oxide memristor." RSC Advances 9, no. 42 (2019): 24595–602. http://dx.doi.org/10.1039/c9ra04119b.

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Memristors, which feature small sizes, fast speeds, low power, CMOS compatibility and nonvolatile modulation of device resistance, are promising candidates for next-generation data storage and in-memory computing paradigms.

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Kasimov, D. R., A. V. Kuchuganov, V. N. Kuchuganov, and P. P. Oskolkov. "Vectorization of raster mechanical drawings on the base of ternary segmentation and soft computing." Programming and Computer Software 43, no. 6 (November 2017): 337–44. http://dx.doi.org/10.1134/s0361768817060056.

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Gomez, Juan D., William G. P. Mayner, Maggie Beheler-Amass, Giulio Tononi, and Larissa Albantakis. "Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements." Entropy 23, no. 1 (December 22, 2020): 6. http://dx.doi.org/10.3390/e23010006.

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Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.

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Saksena, Radhika S., Marco D. Mazzeo, Stefan J. Zasada, and Peter V. Coveney. "Petascale lattice-Boltzmann studies of amphiphilic cubic liquid crystalline materials in a globally distributed high-performance computing and visualization environment." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1925 (August 28, 2010): 3983–99. http://dx.doi.org/10.1098/rsta.2010.0160.

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We present very large-scale rheological studies of self-assembled cubic gyroid liquid crystalline phases in ternary mixtures of oil, water and amphiphilic species performed on petascale supercomputers using the lattice-Boltzmann method. These nanomaterials have found diverse applications in materials science and biotechnology, for example, in photovoltaic devices and protein crystallization. They are increasingly gaining importance as delivery vehicles for active agents in pharmaceuticals, personal care products and food technology. In many of these applications, the self-assembled structures are subject to flows of varying strengths and we endeavour to understand their rheological response with the objective of eventually predicting it under given flow conditions. Computationally, our lattice-Boltzmann simulations of ternary fluids are inherently memory- and data-intensive. Furthermore, our interest in dynamical processes necessitates remote visualization and analysis as well as the associated transfer and storage of terabytes of time-dependent data. These simulations are distributed on a high-performance grid infrastructure using the application hosting environment; we employ a novel parallel in situ visualization approach which is particularly suited for such computations on petascale resources. We present computational and I/O performance benchmarks of our application on three different petascale systems.

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Chen, Qilai, Tingting Han, Jianmin Zeng, Zhilong He, Yulin Liu, Jinglin Sun, Minghua Tang, Zhang Zhang, Pingqi Gao, and Gang Liu. "Perovskite-Based Memristor with 50-Fold Switchable Photosensitivity for In-Sensor Computing Neural Network." Nanomaterials 12, no. 13 (June 28, 2022): 2217. http://dx.doi.org/10.3390/nano12132217.

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In-sensor computing can simultaneously output image information and recognition results through in-situ visual signal processing, which can greatly improve the efficiency of machine vision. However, in-sensor computing is challenging due to the requirement to controllably adjust the sensor’s photosensitivity. Herein, it is demonstrated a ternary cationic halide Cs0.05FA0.81MA0.14 Pb(I0.85Br0.15)3 (CsFAMA) perovskite, whose External quantum efficiency (EQE) value is above 80% in the entire visible region (400–750 nm), and peak responsibility value at 750 nm reaches 0.45 A/W. In addition, the device can achieve a 50-fold enhancement of the photoresponsibility under the same illumination by adjusting the internal ion migration and readout voltage. A proof-of-concept visually enhanced neural network system is demonstrated through the switchable photosensitivity of the perovskite sensor array, which can simultaneously optimize imaging and recognition results and improve object recognition accuracy by 17% in low-light environments.

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Li, Ruixuan, Takaya Yuizono, and Xianghui Li. "Affective computing of multi-type urban public spaces to analyze emotional quality using ensemble learning-based classification of multi-sensor data." PLOS ONE 17, no. 6 (June 3, 2022): e0269176. http://dx.doi.org/10.1371/journal.pone.0269176.

