Boolean Operations Research Articles

Performing Regular Operations with 1-Limited Automata

The descriptional complexity of basic operations on regular languages using 1-limited automata, a restricted version of one-tape Turing machines, is investigated. When simulating operations on deterministic finite automata with deterministic 1-limited automata, the sizes of the resulting devices are polynomial in the sizes of the simulated machines. The situation is different when the operations are applied to deterministic 1-limited automata: while for boolean operations the simulations remain polynomial, for product, star, and reversal they cost exponential in size. The costs for product and star do not reduce if the given machines are sweeping two-way deterministic finite automata. These bounds are tight.

Fast extraction of cutter-workpiece engagement for milling force prediction in multi-axis machining

The paper proposes a fast extraction method for cutter-workpiece engagement (CWE), which greatly facilitates the milling force prediction during multi-axis machining. One of the key cores of the method is to reconstruct the nearby cut-off material of workpiece using a set of past neighboring cutter location points (CLPs), and obtain the CWE entity through local Boolean operation among the current tool, workpiece blank, and reconstructed entity. Moreover, by performing 2-dimensional (2D) image mapping, the engagement boundary of CWE entity will be quickly obtained. Combining with the analytical formula of instantaneous undeformed chip thicknesses (IUCTs), the composite IUCT for tool side and bottom cutting edges during actual immersion is further derived. Finally, accurate and fast prediction of milling force with consideration of tool attitude, corner feature and bottom cutting effect is achieved. The results reveal that the method can predict milling force with an excellent performance of first-order computation complexity.

Global Methods for Calculating Shading and Blocking Efficiency in Central Receiver Systems

This paper presents three new methods for calculating the shading and blocking efficiency in Central Receiver Systems (CRSs). All of them are characterized by the calculation of multiple useful and total reflecting areas without the need to resort to parallel calculation in the CPU or GPU, and by low computation times and minimum errors. They are being specially designed for implementation in codes focused on heliostat field design and optimization in CRSs. The proposed methods have been compared against two outstanding “individual” methods (homology and Boolean operations), in addition to a reference case based on the Monte Carlo ray-tracing (MCRT) technique. The results indicate that one of the proposed methods presents reduced error values and high computational speed, even relaxing the restrictions on candidate filtering. At the same error level, the global method is up to 7.80 times faster than the fastest individual method (homology) and up to 194 times faster than the method based on the MCRT technique. The causes of the main errors of each method are also analyzed.

Virtual-Trim: A parametric geometric modeling method for heterogeneous strut-based lattice structures

Abstract Geometric modeling has been integral to the design process with the introduction of Computer-Aided Design. With additive manufacturing (AM), design freedom has reached new heights, allowing for the production of complex lattice structures not feasible with traditional manufacturing methods. However, there remains a significant challenge in the geometric modeling of these lattice structures, especially for heterogeneous strut-based lattice structures. Current methods show limitations in accuracy or geometric control. This paper presents the Virtual-Trim, a novel method for the geometric modeling of heterogeneous strut-based lattice structures that is both efficient and robust. Virtual-Trim begins with user-defined wireframe models and geometric information to create STL (STereoLithography) models ready for AM, eliminating the need for labor-intensive Boolean operations. The fundamental principles and steps involved in Virtual-Trim are extensively described within. Additionally, various models using Virtual-Trim method are designed, and the performance of Virtual-Trim in terms of generation time and model size is analyzed. The successful printing of these models attests to the method’s excellent manufacturability.

Microbiome abundance patterns as attractors and the implications for the inference of microbial interaction networks

Inferring microbial interaction networks from abundance patterns is an important approach to advance our understanding of microbial communities in general and the human microbiome in particular. Here we suggest discriminating two levels of information contained in microbial abundance data: (1) the quantitative abundance values and (2) the pattern of presences and absences of microbial organisms. The latter allows for a binary view on microbiome data and a novel interpretation of microbial data as attractors, or more precisely as fixed points, of a Boolean network.Starting from these attractors, our aim is to infer an interaction network between the species present in the microbiome samples. To accomplish this task, we introduce a novel inference method that combines the previously published ESABO (Entropy Shifts of Abundance vectors under Boolean Operations) method with an evolutionary algorithm. The key idea of our approach is that the inferred network should reproduce the original set of (observed) binary abundance patterns as attractors.We study the accuracy and runtime properties of this evolutionary method, as well as its behavior under incomplete knowledge of the attractor sets. Based on this theoretical understanding of the method we then show an application to empirical data.

