Gray Code Research Articles

Pivot Gray Codes for the Spanning Trees of a Graph ft. the Fan

Pivot Gray Codes for the Spanning Trees of a Graph ft. the Fan

Design of energy, cost-efficient binary to gray code converter with temperature and stability analysis

The Quantum Dot Cellular Automata (QCA) is an emerging quantum electronics technology in which quantum cells are the fundamental building blocks. In this work, a Binary to Gray (BTG) code converter design is proposed and implemented using the QCA Designer Tool. This code converter design requires fewer cells than earlier designs and also increases the converter’s implementation bit size to five. The primary objective of this proposal is to introduce a BTG code converter design that excels in temperature stability and energy efficiency. The cell count in the proposed converter design for two-bit, three-bit, and four-bit is decreased by 68.55 %, 66.52 %, and 67.77 %, respectively and the overall area improved by 46.15 %, 52.17 %, and 57.58 % for 2- bit,3-bit and 4-bit, respectively by considering a latency of 0.75. The five-bit BTG has an area of 0.20 µm2 with a cell count of 141 and a latency of 0.75. To validate the functionality of the proposed design, extensive simulations were carried out using the QCA Designer tool, QCA DesignerE tool, and QCA Pro tool respectively.

Another Infinite Family of Binary Cyclic Codes With Best Parameters Known

Another Infinite Family of Binary Cyclic Codes With Best Parameters Known

Numerical Analysis of All-Optical Binary to Gray Code Converter Using Silicon Microring Resonator

Numerical Analysis of All-Optical Binary to Gray Code Converter Using Silicon Microring Resonator

Accurate and Real-Time Variant Hand Pose Estimation Based on Gray Code Bounding Box Representation

Accurate and Real-Time Variant Hand Pose Estimation Based on Gray Code Bounding Box Representation

The grey decision model and its application based on generalized greyness of interval grey number

PurposeIn order to solve the decision-making problem that the attributive weight and attributive value are both interval grey numbers, this paper tries to construct a multi-attribute grey decision-making model based on generalized greyness of interval grey number.Design/methodology/approachFirstly, according to the nature of the generalized gresness of interval grey number, the generalized weighted greyness distance between interval grey numbers is given, and the transformation relationship between greyness distance and real number distance is analyzed. Then according to the objective function that the square sum of generalized weighted greyness distances from the decision scheme to the best scheme and the worst scheme is the minimum, a multi-attribute grey decision-making model is constructed, and the simplified form of the model is given. Finally, the grey decision-making model proposed in this paper is applied to the evaluation of technological innovation capability of 6 provinces in China to verify the effectiveness of the model.FindingsThe results show that the grey decision-making model proposed in this paper has a strict mathematical foundation, clear physical meaning, simple calculation and easy programming. The application example shows that the grey decision model in this paper is feasible and effective. The research results not only enrich the grey system theory, but also provide a new way for the decision-making problem that the attributive weights and attributive values are interval grey numbers.Practical implicationsThe decision-making model proposed in this paper does not need to seek the optimal solution of the attributive weight and the attributive value, and can save the decision-making labor and capital investment. The model in this paper is also suitable for the decision-making problem that deals with the coexistence of interval grey numbers and real numbers.Originality/valueThe paper succeeds in realizing the multi-attribute grey decision-making model based on generalized gresness and its simplified forms, which provide a new method for grey decision analysis.

DNA Molecular Computation Using the CRISPR-Mediated Reaction and Surface Growth of Gold Nanoparticles.

DNA has emerged as a promising tool to build logic gates for biocomputing. However, prevailing methodologies predominantly rely on hybridization reactions or structural alterations to construct DNA logic gates, which are limited in simplicity and diversity. Herein, we developed simple and smart DNA-based logic gates for biocomputing through the DNA-mediated growth of gold nanomaterials without precise structure design and probe modification. Capitalizing on their excellent plasmonic properties, the surface growth of gold nanomaterials enables distinct wavelength shifts and unique shapes, which are modulated by the composition, length, and concentration of the DNA sequences. Combined with a CRISPR-mediated reaction, we constructed DNA circuits to achieve complicated biocomputing to modulate the surface growth of gold nanomaterials. By implementing logic functions controlled by input-mediated growth of gold nanomaterials, we established YES/NOT, AND/NAND, OR/NOR, XOR, and INHIBIT gates and further constructed cascade logic circuits, parity checker for natural numbers, and gray code encoder, which are promising for DNA biocomputing.

