scholarly journals Foundations for Applications of Gibbs Derivatives in Logic Design and VLSI

VLSI Design ◽  
2002 ◽  
Vol 14 (1) ◽  
pp. 65-81 ◽  
Author(s):  
Radomir S. Stanković ◽  
Milena Stanković ◽  
Reiner Creutzburg
Keyword(s):  
New Technologies ◽  
Differential Operators ◽  
Rate Of Change ◽  
Logic Design ◽  
Logic Function ◽  
Spectral Techniques ◽  
Cad Systems ◽  
Vlsi Cad ◽  
Efficient Calculation ◽  
Logic Functions

New technologies and increased requirements for performances of digital systems require new mathematical theories and tools as a basis for future VLSI CAD systems. New or alternative mathematical approaches and concepts must be suitable to solve some concrete problems in VLSI and efficient algorithms for their efficient application should be provided. This paper is an attempt in this direction and relates with the recently renewed interest in arithmetic expressions for switching functions, instead representations in Boolean structures, and spectral techniques and differential operators in switching theory and applications. Logic derivatives are efficiently used in solving different tasks in logic design, as for example, fault detection, functional decomposition, detection of symmetries and co-symmetries of logic functions, etc. Their application is based on the property that by differential operators, we can measure the rate of change of a logic function. However, by logic derivatives, we can hardly distinguish the direction of the change of the function, since they are defined in finite algebraic structures. Gibbs derivatives are a class of differential operators on groups, which applied to logic functions, permit to overcome this disadvantage of logic derivatives. Therefore, they may be useful in logic design in the same areas where the logic derivatives have been already using. For such applications, it is important to provide fast algorithms for calculation of Gibbs derivatives on finite groups efficiently in terms of space and time. In this paper, we discuss the methods for efficient calculation of Gibbs derivatives. These methods should represent a basis for further applications of these and related operators in VLSI CAD systems.

scholarly journals LOCAL AND NONLOCAL DIFFERENTIAL OPERATORS: A COMPARATIVE STUDY OF HEAT AND MASS TRANSFERS IN MHD OLDROYD-B FLUID WITH RAMPED WALL TEMPERATURE

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040033 ◽  
Author(s):  
MUHAMMAD BILAL RIAZ ◽  
ABDON ATANGANA ◽  
THABET ABDELJAWAD
Keyword(s):  
Wall Temperature ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Differential Operators ◽  
Classical Mechanics ◽  
Rate Of Change ◽  
Dynamical Process ◽  
New Class ◽  
Mass Transfers ◽  
And Inversion

Study of heat and mass transfers is carried out for MHD Oldroyd-B fluid (OBF) over an infinite vertical plate having time-dependent velocity and with ramped wall temperature and constant concentration. It is proven in many already published articles that the heat and mass transfers do not really or always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such dynamical process very accurately, thus, a different concept of differentiation is needed to capture such process. Very recently, a new class of differential operators were introduced and have been recognized to be efficient in capturing processes following the power-law, the decay law and the crossover behaviors. For the study of heat and mass transfers, we applied the newly introduced differential operators to model such flow and compare the results with integer-order derivative. Laplace transform and inversion algorithms are used for all the cases to find analytical solutions and to predict the influences of different parameters. The obtained analytical solutions were plotted for different values of fractional orders [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] on the velocity field. In comparison, Atangana–Baleanu (ABC) fractional derivatives are found to be the best to explain the memory effects than the classical, Caputo (C) and Caputo–Fabrizio (CF) fractional derivatives. Some calculated values for Nusselt number and Sherwood number are presented in tables. Moreover, from the present solutions, the already published results were found as limiting cases.

DESIGN AND APPLICATION OF AN INTERACTIVE WHEELCHAIR TRAINING SYSTEM

2008 ◽  
Vol 20 (06) ◽  
pp. 377-385 ◽  
Author(s):  
Chern-Sheng Lin ◽  
Chia-Chang Chang ◽  
Wei-Lung Chen
Keyword(s):  
Control Function ◽  
Training System ◽  
Digital Logic ◽  
3D Simulation ◽  
Initial Time ◽  
Logic Function ◽  
Wheelchair Users ◽  
Rehabilitation Training ◽  
Direction Control ◽  
Logic Functions

In this paper we constructed an interactive wheelchair rehabilitation training platform. The roller wheel on the platform is driven mainly by turning the wheelchair, and then the relative position of wheelchair on the screen can be adjusted based on the rotation speed of left and right wheels on the platform. Comparing the digital logic function when two wheels rotate at the same time and judging the variance in digital logic, the steering direction of wheels can be known and be controlled forward or backward. Additionally, the standard digital logic function could be individually judged when left wheel rotates and vice versa, so as to control the steering. Through judging three digital logic functions, the initial time of left wheel, next signal selecting time of left wheel, initial time of right wheel, and next signal selecting time of right wheel could be obtained, then the system can achieve the required direction control function through the judgment formula. The direction control function is indicated by standard digital logic function, so that the user can operate smoothly in the interactive situation software and make an interaction with the computer 3D simulation scene, the patient would have rehabilitation training through various 3D simulation real exteriors. This study not only provides basic trainings but also records the service behavior of wheelchair users, so that the rehabilitation consultant would have reference for the future diagnosis.