A Novel Derivative Free Methodology for Multi-Material Topology Optimization Based on Projective Transformations and Boolean Operations

A Novel Derivative Free Methodology for Multi-Material Topology Optimization Based on Projective Transformations and Boolean Operations

Coordination nanosheets based molecular computing for detection and differentiation of high-energy explosives TATB and FOX-7

Detection and differentiation of explosives is an issue of immediacy for security and environmental monitoring. At present, the most operated explosive system combines primary and secondary explosives. Although various advances are presently equipped for identifying primary explosives, the insensitive nature of secondary explosives makes their detection and differentiation challenging. Here, we report three coordination nanosheets (CNs) AM-8-Eu, AM-8-Tb, and AM-8-Zn containing three-way terpyridine ligands (AM-8) and Eu(III), Tb(III), and Zn(II) ions. These CNs act as a highly selective platform for detecting unexplored high-energy explosive 1,1-Diamino-2,2-dinitro ethylene (FOX-7) in solid and solution phases. For AM-8-Zn, calculated molecular electrostatic surface potential revealed two modes of interactions for triaminotrinitrobenzene (TATB) and FOX-7, producing two distinct spectral responses. Digital analysis of these responses revealed a complimentary implication (IMP)/not implication (NIMP) logic function. Finally, the unique feature of IMP gate is used to define all possible sixteen distinct binary Boolean operations on two logic values for “functional completeness”. The detection and differentiation of such insensitive high-energy explosives TATB and FOX-7, where Boolean logic can process information through distinct binary responses in solid and solution phases, have not been witnessed hitherto in a single chemical platform.

Bone deformity in sports-related elbow osteoarthritis: influence of osteochondritis dissecans of the capitellum-a cross-sectional study.

Sports activity can cause elbow osteoarthritis, which subsequently induces bone deformity. Osteochondritis dissecans (OCD) of the capitellum develops defects of articular surfaces and can exacerbate bone deformity. This study aimed to investigate whether OCD exacerbates deformities in sports-related elbow osteoarthritis. Twenty-one patients who underwent bilateral computed tomography preoperatively followed by surgery for sports-related elbow osteoarthritis were included. Patients were divided into two groups according to the presence or absence of an OCD history: OCD + (n = 6) and OCD- (n = 15). Bilateral three-dimensional bone models of the humerus, ulna, and radius were created using computed tomography data, and bone deformities were extracted by subtracting healthy mirror models from the affected models using a Boolean operation. Bone deformities were divided into 22 regions in the 3 bones. The volume of the deformity was estimated by correlating the anteroposterior and lateral diameters of the OCD and by comparing the two groups. The anteroposterior diameter of the OCD correlated with the articular surface of the medial trochlear notch, whereas the lateral diameter correlated with the whole ulna, medial gutter of the ulna, whole radius, and lateral side of the radial head. The deformities were 2.2 times larger in the whole humerus, 1.9 times larger in the whole ulna, and 3.0 times larger in the whole radius in the OCD + group than in the OCD- group. The deformities were significantly larger in the OCD + group than in the OCD- group in the radial fossa, posterior capitellum, medial gutter, and lateral gutter in the humerus, medial gutter in the ulna, and lateral, anterior, and posterior sides of the radial head. Larger OCD exacerbated deformity in elbow OA, and the presence of OCD exacerbated deformities in sports-related elbow OA. These results demonstrate the highlight of preventing OCD progression.

Validated, high-resolution, non-linear, explicit finite element models for simulating screw - bone interaction

Background and ObjectivePrimary stability evaluation of screw implants through pull-out or push-in experiments is commonly used to investigate the mechanism of screw loosening. Numerical models simulating these testing methods could provide an enhanced understanding of the underlying attachment mechanisms as well as save time and cost in the development of new screws. However, previous numerical models have been limited by compromises between modelling the trabecular structure at high resolution versus incorporating sophisticated mechanical properties and boundary conditions, leading to overestimated mechanical performance. The aim of this study was to overcome these limitations. MethodsWe developed explicit models incorporating the microstructure of trabecular bone, with frictional contact, and a non-linear material model incorporating damage. One model digitally inserted the screw into the trabecular bone structure using Boolean operations, while another model simulated the screw's rotational insertion. ResultsThe results showed a strong correlation between numerical and experimental results (R2: 0.54–0.93) for force-displacement response in terms of stiffness and strength. We found that the damage induced by the screw insertion process is an important factor to be considered, as the absence of modelling it led to an overestimated stiffness in previous studies. ConclusionsThe study highlights the importance of including frictional contact and also identified screw insertion damage as an important part of the simulating screw-bone interaction. Our findings demonstrate the potential of explicit finite element models for accurately replicating experimental push-in results and optimizing orthopaedic screws. The code is available at https://github.com/zhou436/Bone-Screw-Constructs-eFEM.