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The quality of urban public spaces affects the emotional response of users; therefore, the emotional data of users can be used as indices to evaluate the quality of a space. Emotional response can be evaluated to effectively measure public space quality through affective computing and obtain evidence-based support for urban space renewal. We proposed a feasible evaluation method for multi-type urban public spaces based on multiple physiological signals and ensemble learning. We built binary, ternary, and quinary classification models based on participants’ physiological signals and self-reported emotional responses through experiments in eight public spaces of five types. Furthermore, we verified the effectiveness of the model by inputting data collected from two other public spaces. Three observations were made based on the results. First, the highest accuracies of the binary and ternary classification models were 92.59% and 91.07%, respectively. After external validation, the highest accuracies were 80.90% and 65.30%, respectively, which satisfied the preliminary requirements for evaluating the quality of actual urban spaces. However, the quinary classification model could not satisfy the preliminary requirements. Second, the average accuracy of ensemble learning was 7.59% higher than that of single classifiers. Third, reducing the number of physiological signal features and applying the synthetic minority oversampling technique to solve unbalanced data improved the evaluation ability.

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Ahmed, Faisal, and Emam Hossain. "Automated Facial Expression Recognition Using Gradient-Based Ternary Texture Patterns." Chinese Journal of Engineering 2013 (December 25, 2013): 1–8. http://dx.doi.org/10.1155/2013/831747.

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Recognition of human expression from facial image is an interesting research area, which has received increasing attention in the recent years. A robust and effective facial feature descriptor is the key to designing a successful expression recognition system. Although much progress has been made, deriving a face feature descriptor that can perform consistently under changing environment is still a difficult and challenging task. In this paper, we present the gradient local ternary pattern (GLTP)—a discriminative local texture feature for representing facial expression. The proposed GLTP operator encodes the local texture of an image by computing the gradient magnitudes of the local neighborhood and quantizing those values in three discrimination levels. The location and occurrence information of the resulting micropatterns is then used as the face feature descriptor. The performance of the proposed method has been evaluated for the person-independent face expression recognition task. Experiments with prototypic expression images from the Cohn-Kanade (CK) face expression database validate that the GLTP feature descriptor can effectively encode the facial texture and thus achieves improved recognition performance than some well-known appearance-based facial features.

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Thakare, Vaishali R., and K. John Singh. "An efficient ternary tree-based TGDH protocol for dynamic secure group data sharing in cloud computing." International Journal of Embedded Systems 10, no. 4 (2018): 273. http://dx.doi.org/10.1504/ijes.2018.093686.

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Thakare, Vaishali R., and K. John Singh. "An efficient ternary tree-based TGDH protocol for dynamic secure group data sharing in cloud computing." International Journal of Embedded Systems 10, no. 4 (2018): 273. http://dx.doi.org/10.1504/ijes.2018.10014924.

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Tarkov, Mikhail, Fedor Tikhonenko, Vladimir Popov, Valentin Antonov, Andrey Miakonkikh, and Konstantin Rudenko. "Ferroelectric Devices for Content-Addressable Memory." Nanomaterials 12, no. 24 (December 19, 2022): 4488. http://dx.doi.org/10.3390/nano12244488.

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In-memory computing is an attractive solution for reducing power consumption and memory access latency cost by performing certain computations directly in memory without reading operands and sending them to arithmetic logic units. Content-addressable memory (CAM) is an ideal way to smooth out the distinction between storage and processing, since each memory cell is a processing unit. CAM compares the search input with a table of stored data and returns the matched data address. The issues of constructing binary and ternary content-addressable memory (CAM and TCAM) based on ferroelectric devices are considered. A review of ferroelectric materials and devices is carried out, including on ferroelectric transistors (FeFET), ferroelectric tunnel diodes (FTJ), and ferroelectric memristors.

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Zhi-Chang, Wang, Reinhard Lück, and Bruno Predel. "New models for computing thermodynamic properties and phase diagrams of ternary systems Part 1. Three-factor models." Calphad 14, no. 3 (July 1990): 217–34. http://dx.doi.org/10.1016/0364-5916(90)90023-s.

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Zhi-chang, Wang, Reinhard Lück, and Bruno Predel. "New models for computing thermodynamic properties and phase diagrams of ternary systems Part 2. Multi-factor models." Calphad 14, no. 3 (July 1990): 235–56. http://dx.doi.org/10.1016/0364-5916(90)90024-t.

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Calderón, Silvia M., Jussi Malila, and Nønne L. Prisle. "Model for estimating activity coefficients in binary and ternary ionic surfactant solutions." Journal of Atmospheric Chemistry 77, no. 4 (November 7, 2020): 141–68. http://dx.doi.org/10.1007/s10874-020-09407-4.

