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The author discusses a method for obtaining the Boolean functions describing the structure of a control circuit by means of AS operators whose sequence of operations is given in the form of a logical scheme or matrix scheme for an algorithm. An example of AS synthesis is given.
A family of standardized thick-oxide P-MOS building blocks (standard cells) is described. The information is presented in a form useful for systems designs, logic design, and the preparation of inputs to both sets of Design Automation programs for array design and analysis. A data sheet is provided for each cell and gives the cell name, the cell number, its logic symbol, Boolean equation, truth table, circuit schematic circuit composite, input-output capacitances, and revision date. The circuit type file, also given for each cell, together with the logic drawing contained on the data sheet provides all the information required to prepare input data files for the Design Automation Systems. A detailed description of the electrical design procedure is included.
Artificial intelligence (AI) based software and hardware concepts are applied to the handling system malfunctions during flight tests. A representation of malfunction procedure logic using Boolean normal forms are presented. The representation facilitates the automation of malfunction procedures and provides easy testing for the embedded rules. It also forms a potential basis for a parallel implementation in logic hardware. The extraction of logic control rules, from dynamic simulation and their adaptive revision after partial failure are examined. It uses a simplified 2-dimensional aircraft model with a controller that adaptively extracts control rules for directional thrust that satisfies a navigational goal without exceeding pre-established position and velocity limits. Failure recovery (rule adjusting) is examined after partial actuator failure. While this experiment was performed with primitive aircraft and mission models, it illustrates an important paradigm and provided complexity extrapolations for the proposed extraction of expertise from simulation, as discussed. The use of relaxation and inexact reasoning in expert systems was also investigated.
The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and $\mathbb{Z}$ 2 ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W$\land$H has a unique W, a unique H (for a fixed W), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMFk, and show on numerical examples that BMFk not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.
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Rhodococcus opacus PD630 (R. opacus) is a non-model, gram-positive bacterium which holds promise as a biological catalyst for the conversion of lignocellulosic biomass into value-added products. In particular, it demonstrates both a high tolerance for and an ability to consume inhibitory lignin-derived aromatics, generates large quantities of lipids, exhibits a relatively rapid growth rate, and has a growing genetic toolbox for engineering. Yet, the availability of genetic parts for tunable, high-activity gene expression is still limited in R. opacus. Moreover, genetic logic circuits for sophisticated gene regulation have never been demonstrated in Rhodococcus spp. To address these shortcomings, two inducible T7 RNA polymerase-based expression systems were implemented for the first time in R. opacus and applied to constructing AND and NAND genetic logic gates. Additionally, three IPTG-inducible promoters were created by inserting LacI binding sites into newly-characterized constitutive promoters. Furthermore, four novel aromatic sensors for 4-hydroxybenzoic acid, vanillic acid, sodium benzoate, and guaiacol were developed, expanding the gene expression toolbox. Lastly, the T7 RNA polymerase platform was combined with a synthetic IPTG-inducible promoter to create an IMPLY logic gate. Overall, this work represents the first demonstration of a heterologous RNA polymerase system and synthetic genetic logic in R. opacus, enabling complex and tunable gene regulation in this promising non-model host for bioproduction.
Abstract The Research Collaboratory for Structural Bioinformatics Protein Data Bank (RCSB PDB), the US data center for the global PDB archive and a founding member of the Worldwide Protein Data Bank partnership, serves tens of thousands of data depositors in the Americas and Oceania and makes 3D macromolecular structure data available at no charge and without restrictions to millions of RCSB.org users around the world, including >660 000 educators, students and members of the curious public using PDB101.RCSB.org. PDB data depositors include structural biologists using macromolecular crystallography, nuclear magnetic resonance spectroscopy, 3D electron microscopy and micro-electron diffraction. PDB data consumers accessing our web portals include researchers, educators and students studying fundamental biology, biomedicine, biotechnology, bioengineering and energy sciences. During the past 2 years, the research-focused RCSB PDB web portal (RCSB.org) has undergone a complete redesign, enabling improved searching with full Boolean operator logic and more facile access to PDB data integrated with >40 external biodata resources. New features and resources are described in detail using examples that showcase recently released structures of SARS-CoV-2 proteins and host cell proteins relevant to understanding and addressing the COVID-19 global pandemic.