Application of STBC in MIMO-OFDM Broadband Wireless Communications

The Space Time Block Coding (STBC) is applied in multiple transmit antennas using data transfer for fading channels. After being encoded, the data is broken into n streams of continuously broadcast strings over n transmit antennas using STBC. The received signal is the combination of n broadcast signals and it becomes erroneous due to the entry of noise at receiver end. The probabilistic decoding approach is applied instead of joint detection approach for recovering data via decoupling of signals delivered from various antennas. The maximum likelihood decoding scheme employs the orthogonal structure of STBC called as OSTBC (Orthogonal Space Time Block Code) for providing the maximum likelihood decoding algorithm depending upon linear computation at receiver. In the present work, a MATLAB/SIMULINK environment of OSTBC has been used in order to acquire the highest dimension of variability for specific number of broadcasts as well as receive antennas utilizing a simple decoding techniques. With or without Grey Coding, OSTBC / STBC is used in MATLAB / SIMULINK blocs. The OSTBC algorithm calculates the highest achievable transmission rate for every amount of transmit antennas in any constellations including M-PSK array. M-PSK STBCs are used for different complex constellations to achieve ½ as well as ¾ of highest allowable transmission rate for Multiple Input Multiple Output (MIMO) transmit antennas utilizing various constellations

Enhancement of the Defining Interrelationships Between Ranked Criteria II Method Using Interval Grey Numbers for Application in the Grey-Rough MCDM Model

Enhancement of the Defining Interrelationships Between Ranked Criteria II Method Using Interval Grey Numbers for Application in the Grey-Rough MCDM Model

Efficient preparation of lossless quantum images based on Gray code

Efficient preparation of lossless quantum images based on Gray code

Grey conflict analysis approach with constraints

PurposeWe attempt to construct a grey three-way conflict analysis model with constraints to deal with correlated conflict problems with uncertain information.Design/methodology/approachIn order to address these correlated conflict problems with uncertain information, considering the interactive influence and mutual restraints among agents and portraying their attitudes toward the conflict issues, we utilize grey numbers and three-way decisions to propose a grey three-way conflict analysis model with constraints. Firstly, based on the collected information, we introduced grey theory, calculated the degree of conflict between agents and then analyzed the conflict alliance based on the three-way decision theory. Finally, we designed a feedback mechanism to identify key agents and key conflict issues. A case verifies the effectiveness and practicability of the proposed model.FindingsThe results show that the proposed model can portray their attitudes toward conflict issues and effectively extract conflict-related information.Originality/valueBy employing this approach, we can provide the answers to Deja’s fundamental questions regarding Pawlak’s conflict analysis: “what are the underlying causes of conflict?” and “how can a viable consensus strategy be identified?”

A 500 mVpp Input Range First-Order VCO-Based ADC with a Multi-Phase Quantizer for EEG Recording Front Ends

This paper proposes a VCO-based ADC with first-order noise shaping for EEG signal recording front ends. Addressing the challenge of applying analog integrators in advanced processes due to low voltage issues, a multi-phase quantizer structure is introduced based on V-F conversion within the VCO structure, resulting in lower analog power consumption at the same output bit-width. By introducing a form of Gray code encoding, errors caused by circuit metastability are limited to within 1 bit. Considering the effects of motion artifacts and the electrode DC offset, the circuit achieves a wide input range of 500 mVpp by adjusting the feedback coefficients. A prototype ADC is fabricated using 180 nm CMOS technology, operating at a 1.8 V/1 V power supply voltage, with power consumption of 17.1 μW, while achieving a 62.1 dB signal-to-noise and distortion ratio (SNDR) and 55.2 dB dynamic range (DR). The proposed ADC exhibits input noise of 8.64 μVrms within a bandwidth of 0.5 Hz–5 kHz.

Efficient Multi-stimulus-Responsive Luminescent Eu(III)-Modified HOFs Materials: Detecting Thiram and Caffeic Acid and Constructing a Flexible Substrate Anti-counterfeiting Platform.