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AbstractWe introduce the CMC based Ionic Surfactant Activity model (CISA) to calculate activity coefficients in ternary aqueous solutions of an ionic surfactant and an inorganic salt. The surfactant can be either anionic or cationic and in the present development, the surfactant and inorganic salts share a common counterion. CISA incorporates micellization into the Pitzer–Debye–Hückel (PDH) framework for activities of mixed electrolyte solutions. To reduce computing requirements, a parametrization of the critical micelle concentration (CMC) is used to estimate the degree of micellization instead of explicit equilibrium calculations. For both binary and ternary systems, CISA only requires binary experimentally-based parameters to describe water–ion interactions and temperature–composition dependency of the CMC. The CISA model is intended in particular for atmospheric applications, where higher-order solution interaction parameters are typically not constrained by experiments and the description must be reliable across a wide range of compositions. We evaluate the model against experimental activity data for binary aqueous solutions of ionic surfactants sodium octanoate and sodium decanoate, as common components of atmospheric aerosols, and sodium dodecylsulfate, the most commonly used model compound for atmospheric surfactants. Capabilities of the CISA model to describe ternary systems are tested for the water–sodium decanoate–sodium chloride system, a common surrogate for marine background cloud condensation nuclei and to our knowledge the only atmospherically relevant system for which ternary activity data is available. For these systems, CISA is able to provide continuous predictions of activity coefficients both below and above CMC and in all cases gives an improved description of the water activity above the CMC, compared to the alternative model of Burchfield and Wolley [J. Phys. Chem., 88(10), 2149–2155 (1984)]. The water activity is a key parameter governing the formation and equilibrium growth of cloud droplets. The CISA model can be extended from the current form to include the effect of other inorganic salts with the existing database of binary PDH parameters and using appropriate mixing rules to account for ion specificity in the micellization process.

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CASSAIGNE, JULIEN, MARC ESPIE, DANIEL KROB, JEAN-CHRISTOPHE NOVELLI, and FLORENT HIVERT. "THE CHINESE MONOID." International Journal of Algebra and Computation 11, no. 03 (June 2001): 301–34. http://dx.doi.org/10.1142/s0218196701000425.

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Résumé: Cet article présente une étude combinatoire du monoïde Chinois, un monoïde ternaire proche du monoïde plaxique, fondé sur le schéma cba≡bca≡cab. Un algorithme proche de l'algorithme de Schensted nous permet de caractériser les classes d'équivalence et d'exhiber une section du monoïde. Nous énonçons également une correspondance de Robinson–Schensted pour le monoïde Chinois avant de nous intéresser au calcul du cardinal de certaines classes. Ce travail a permis de développer de nouveaux outils combinatoires. Entre autres, nous avons trouvé un plongement de chacune des classes d'équivalence dans la plus grande classe. Quant à la dernière partie de cet article, elle présente l'étude des relations de conjugaison. This paper presents a combinatorial study of the Chinese monoid, a ternary monoid related to the plactic monoid and based on the relation scheme cba≡bca≡cab. An algorithm similar to Schensted's algorithm yields a characterization of the equivalence classes and a cross-section theorem. We also establish a Robinson–Schensted correspondence for the Chinese monoid before computing the order of specific Chinese classes. For this work, we had to develop some new combinatorial tools. Among other things we discovered an embedding of every equivalence class in the largest one. Finally, the end of this paper is devoted to the study of conjugacy classes.

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RAVIKUMAR, BALA. "THE BENFORD-NEWCOMB DISTRIBUTION AND UNAMBIGUOUS CONTEXT-FREE LANGUAGES." International Journal of Foundations of Computer Science 19, no. 03 (June 2008): 717–27. http://dx.doi.org/10.1142/s0129054108005905.

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For a string w ∈ {0,1, 2,…, d-1}*, let vald(w) denote the integer whose base d representation is the string w and let MSDd(x) denote the most significant or the leading digit of a positive integer x when x is written as a base d integer. Hirvensalo and Karhumäki [9] studied the problem of computing the leading digit in the ternary representation of 2x ans showed that this problem has a polynomial time algorithm. In [16], some applications are presented for the problem of computing the leading digit of AB for given inputs A and B. In this paper, we study this problem from a formal language point of view. Formally, we consider the language Lb,d,j = {w|w ∈ {0,1, 2,…, d-1}*, 1 ≤ j ≤ 9, MSDb(dvalb(w))) = j} (and some related classes of languages) and address the question of whether this and some related languages are context-free. Standard pumping lemma proofs seem to be very difficult for these languages. We present a unified and simple combinatorial technique that shows that these languages are not unambiguous context-free languages. The Benford-Newcomb distribution plays a central role in our proofs.