3D Visualization Model and Sample Implementation of 0-1 Function on Variant Logic

2013 ◽  
Vol 718-720 ◽  
pp. 480-483
Author(s):  
Huan Wang ◽  
Jie Ao Zhu ◽  
Xue Liu ◽  
Jeffrey Zheng
Keyword(s):  
Data Visualization ◽  
3D Visualization ◽  
Random Sequence ◽  
Relevant Logic ◽  
Complex Data ◽  
Paper Sample ◽  
Logic Function ◽  
Visual Model ◽  
Logic Functions ◽  
Visual Results

Random sequences generated by different logic functions play an important role in cryptography. The structure and the special properties of the logic function has been one of the most active areas of research. In order to study the random sequence and its related logic functions, many models have been established, and different advanced tools are applied to make complex data visualization. In this paper, sample logic functions are transferred into variant logic expressions to form a set of measurements. Using selected measurements, a 3D visual model is proposed. Selected 3D visual results are shown their intrinsic 3D spatial characteristics of relevant logic functions respectively.

scholarly journals Study of T-norms and Quantum Logic Functions on BL-algebra and Their Relationships to the Classical Probability Structures

2020 ◽  
pp. 591-599
Author(s):  
Ahmed AL-Adilee ◽  
Habeeb Kareem Abdullah ◽  
Hawraa A. AL-Challabi
Keyword(s):  
Quantum Logic ◽  
Probability Space ◽  
Binary Operation ◽  
The Other ◽  
Symmetric Difference ◽  
Logic Function ◽  
Classical Probability ◽  
Binary Operations ◽  
Basic Probability ◽  
Logic Functions

This paper is concerned with the study of the T-norms and the quantum logic functions on BL-algebra, respectively, along with their association with the classical probability space. The proposed constructions depend on demonstrating each type of the T-norms with respect to the basic probability of binary operation. On the other hand, we showed each quantum logic function with respect to some binary operations in probability space, such as intersection, union, and symmetric difference. Finally, we demonstrated the main results that explain the relationships among the T-norms and quantum logic functions. In order to show those relations and their related properties, different examples were built.

scholarly journals Synthetic metabolic computation in a bioluminescence-sensing system

2019 ◽  
Vol 47 (19) ◽  
pp. 10464-10474 ◽  
Author(s):  
Natalia Barger ◽  
Phyana Litovco ◽  
Ximing Li ◽  
Mouna Habib ◽  
Ramez Daniel
Keyword(s):  
Protein Interactions ◽  
Detection Threshold ◽  
Living Cells ◽  
Genetic Circuit ◽  
Biological Research ◽  
Protein Protein Interactions ◽  
Genetic Circuits ◽  
Logic Function ◽  
Single Input ◽  
Logic Functions

Abstract Bioluminescence is visible light produced and emitted by living cells using various biological systems (e.g. luxCDABE cassette). Today, this phenomenon is widely exploited in biological research, biotechnology and medical applications as a quantitative technique for the detection of biological signals. However, this technique has mostly been used to detect a single input only. In this work, we re-engineered the complex genetic structure of luxCDABE cassette to build a biological unit that can detect multi-inputs, process the cellular information and report the computation results. We first split the luxCDABE operon into several parts to create a genetic circuit that can compute a soft minimum in living cells. Then, we used the new design to implement an AND logic function with better performance as compared to AND logic functions based on protein-protein interactions. Furthermore, by controlling the reverse reaction of the luxCDABE cassette independently from the forward reaction, we built a comparator with a programmable detection threshold. Finally, we applied the redesigned cassette to build an incoherent feedforward loop that reduced the unwanted crosstalk between stress-responsive promoters (recA, katG). This work demonstrates the construction of genetic circuits that combine regulations of gene expression with metabolic pathways, for sensing and computing in living cells.

scholarly journals The evolvability of programmable hardware

2010 ◽  
Vol 8 (55) ◽  
pp. 269-281 ◽  
Author(s):  
Karthik Raman ◽  
Andreas Wagner
Keyword(s):  
Fault Tolerant ◽  
Biological Systems ◽  
Neutral Network ◽  
Logic Function ◽  
Vast Number ◽  
Functional Flexibility ◽  
Neutral Networks ◽  
Electronic Circuitry ◽  
Genotype Space ◽  
Logic Functions