The powerful capability of multi-stimulus-responsive luminescent hydrogen-bonded organic frameworks (HOFs) to respond to external chemical or physical stimuli in various manners makes them appealing in the luminescence anti-counterfeiting field. Herein, a novel Eu3+-functionalized HOF (Eu@GC-2) that combines the emission of HOFs with the characteristic emission of Eu3+ ions has been successfully synthesized, which can generate various fluorescence at different excitation wavelengths. Eu@GC-2 has enormous potential as a raw material for a paper-based sensor that is designed for detecting the pesticides thiram and caffeic acid in crops with favorable selectivity, anti-interference, and high efficiency. Based on the above excellent properties, Ln3+-functionalized HOFs (Ln@GC-2) were then employed to produce four luminescent anti-counterfeiting inks. With the incorporation of back-propagation neural network and Gray code conversion functions, a multi-stimulus-responsive luminescent anti-counterfeiting platform, coregulated by the excitation light and the chemical reagent, has been constructed. This approach can not only achieve multiple encryptions and fast information identification but also enhance the code-breaking complexity, making it an efficient strategy for information encryption and decryption.

A ternary complementary Gray code phase unwrapping method in fringe projection profilometry

This paper proposes a phase unwrapping method based on ternary Gray code in fringe projection profilometry. This method does not require additional projection images or any prior knowledge. It accurately determines the segmentation thresholds of the ternary Gray code using only the average intensity and intensity modulation calculated from phase-shifting fringes, effectively reducing projection costs and achieving lower codeword errors. Additionally, a segment selection strategy suitable for the ternary Gray code is proposed. By employing the complementary method, three sets of candidate orders with certain codeword shifts can be generated. The wrapped phase is then divided into three segments: upper, middle, and lower segments, and correspondingly matched with the central regions of the three sets of candidate orders, thus enabling the solution of the absolute phase. Through the segment selection strategy, error-prone areas at the edges of orders are effectively avoided, further enhancing the accuracy of measurement results. Compared to the binary Gray code, the ternary complementary Gray code can encode up to 3m−1 orders when the number of Gray code patterns is m; when the required number of encoding orders is K, only ⌈log3K⌉+1 Gray code patterns are needed. Its additional value capacity precisely enables it to encode more orders, thereby increasing the frequency of phase-shifting fringes and further enhancing measurement efficiency. A series of experiments validates the feasibility, robustness, and superiority of this method.

An Infinite Family of Binary Cyclic Codes With Best Parameters

An Infinite Family of Binary Cyclic Codes With Best Parameters

A Performance Evaluation Approach for Satellite Attitude Control System in Tracking Mode

The study of satellite performance evaluation can reveal the ability of satellite systems to fulfil corresponding tasks in the space environment, and provide information support for the resource allocation and mission scheduling of in-orbit satellites. In this paper, we took the satellite attitude control system in attitude tracking mode as the research object. In accordance with the system’s mission requirements, the control performance evaluation indicator set, characterized by a generalized grey number, is constructed to tackle the uncertainty and inadequacy of information contained in flight status data resulting from the complex space operating environment and sensor measurement noise. An improved principal component analysis method based on generalized grey number is proposed to solve the weight amplification caused by the correlation between performance indicators and realize the weight allocation of the indicators. Finally, the grey-target decision model is established to determine the weights of the performance indicators, and the performance evaluation model is established under the tracking mode. The feasibility of the grey-target decision-evaluation model based on the improved principal component is confirmed through comparative experiments.

Towards healthy cities: Modeling restorative potential of urban environments by coupling LiDAR-derived 3D metrics with panorama-based online survey