A practical algorithm for the design of multiple-sized porous scaffolds with triply periodic structures

In this study, we present a practical volume-merging method for generating multiple-sized porous structures that exhibit geometries with triply periodic minimal surface (TPMS) lattice structures. The proposed method consists of three stages: (1) designing the physical models with a signed distance field, (2) performing a merging operation for the porous scaffolds, and (3) assembling different units into a composite structure. The significant advantages of the proposed algorithm can be summarized as follows: Our method is independent of the model shape; the designed structures maintain a smooth surface with a constant mean curvature, and the mathematical computational complexity is low. We can join two different-sized triply periodic minimal surface lattices in the radial direction, where the transition region is obtained by smooth interpolation between the two lattice structures with different cell sizes or types. However, constructing large-sized models is only conceptually possible due to computational cost and memory storage constraints. To overcome these limitations, we present a practical method that can efficiently assemble large-scaled models at a low computational cost. The proposed method is based on a Boolean union operation of basic units of TPMS. Thus, it is simple to generate large-scale three-dimensional multiple-sized porous volumes based on our proposed method, which can be applied to many applications in mechanical and electrical engineering. The produced multi-scale compound scaffolds have smooth surfaces without fractures, making them suitable for straightforward application in additive manufacturing. Several numerical tests are conducted to validate the efficiency of the proposed algorithm.

Logical activation functions for training arbitrary probabilistic Boolean operations

In this work, we introduce a family of novel activation functions for deep neural networks that approximate n-ary, or n-argument, probabilistic logic. Logic has long been used to encode complex relationships between claims that are either true or false. Thus, these activation functions provide a step towards models that can efficiently encode information. Unfortunately, typical feedforward networks with elementwise activation functions cannot capture certain relationships succinctly, such as the exclusive disjunction (p xor q) and conditioned disjunction (if c then p else q). Our n-ary activation functions address this challenge by approximating belief functions (probabilistic Boolean logic) with logit representations of probability and experiments demonstrate the ability to learn arbitrary logical ground truths in a single layer. Further, by representing belief tables using a basis that associates the number of nonzero parameters with the effective arity of each belief function, we forge a concrete relationship between logical complexity and sparsity, thus opening new optimization approaches to suppress logical complexity during training. We provide a computationally efficient PyTorch implementation and test our activation functions against other logic-approximating activation functions on both traditional machine learning tasks as well as reproducing known logical relationships.

Fully CMOS‐Based p‐Bits with a Bistable Resistor for Probabilistic Computing

AbstractProbabilistic computing can solve complex combinatorial optimization problems more efficiently than conventional deterministic computing. A probabilistic bit (p‐bit) with an n‐p‐n bistable resistor (biristor) is demonstrated for probabilistic computing. It is fabricated on an 8‐inch wafer with complementary metal–oxide–semiconductor (CMOS) compatible technologies. Its stochastic behavior of threshold switching, which is based on the phenomenon of a single transistor latch, provides output with a Boltzmann distribution. The p‐bit is composed of a biristor, a serial resistor, and a comparator. The output probability of the biristor‐based p‐bits shows a sigmoidal relationship with the input voltage, showing typical p‐bit characteristics. Invertible Boolean logic operations with p‐bits are demonstrated, and weighted maximum Boolean satisfiability problems are solved with high energy efficiency and accuracy. The biristor‐based p‐bits with perfect CMOS compatibility show sufficient device stability, demonstrating the possibility of large‐scale integration with a p‐bit array for complex optimization solvers.

