Boolean Algebra Research Articles

Logic-Compatible Embedded DRAM Architecture for Multifunctional Digital Storage and Compute-in-Memory

The compute-in-memory (CIM) which embeds computation inside memory is an attractive scheme to circumvent von Neumann bottlenecks. This study proposes a logic-compatible embedded DRAM architecture that supports data storage as well as versatile digital computations. The proposed configurable memory unit operates in three modes: (1) memory mode in which it works as a normal dynamic memory, (2) logic–arithmetic mode where it performs bit-wise Boolean logic and full adder operations on two words stored within the memory array, and (3) convolution mode in which it executes digitally XNOR-and-accumulate (XAC) operation for binarized neural networks. A 1.0-V 4096-word × 8-bit computational DRAM implemented in a 45-nanometer CMOS technology performs memory, logic and arithmetic operations at 241, 229, and 224 MHz while consuming the energy of 7.92, 8.09, and 8.19 pJ/cycle. Compared with conventional digital computing, it saves energy and latency of the arithmetic operation by at least 47% and 46%, respectively. For VDD = 1.0 V, the proposed CIM unit performs two 128-input XAC operations at 292 MHz with an energy consumption of 20.8 pJ/cycle, achieving 24.6 TOPS/W. This marks at least 11.9× better energy efficiency and 38.8× better delay, thereby achieving at least 461× better energy-delay product than traditional 8-bit wide computing hardware.

Inferential-connexive mixed logics

Abstract In this article, we present a new type of connexive-like logics. We call them inferential-connexive mixed logics, as they satisfy inferential versions of the main four connexive principles: AT, AT’, BT and BT’. We focus first on some Strong-Kleene type of mixed and inferentially connexive logics that cannot be interpreted as truth-preserving, but that can receive other interpretations in terms to falsity-preservation and related features. We introduce afterwards the notion of inferential-connexive Boolean logic, and present some logics that fall in this ballpark. We also explain the relation between inferentially-connexive Boolean logics and some inferentially-connexive Strong-Kleene logics, and show how they can also be interpreted in epistemic (or attitudinal)-related terms.

Boolean Delay Equations: a dynamical approach to modeling complex systems

Boolean delay equations (BDEs) are equations with discrete variables evolving in continuous time. They serve as exploratory tools in the study of nonlinear and complex systems. In this review paper, we outline their formulation and illustrate their properties by application to a solid-earth problem and a climate one. The first problem is the seismotectonic description and prediction of earthquakes and of their clustering. The second one is that of the coupled atmosphere-ocean phenomenon of the El Niño-Southern Oscillation (ENSO). Both involve irregular behavior that is hard to predict, although some form of cyclicity is present in both, especially in ENSO. The paper concludes with broad perspectives on the further use of BDEs in the geosciences and elsewhere.

Implementation of Digital Computing by Colloidal Crystal Engineering with DNA.

Toehold-mediated strand displacement (TMSD) provides a versatile toolbox for developing DNA digital computing systems. Although different logic circuits with diverse functions have achieved good performance in terms of complexity and scalability, most previous DNA logic circuits perform information processing only at the molecular level, and nonspecific signal leakages are often difficult to avoid. Here, we demonstrate the feasibility of constructing leakless digital computing systems in three-dimensionally ordered colloidal supercrystals. These systems possess a unique signal leakage resistance by integrating different TMSD-based logic gates with the catalytic assembly of DNA-functionalized gold colloids. A complete set of basic Boolean logic gates and different cascaded logic circuits is constructed on the basis of the catalytic assembly strategy enabled by a facilely designed catassembler, where the output signals are recognized by determining whether specific colloidal supercrystals are formed or not. In addition, a half adder is built through a combination of XOR and AND logic gates with two distinct crystal types as readouts. Finally, a leakless two-digit DNA keypad lock for information security protection is demonstrated. The combination of TMSD-based logic circuits with the universal nanoparticle catalytic assembly offers the possibility to develop highly complicated and leakage-free digital computing systems and promotes macroscopic colloidal superlattice materials with programmable logic functions.

Translating weighted probabilistic bits to synthetic genetic circuits.