In biological systems, individual phenotypes are typically adopted by multiple genotypes. Examples include protein structure phenotypes, where each structure can be adopted by a myriad individual amino acid sequence genotypes. These genotypes form vast connected ‘neutral networks’ in genotype space. The size of such neutral networks endows biological systems not only with robustness to genetic change, but also with the ability to evolve a vast number of novel phenotypes that occur near any one neutral network. Whether technological systems can be designed to have similar properties is poorly understood. Here we ask this question for a class of programmable electronic circuits that compute digital logic functions. The functional flexibility of such circuits is important in many applications, including applications of evolutionary principles to circuit design. The functions they compute are at the heart of all digital computation. We explore a vast space of 10 45 logic circuits (‘genotypes’) and 10 19 logic functions (‘phenotypes’). We demonstrate that circuits that compute the same logic function are connected in large neutral networks that span circuit space. Their robustness or fault-tolerance varies very widely. The vicinity of each neutral network contains circuits with a broad range of novel functions. Two circuits computing different functions can usually be converted into one another via few changes in their architecture. These observations show that properties important for the evolvability of biological systems exist in a commercially important class of electronic circuitry. They also point to generic ways to generate fault-tolerant, adaptable and evolvable electronic circuitry.

scholarly journals Proving a Concept of Flexible Under-Frequency Load Shedding with Hardware-in-the-Loop Testing

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3607 ◽  
Author(s):  
Denis Sodin ◽  
Rajne Ilievska ◽  
Andrej Čampa ◽  
Miha Smolnikar ◽  
Urban Rudez
Keyword(s):  
Power Systems ◽  
Smart Grids ◽  
New Technologies ◽  
Electronic Device ◽  
Electrical Power ◽  
Rate Of Change ◽  
Load Shedding ◽  
Hardware In The Loop ◽  
Protection Scheme ◽  
Readiness Level

It is widely recognized that in the transition from conventional electrical power systems (EPSs) towards smart grids, electrical voltage frequency will be greatly affected. This is why this research is extremely valuable, especially since rate-of-change-of-frequency (RoCoF) is often considered as a potential means of resolving newly arisen problems, but is often challenged in practice due to the noise and its oscillating character. In this paper, the authors further developed and tested one of the new technologies related to under-frequency load shedding (UFLS) protection. Since the basic idea was to enhance the selected technology’s readiness level, a hardware-in-the-loop (HIL) setup with an RTDS was assembled. The under-frequency technology was implemented in an intelligent electronic device (IED) and included in the HIL setup. The IED acted as one of several protection devices, representing a last-resort system protection scheme. All main contributions of this research deal with using RoCoF in an innovative UFLS scheme under test: (i) appropriate selection and parameterization of RoCoF filtering techniques does not worsen under-frequency load shedding during fast-occurring events, (ii) locally measured RoCoF can be effectively used for bringing a high level of flexibility to a system-wide scheme, and (iii) diversity of relays and RoCoF-measuring techniques is an advantage, not a drawback.

scholarly journals Method for analytical description and modeling of the working space of a manipulation robot

2021 ◽  
Vol 6 (7 (114)) ◽  
Author(s):  
Akambay Beisembayev ◽  
Anargul Yerbossynova ◽  
Petro Pavlenko ◽  
Mukhit Baibatshayev
Keyword(s):  
Normal Form ◽  
Analytical Description ◽  
Disjunctive Normal Form ◽  
Necessary Condition ◽  
Logic Function ◽  
Working Space ◽  
Graphic Image ◽  
Logic Functions ◽  
Manipulation Robot ◽  
Boundary Surfaces

This paper reports a method, built in the form of a logic function, for describing the working spaces of manipulation robots analytically. A working space is defined as a work area or reachable area by a manipulation robot. An example of describing the working space of a manipulation robot with seven rotational degrees of mobility has been considered. Technological processes in robotic industries can be associated with the positioning of the grip, at the required points, in the predefined coordinates, or with the execution of the movement of a working body along the predefined trajectories, which can also be determined using the required points in the predefined coordinates. A necessary condition for a manipulation robot to execute a specified process is that all the required positioning points should be within a working space. To solve this task, a method is proposed that involves the analysis of the kinematic scheme of a manipulation robot in order to acquire a graphic image of the working space to identify boundary surfaces, as well as identify additional surfaces. The working space is limited by a set of boundary surfaces where additional surfaces are needed to highlight parts of the working space. Specifying each surface as a logic function, the working space is described piece by piece. Next, the resulting parts are combined with a logical expression, which is a disjunctive normal form of logic functions, which is an analytical description of the working space. The correspondence of the obtained analytical description to the original graphic image of working space is verified by simulating the disjunctive normal form of logic functions using MATLAB (USA).

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