With the growing concern for the psychological well-being of urban dwellers, there has been a recognized need to explore the role of green environments in facilitating mental restorative benefits from the demands of city life. However, a significant gap exists in quantitatively modeling the restorative potential of urban environments, especially in terms of comprehensive 3D characteristics beyond mere greenery. This research gap has hindered our understanding of how to plan and design urban spaces that promote mental health. To bridge this gap, we conducted a study using Singapore as a case study to model the restorative potential for landscape planning and design by integrating LiDAR-derived 3D metrics, outcomes of an online survey, and a machine learning-based regularized regression model. We first collected data from 100 scenes, including both residential neighborhoods and urban parks, by extracting point cloud information from LiDAR scans for calculating a diverse set of 41 3D spatial metrics. Alongside these objective measurements, we conducted an online survey (N = 1500) using the Perceived Restorativeness Scale (PRS) where respondents evaluated the restorative potential of these scenes presented as interactive panoramic images. We subsequently utilized a regularized regression technique based on machine learning by conducting K-fold cross-validation (K = 10) with 1251 tests to identify the feature metrics significantly contributing to restorative potential. Our findings highlighted the importance of the green volumetric ratio as the most significant positive factor for restorative potential. Additionally, the results on the metrics of grey horizontal diversity and grey cluster number indicated a positive impact of unregulated and unaggregated grey components on restorative potential. The results on green horizontal diversity suggested that a uniform and concentrated spatial arrangement of greenery is a positive predictor, while other factors like front-background ratio, colorfulness, and slope variation also positively influenced restorative potential. In essence, our study not only provides novel insights but also introduces innovative methods for quantitatively assessing and characterizing the quality of urban environments that enhance psychological well-being. These findings inform the practical planning and design strategies aimed at fostering healthy and sustainable urban spaces.

Optimizing Data Transfer Across Asynchronous Clock Domains: A Comprehensive Approach to Asynchronous FIFO Circuit Design

As integrated circuit (IC) design continues to advance in scale, there is a growing trend towards integrating more components onto the same IC board, resulting in larger circuit boards. These expanded circuit boards often encompass diverse asynchronous clock domains, leading to inevitable data transfer challenges between these distinct clock domains. This research article focuses on Verilog-based asynchronous first in first out (FIFO) design as a solution to effectively address this issue and offers a robust design approach to enhance circuit integration and stability. By employing conventional asynchronous FIFO design principles, such as the utilization of binary conversion Gray code to synchronize clock operations for pointer-to-address mapping and the incorporation of empty/full flag status bits to facilitate empty/full signal generation determination, seamless data transfer between various asynchronous clock domains is successfully achieved. Furthermore, this article includes comprehensive testing and simulation using Testbench to validate the asynchronous FIFO circuit, with successful results. The primary objective of this article is to present a well-established and comprehensive design methodology for asynchronous FIFO circuits, equipping designers with a mature and reliable approach to tackle the challenges posed by increasingly complex IC designs.

APPLICATION OF PFAHP-GTOPSIS METHODS FOR THIRD-PARTY LOGISTICS PROVIDER SELECTION

Companies are now considering the option of outsourcing as hedges cost and increase productivity by concentrating on their core skills to update their supply chains due to the competition in global markets, the use of higher-quality products, and rising customer demands. They must carefully select and identify which company to collaborate with before outsourcing their numerous logistics-related tasks to Third-Party Logistics Providers (3PLP). However, the existence of uncertainties and human influence in 3PLP selection problems leads to the usage of fuzzy or related set theories. By incorporating Multi-Criteria Decision Making (MCDM) methods with fuzzy numbers and grey numbers, practical tools can be composed to address the imprecision of subjective judgments. From this perspective, an integrated MCDM model is proposed to provide insight into the 3PLP evaluation and selection. The model comprises an integrated framework with Pythagorean fuzzy numbers and grey numbers. The proposed model has applied a 3PLP a company in the food industry to fulfill customer orders. The evaluation criteria weights are calculated using the Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) method, and the 3PLPs are ranked using the grey Technique for Order Preference by Similarity to Ideal Solution (GTOPSIS) methods to find the best 3PLP. The analyses and findings concluded that cost, service quality, and on-time delivery were the three criteria that had the greatest influence

Grey preference for analyzing the influence of externality within the graph model for conflict resolution

Externality may have uncertain influence on decision makers (DMs). To address the conflicts with uncertain preference and externality, this study adopts the general grey number to measure the uncertain value of DMs’ option statements influenced by externality. It constructs adjustable grey preference influenced by externality (GPE), which can be dynamically adjusted according to the influence of externality. Subsequently, the study defines four equilibrium solutions for the graph model for conflict resolution based on grey preference influenced by externality (GPE-GMCR). Finally, the method is applied to a commercial bank operating conflict triggered by the Silicon Valley Bank (SVB) collapse in the United States, resulting in optimal results for conflict resolution. Specifically, the new model provides a practical tool for DMs, managers and policy makers to address conflicts arising from DMs’ uncertain preference under the influence of externality in complex environments.