In this study, a compact and novel ferroelectric (FE) programmable majority gate is proposed and its novel application in Binary Neural Network (BNNs) is investigated. We demonstrate: i) by integrating N metal-ferroelectric-metal (MFM) capacitors on the gate of a transistor (1T-N-MFM structure), a nonvolatile and programmable majority (MAJ) gate that performs MAJ of AND between the gate input and polarization is realized; ii) validation the functionality of our 3-input MAJ of AND gate through comprehensive theoretical and experimental investigations; iii) a compact implementation of 3-input MAJ of XNOR gate that leverages only five of our 3-input MAJ of AND gates connected in parallel; iv) application of MAJ of XNOR gates to replace the XNOR gates and the first layer of the adder tree in the BNNs for up to 21x area saving on top of eliminating the energy-hungry memory accesses due to the compute-in-memory nature.
In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.
Single-threshold-element synthesis in approach based on correlation techniques
The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product rule and Bayes Theorem, and the measure resulting from this generalization is probability. In this paper, I will describe how Cox s technique can be further generalized to include other algebras and hence other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information theory, and quantum mechanics.
For over a century, the study of logic has focused on the algebra of logical statements. This work, first performed by George Boole, has led to the development of modern computers, and was shown by Richard T. Cox to be the foundation of Bayesian inference. Meanwhile the logic of questions has been much neglected. For our computing machines to be truly intelligent, they need to be able to ask relevant questions. In this paper I will show how the Boolean lattice of logical statements gives rise to the free distributive lattice of questions thus defining their algebra. Furthermore, there exists a quantity analogous to probability, called relevance, which quantifies the degree to which one question answers another. I will show that relevance is not only a natural generalization of information theory, but also forms its foundation.
The paper describes the fabrication and operation of an optical parallel logic (OPAL) device which performs Boolean algebraic operations on binary images. Several logic operations on two input binary images were demonstrated using an 8 x 8 device with a CdS photoconductor and a twisted nematic liquid crystal. Two such OPAL devices can be interconnected to form a half-adder circuit which is one of the essential components of a CPU in a digital signal processor.
The paper describes the general physical theory of signals, carriers of information, which supplements Shannon’s abstract classical theory and is applicable in much broader fields, including nuclear physics. It is shown that in the absence of classical noise its place should be taken by the physical threshold of signal perception for objects of both macrocosm and microcosm. The signal perception threshold allows the presence of subthreshold (virtual) signal states. For these states, Boolean algebra of logic (A = 0/1) is transformed into the “algebraic logic” of probabilities (0 ≤ a ≤ 1). The similarity and difference of virtual states of macroand microsignals are elucidated. “Real” and “quantum” information for computers is considered briefly. The maximum information transmission rate is estimated based on physical constants.
Correspondence between logical relations of Boolean function implicants and numerical relations between identifiers
Logic networks of Boolean analogs analyzed by algebraic signal flow theory, introducing variational derivative for test detection in combinational and sequential networks
Bayesian probability theory is an inference calculus, which originates from a generalization of inclusion on the Boolean lattice of logical assertions to a degree of inclusion represented by a real number. Dual to this lattice is the distributive lattice of questions constructed from the ordered set of down-sets of assertions, which forms the foundation of the calculus of inquiry-a generalization of information theory. In this paper we introduce this novel perspective on these spaces in which machine learning is performed and discuss the relationship between these results and several proposed generalizations of information theory in the literature.
The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a valuation called relevance or bearing, which is a measure of the degree to which one question answers another. Richard Cox conjectured that this degree can be expressed as a generalized entropy. With the assistance of yet another important result from Janos Acz6l, I show that this is indeed the case; and that the resulting inquiry calculus is a natural generalization of information theory. This approach provides a new perspective of the Principle of Maximum Entropy.