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Deng, Weiping, Qing Wei, and Xuan Liu. "A New Density Model of Quartz Solubility in H2O-CO2-NaCl Ternary Systems up to High Temperatures and High Pressures." Geofluids 2021 (February 12, 2021): 1–23. http://dx.doi.org/10.1155/2021/6631152.

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A novel density model for computing quartz solubility in H2O-CO2-NaCl hydrothermal fluids applicable to wide ranges of temperature and pressure is proposed. Based on the models of Akinfiev and Diamond (2009) and Wei et al. (2012), the effective partial molar volume of water ( V H 2 O ∗ ) is replaced by the partial molar volume of water ( V ¯ H 2 O ) by implementing an empirical correction, and water molar fraction ( x H 2 O ) is modified with water activity ( a H 2 O ), in addition to a series of changes to the model coefficient forms. The absolute values of averaged relative deviation of this model compared to the experimental data sets in pure water, H2O-CO2, and H2O-NaCl solutions are 5.74%, 6.69%, and 7.09%, respectively, which are better than existing models in the literature. The model can be reliably used for computing quartz solubilities in pure water from 0°C to 1000°C, from 0 bar to 20,000 bar, and in CO2- and/or NaCl-bearing solutions from 0°C to 1000°C, from 0 bar to 10,000 bar (with slightly lower accuracy at 5000-10,000 bar in H2O-NaCl systems) in the single liquid region. Moreover, the trends and overall ranges of this model may probably be more accurate in the H2O-CO2-NaCl fluid mixtures compared to the limited experimental data. In addition, a bisection algorithm for deriving the isopleths of quartz solubilities based on this new model is first proposed, and application perspectives are discussed for various geologic settings including subduction zone, lower crust-upper mantle, migmatite, pegmatite, porphyry, and orogenic deposits.

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Mattedi, Giulio, Silvia Acosta-Gutiérrez, Timothy Clark, and Francesco Luigi Gervasio. "A combined activation mechanism for the glucagon receptor." Proceedings of the National Academy of Sciences 117, no. 27 (June 22, 2020): 15414–22. http://dx.doi.org/10.1073/pnas.1921851117.

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We report on a combined activation mechanism for a class B G-protein–coupled receptor (GPCR), the glucagon receptor. By computing the conformational free-energy landscape associated with the activation of the receptor–agonist complex and comparing it with that obtained with the ternary complex (receptor–agonist–G protein) we show that the agonist stabilizes the receptor in a preactivated complex, which is then fully activated upon binding of the G protein. The proposed mechanism contrasts with the generally assumed GPCR activation mechanism, which proceeds through an opening of the intracellular region allosterically elicited by the binding of the agonist. The mechanism found here is consistent with electron cryo-microscopy structural data and might be general for class B GPCRs. It also helps us to understand the mode of action of the numerous allosteric antagonists of this important drug target.

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Morell, Antoni, Elvis Díaz Machado, Enrique Miranda, Guillem Boquet, and Jose Lopez Vicario. "Ternary Neural Networks Based on on/off Memristors: Set-Up and Training." Electronics 11, no. 10 (May 10, 2022): 1526. http://dx.doi.org/10.3390/electronics11101526.

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Neuromorphic systems based on hardware neural networks (HNNs) are expected to be an energy and time-efficient computing architecture for solving complex tasks. In this paper, we consider the implementation of deep neural networks (DNNs) using crossbar arrays of memristors. More specifically, we considered the case where such devices can be configured in just two states: the low-resistance state (LRS) and the high-resistance state (HRS). HNNs suffer from several non-idealities that need to be solved when mapping our software-based models. A clear example in memristor-based neural networks is conductance variability, which is inherent to resistive switching devices, so achieving good performance in an HNN largely depends on the development of reliable weight storage or, alternatively, mitigation techniques against weight uncertainty. In this manuscript, we provide guidelines for a system-level designer where we take into account several issues related to the set-up of the HNN, such as what the appropriate conductance value in the LRS is or the adaptive conversion of current outputs at one stage to input voltages for the next stage. A second contribution is the training of the system, which is performed via offline learning, and considering the hardware imperfections, which in this case are conductance fluctuations. Finally, the resulting inference system is tested in two well-known databases from MNIST, showing that is competitive in terms of classification performance against the software-based counterpart. Additional advice and insights on system tuning and expected performance are given throughout the paper.

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Journal articles on the topic 'Ternary computing'

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