Synthetic genetic circuits in plants could be the next technological horizon in plant breeding, showcasing potential for precise patterned control over expression. Nevertheless, uncertainty in metabolic environments prevents robust scaling of traditional genetic circuits for agricultural use, and studies show that a deterministic system is at odds with biological randomness. We analyze the necessary requirements for assuring Boolean logic gate sequences can function in unpredictable intracellular conditions, followed by interpreted pathways by which a mathematical representation of probabilistic circuits can be translated to biological implementation. This pathway is utilized through translation of a probabilistic circuit model presented by Pervaiz that works through a series of bits; each composed of a weighted matrix that reads inputs from the environment and a random number generator that takes the matrix as bias and outputs a positive or negative signal. The weighted matrix can be biologically represented as the regulatory elements that affect transcription near promotors, allowing for an electrical bit to biological bit translation that can be refined through tuning using invertible logic prediction of the input to output relationship of a genetic response. Failsafe mechanisms should be introduced, possibly through the use of self-eliminating CRISPR-Cas9, dosage compensation, or cybernetic modeling (where CRISPR is clustered regularly interspaced short palindromic repeats and Cas9 is clustered regularly interspaced short palindromic repeat-associated protein 9). These safety measures are needed for all biological circuits, and their implementation is needed alongside work with this specific model. With applied responses to external factors, these circuits could allow fine-tuning of organism adaptation to stress while providing a framework for faster complex expression design in the field.

The prevalence of occupational-related low back pain among working populations in sub-saharan Africa: a systematic review and meta-analysis

IntroductionWork-related musculoskeletal disorders represent a major public health problem, contributing significantly to the global burden of disability-adjusted life years and affecting the quality of life of all population groups. The main problem in most musculoskeletal disorders is low back pain. Therefore, our study aims to identify the overall prevalence of work-related low back pain among the working population in sub-Saharan Africa.MethodsResearch published between 2010 and 2023 in English, conducted in Sub-Saharan Africa was included in this systematic review and meta-analysis. Using Boolean logic operators and targeted keywords, we searched for publications on a number of electronic databases (Web of Science, PubMed, Google Scholar, African Journals Online (AJOL), and Science Direct). The Joanna Briggs Institute Critical Appraisal techniques were utilized to conduct a quality assessment of the papers and ascertain their relevance to the study. The degree of heterogeneity among the included studies, the 95% confidence interval, and the pooled prevalence were estimated using a random effects model. Sensitivity studies were carried out to determine the causes of heterogeneity and the impact of outliers.ResultsIn this study, a total of 970 articles were retrieved, and 35 studies were included in the systematic review and meta-analysis. The overall estimated pooled prevalence of low back pain among the working population in sub-Saharan Africa was (55.05% [95% CI: 49.34, 60.76]). Based on a sub-group analysis by countries, the higher pooled prevalence of low back pain was found in Uganda at (61.48% [95% CI: 40.39, 82.57]), while the lower pooled prevalence of low back pain was in Ghana at (34.48% [95% CI: 17.96, 51.01]).ConclusionsThis systematic review and meta-analysis found that 55.05% of the included study participants experienced low back pain in the previous years. Therefore, it is recommended that policymakers incorporate and enhance strategies for the prevention and management of low back pain within the health system management guidelines of each country.

Boolean Computation in Single-Transistor Neuron.

Brain neurons exhibit far more sophisticated and powerful information-processing capabilities than the simple integrators commonly modeled in neuromorphic computing. A biological neuron can in fact efficiently perform Boolean algebra, including linear nonseparable operations. Traditional logic circuits require more than a dozen transistors combined as NOT, AND, and OR gates to implement XOR. Lacking biological competency, artificial neural networks require multilayered solutions to exercise XOR operation. Here, it is shown that a single-transistor neuron, harnessing the intrinsic ambipolarity of graphene and ionic filamentary dynamics, can enable in situ reconfigurable multiple Boolean operations from linear separable to linear nonseparable in an ultra-compact design. By leveraging the spatiotemporal integration of inputs, bio-realistic spiking-dependent Boolean computation is fully realized, rivaling the efficiency of a human brain. Furthermore, a soft-XOR-based neural network via algorithm-hardware co-design, showcasing substantial performance improvement, is demonstrated. These results demonstrate how the artificial neuron, in the ultra-compact form of a single transistor, may function as a powerful platform for Boolean operations. These findings are anticipated to be a starting point for implementing more sophisticated computations at the individual transistor neuron level, leading to super-scalable neural networks for resource-efficient brain-inspired information processing.

Advancing psychiatric nosology through philosophical inquiry.

Here, we have utilised the concept of fuzzy logic and Karl Popper's notion of verisimilitude to advocate navigating the complexity of psychiatric nosology, emphasising that psychiatric disorders defy Boolean logic. We underscore the importance of embracing imprecision and collecting extensive data for a more nuanced understanding of psychiatric disorders, asserting that falsifiability is crucial for scientific progress. We encourage the advancement of personalised psychiatric taxonomy, urging the continual accumulation of data to inform emerging advancements like artificial intelligence in reshaping current psychiatric nosology.

Rewiring native post-transcriptional global regulators to achieve designer, multi-layered genetic circuits

As synthetic biology expands, creating “drag-and-drop” regulatory tools that can achieve diverse regulatory outcomes are paramount. Herein, we develop a approach for engineering complex post-transcriptional control by rewiring the Carbon Storage Regulatory (Csr) Network of Escherichia coli. We co-opt native interactions of the Csr Network to establish post-transcriptional logic gates and achieve complex bacterial regulation. First, we rationally engineer RNA-protein interactions to create a genetic toolbox of 12 BUFFER Gates that achieves a 15-fold range of expression. Subsequently, we develop a Csr-regulated NOT Gate by integrating a cognate 5’ UTR that is natively Csr-activated into our platform. We then deploy the BUFFER and NOT gates to build a bi-directional regulator, two input Boolean Logic gates OR, NOR, AND and NAND and a pulse-generating circuit. Last, we port our Csr-regulated BUFFER Gate into three industrially relevant bacteria simply by leveraging the conserved Csr Network in each species.

Realizing In-Memory Computing using Reliable Differential 8T SRAM for Improved Latency

Traditional von Neumann computing architectures suffer from high energy and lower speed as compared to the requirements of modern applications like those required in neural network accelerators. A modified differential eight transistor (8 + T) static random access memory (SRAM)-based in-memory computing (IMC) structure was presented for realizing bit-wise Boolean logic operations. The 8 + T SRAM-IMC is designed at the 32 nm technology node with throughput of 2.1849, 2.4815, 2.5795, 2.6240, 2.6495, 2.6619, 2.6690, 2.6732, and 2.6749 giga outputs per second for 0.5 to 1.3 V supply voltage range, respectively. The differential 8T cell used to implement logic operations supports NAND and NOR operations with minimal overhead while also performing the standard storage operation with added stability over the conventional 6T and 8T SRAM cells. The SRAM-IMC offers reliable Boolean logic operations by using asymmetric sensing strategy for all process corners, TT, SS, SF, FS, and FF for an operating temperature range of 220 K to 400 K. Monte Carlo simulation considering global threshold voltage deviation of 50 mV was performed for various operating conditions to study the impact of variations on design parameters such as latency.

Logics for contact and measure

Abstract We enrich contact algebras with a new binary relation that compares the size of regions, and provide axiom systems for various logics of contact and measure. Our contribution is three-fold: (1) we characterize the relations on a Boolean algebra that derive from a measure, thereby improving an old result of Kraft, Pratt and Seidenberg; (2) for all $n \geq 1$, we axiomatize the logic of regular closed sets of ${\mathbb{R}}^{n}$ with null boundary; (3) considering a broad class of equational theories that contains all logics of contact, we prove that they all have unitary or finitary unification, and that unification and admissibility are decidable.

BHT-QAOA: The Generalization of Quantum Approximate Optimization Algorithm to Solve Arbitrary Boolean Problems as Hamiltonians.

A new methodology is introduced to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). This methodology is termed the "Boolean-Hamiltonians Transform for QAOA" (BHT-QAOA). Because a great deal of research and studies are mainly focused on solving combinatorial optimization problems using QAOA, the BHT-QAOA adds an additional capability to QAOA to find all optimized approximated solutions for Boolean problems, by transforming such problems from Boolean oracles (in different structures) into Phase oracles, and then into the Hamiltonians of QAOA. From such a transformation, we noticed that the total utilized numbers of qubits and quantum gates are dramatically minimized for the generated Hamiltonians of QAOA. In this article, arbitrary Boolean problems are examined by successfully solving them with our BHT-QAOA, using different structures based on various logic synthesis methods, an IBM quantum computer, and a classical optimization minimizer. Accordingly, the BHT-QAOA will provide broad opportunities to solve many classical Boolean-based problems as Hamiltonians, for the practical engineering applications of several algorithms, digital synthesizers, robotics, and machine learning, just to name a few, in the hybrid classical-quantum domain.

All-optical AND, NAND, OR, NOR and NOT logic gates using two nested microrings in a racetrack ring resonator

Boolean logic gates are essential components for optical computing and communication systems. However, most existing methods for realizing them require complex structures, high power consumption, or multiple devices. Here, we propose a simple and compact system that can realize five Boolean logic gates, including AND, NAND, OR, NOR, and NOT, by applying different polarization modes and tuning intensities to the input signals within a SOI resonator system, formed by two nested micro rings in a racetrack ring resonator (TNMIRTR). A formula was derived for the optical transfer function of the system using the delay-line-signal method and the logic gates were simulated using the variational finite-difference time domain (varFDTD) method. The proposed structure operates by combining amplitude and polarization-conversion. TNMIRTR gate has several advantages, such as its micro-scale size, low cost, and ability to realize multiple logic gates within a single layout.

ТЕОРИЯ НЕЧЕТКИХ МНОЖЕСТВ В ИНТЕЛЛЕКТУАЛЬНОМ АНАЛИЗЕ ДАННЫХ

The article is devoted to the application of data mining (KDD) and fuzzy sets to work with large amounts of data. The digital revolution has led to a significant increase in the volume and speed of data, which makes traditional analysis methods ineffective. Data mining covers the stages of purification, integration, transformation and extraction of knowledge from data. Fuzzy logic, which extends Boolean logic, allows for uncertainty and approximate reasoning, which makes it especially useful for processing complex and noisy data. The article discusses in detail the applications of fuzzy sets in tasks such as clustering, associative rule detection, data generalization, time series analysis, and web applications. Fuzzy logic helps solve problems related to incomplete or inaccurate data by providing more flexible and understandable solutions. The author also notes that the use of fuzzy sets improves the adaptation of systems to specific data requirements and features, which contributes to more accurate analysis and decision-making in areas such as healthcare, finance and telecommunications. These advantages make fuzzy sets an important tool for improving the efficiency of data mining and improving user interaction.

Causes of moral distress among midwives: A scoping review.

Numerous studies have evidenced moral distress among midwives; however, to date no research synthesis on causes of moral distress among midwives has been conducted. A scoping review was carried out to identify, comprehensively map, and categorize possible causes of moral distress among midwives, and to identify knowledge gaps. Six data bases were searched using Boolean logic. To be included, studies had to (a) present empirical findings on (b) causes of moral distress (c) among midwives (d) in English, German, French, or Italian. We included a final set of 43 studies. The vast majority of studies came from high-income countries (83.7%) and used a qualitative approach (69.8%); 48.8% of the studies were published in the past 5years. Identified single reasons of moral distress were grouped into eight broader clusters, forming a coherent framework of reasons of moral distress: societal disregard, contemporary birth culture, resources, institutional characteristics, interprofessional relationships, interpersonal mistreatment of service users, defensive practice, and challenging care situations. These clusters mostly capture moral distress resulting from a conflict between external constraints and personal moral standards, with a smaller proportion also from an intraindividual conflict between multiple personal moral standards. Despite projected increases in demand for midwives, the midwifery workforce globally faces a crisis and is experiencing substantial strain. Moral distress further exacerbates the shortage of midwives, which negatively affects birth experiences and birth outcomes, ultimately rendering it a public health issue. Our findings offer points of leverage to better monitor and alleviate moral distress among midwives, contributing to reducing attrition rates and improving birth experiences and birth outcomes. Further research is essential to explore the issue of ecological moral distress, develop evidence-based interventions aimed at alleviating moral distress among midwives, and evaluate the effects of both individual and system-level interventions on midwives, intrapartum care, and service users' outcomes.

Quantum enhanced Josephson junction field-effect transistors for logic applications

Josephson junction field-effect transistors (JJFETs) have recently re-emerged as promising candidates for superconducting computing. For JJFETs to perform Boolean logic operations, the so-called gain factor αR must be larger than 1. In a conventional JJFET made with a classical channel material, due to a gradual dependence of superconducting critical current on the gate bias, αR is much smaller than 1. In this Letter, we propose a new device structure of quantum enhanced JJFETs in a zero-energy-gap InAs/GaSb heterostructure. We demonstrate that, due to an excitonic insulator quantum phase transition in this zero-gap heterostructure, the superconducting critical current displays a sharp transition as a function of gate bias, and the deduced gain factor αR ∼ 0.06 is more than 50 times that (∼0.001) reported in a classical JJFET. Further optimization may allow achieving a gain factor larger than 1 for logic applications.

Stone Pseudovarieties

We extend the theory of profinite algebras, as it is used in the algebraic theory of regular languages, to the more general setting of Stone topological algebras with the ultimate goal of going beyond classes of regular languages. We introduce Stone pseudovarieties, that is, classes of Stone topological algebras of a fixed topological signature that are closed under taking Stone quotients, closed subalgebras and finite direct products. Looking at the dual Stone spaces of Boolean algebras of subsets of a given topological algebra, we find a simple characterization of when the dual space admits a natural structure of topological algebra; the characterization is given in terms of how the Boolean algebra behaves under the inverses of the operation evaluation mappings of each arity. This provides an alternative, which is presented in the form of an equivalence of categories, to the duality theory of M. Gehrke. As an application, a Stone quotient of a Stone topological algebra that is residually in a given Stone pseudovariety is shown to be also residually in it, thereby extending the corresponding result of M. Gehrke for the Stone pseudovariety of all finite algebras over discrete signatures, which was recently extended to topological signatures jointly by the authors and H. Goulet-Ouellet. The residual closure of a Stone pseudovariety is thus a Stone pseudovariety, and these are precisely the Stone analogues of varieties. A Birkhoff type theorem for Stone varieties is also established and it is shown how Reiterman’s theorem can be derived from it.

Corrections in Boolean Algebra

Here 0=true 1=true but there may be differences

The relationship between cervical lordosis and neck pain: a systematic review and meta-analysis

: The interpretation of the correlation between cervical lordotic angle (CLA) and neck pain (NP) among clinicians remains contentious, reflecting the nuanced nature of this association within clinical discourse. This relationship assumes paramount importance in clinical practice, as it serves as the cornerstone for devising effective therapeutic strategies aimed at the management and prevention of NP. The objective of this study was to determine the difference in CLA between individuals with and without NP. The inclusion criteria entailed observational studies rigorously evaluating CLA through radiological imaging in both NP patients and healthy controls (HC), while pediatric, geriatric populations, and non-degenerative spinal conditions were excluded. We conducted a thorough electronic search across several databases including Medline, Cochrane Library, Embase, CINAHL, and PEDro. The search strategy employed terms pertinent to cervical alignment and NP, using Boolean logic. Specifically, search terms such as "neck pain*", "cervical pain*", and "lordo*" were used to ensure comprehensive coverage of relevant literature. We estimated the standardized Mean Differences (SMD) and their corresponding 95% Confidence Intervals (CI). Additionally, chi-square and I2 statistics were used to evaluate within-group heterogeneity through a random effects model. A total of 6 studies, involving 436 patients with NP and 491 HC, were identified. Overall, individuals with NP demonstrated a tendency towards smaller CLA compared to the HC group.

Parameter-induced logical stochastic resonance in substrate potential with deformable sine-Gordon shape

Logical stochastic resonance (LSR) systems are physical nonlinear systems capable of robust Boolean logic operations under the influence of noise. While LSR systems suitable for electronic circuit implementation have been extensively studied, research on condensed matter LSR systems remains limited to constrained bistability with saturation characteristic. Considering the presence of periodic nonlinearities in many physical systems, a deformable sine-Gordon-shaped Remoissenet–Peyrard potential (RPP)-based LSR system is proposed for the first time in this work. Testing under both noise-free and noisy conditions proves the existence of parameter-induced LSR phenomena in the proposed system. Moreover, we find that a relatively wide potential well shape contributes to enhanced noise robustness in the RPP-based LSR system. Additionally, traditional polynomial nonlinearity-based LSR systems are compared with the proposed system. Regardless of whether the noise is Gaussian white noise or composite noise containing spiking pulses, the RPP-based LSR system exhibits superior robustness. The results demonstrate the exceptional advantages of the RPP-based LSR system and encourage further design of condensed matter LSR systems based on deformable periodic nonlinearities.