Polygon Boolean operations and physical unclonable functions implemented by an Ag-embedded sodium-alginate-based memristor for image encryption/decryption

In this work, we demonstrate the coexistence of nonvolatile memory (NVM) and volatile threshold switching (VTS) behaviors in an Ag-embedded sodium-alginate-based memristor using the current pulse mode. High and low compliance currents allow the device to present stable and reliable NVM and VTS behaviors, respectively. Specifically, NVM and VTS behaviors randomly occur under a compliance current of 40 μA. On this basis, four polygon Boolean operations (AND, OR, NOT, and XOR) and physical unclonable functions (PUFs) with an inter-class Hamming distance of 50.75% are demonstrated simultaneously in memristive devices. Adopting PUF keys, image encryption and decryption are implemented by executing the XOR logic operation. Our memristive devices have the ability of in-memory computing and providing PUFs simultaneously and thus great potential for hardware security applications.

Hybrid chaotic map with L-shaped fractal Tromino for image encryption and decryption

Insecure communication in digital image security and image storing are considered as important challenges. Moreover, the existing approaches face problems related to improper security at the time of image encryption and decryption. In this research work, a wavelet environment is obtained by transforming the cover image utilizing integer wavelet transform (IWT) and hybrid discrete cosine transform (DCT) to completely prevent false errors. Then the proposed hybrid chaotic map with L-shaped fractal Tromino offers better security to maintain image secrecy by means of encryption and decryption. The proposed work uses fractal encryption with the combination of L-shaped Tromino theorem for enhancement of information hiding. The regions of L-shaped fractal Tromino are sensitive to variations, thus are embedded in the watermark based on a visual watermarking technique known as reversible watermarking. The experimental results showed that the proposed method obtained peak signal-to-noise ratio (PSNR) value of 56.82dB which is comparatively higher than the existing methods that are, Beddington, free, and Lawton (BFL) map with PSNR value of 8.10 dB, permutation substitution, and Boolean operation with PSNR value of 21.19 dB and deoxyribonucleic acid (DNA) level permutation-based logistic map with PSNR value of 21.27 dB.

A novel method to design gradient porous structures with conformal density

This work introduces a rapid modeling method for gradient porous structures with conformal density, aiming to address the challenges of transitional variation of porosity, and control of complex gradient variations in multiple directions. In comparison to other methods, this approach overcomes the limitations associated with coordinate systems and shape functions when designing complex gradient variations in multiple directions while achieving density variation with shape under different gradients. The method involves mapping the volumetric distance field to a density field using control functions. By adhering to the constraints of the density field, it employs a weighted random sampling method to attain gradient sites with shape-adaptive distribution. Voronoi polyhedron are then constructed based on these sites, and smooth Voronoi struts are generated using strut distance fields and improved Boolean operations. The boundary adaptation of the porous structure is subsequently achieved based on the volumetric distance field. By establishing the relationship between density and volumetric distance field values, the study illustrates the similarity between density variation in the structure and gradient variations in the control function, indicating the controllability of density variation with shape. Furthermore, the method enables the integration design of structural shape and mechanical properties through adjustments to the number of sites, radius size of struts, and gradient control functions. Finally, the method was validated through numerical simulation and experiments, demonstrating its controllability and effectiveness in generating random porous structures with conformal density gradients, providing important theoretical and practical support for research and application in related fields.

Secure Genomic String Search with Parallel Homomorphic Encryption

Fully homomorphic encryption (FHE) cryptographic systems enable limitless computations over encrypted data, providing solutions to many of today’s data security problems. While effective FHE platforms can address modern data security concerns in unsecure environments, the extended execution time for these platforms hinders their broader application. This project aims to enhance FHE systems through an efficient parallel framework, specifically building upon the existing torus FHE (TFHE) system chillotti2016faster. The TFHE system was chosen for its superior bootstrapping computations and precise results for countless Boolean gate evaluations, such as AND and XOR. Our first approach was to expand upon the gate operations within the current system, shifting towards algebraic circuits, and using graphics processing units (GPUs) to manage cryptographic operations in parallel. Then, we implemented this GPU-parallel FHE framework into a needed genomic data operation, specifically string search. We utilized popular string distance metrics (hamming distance, edit distance, set maximal matches) to ascertain the disparities between multiple genomic sequences in a secure context with all data and operations occurring under encryption. Our experimental data revealed that our GPU implementation vastly outperforms the former method, providing a 20-fold speedup for any 32-bit Boolean operation and a 14.5-fold increase for multiplications.This paper introduces unique enhancements to existing FHE cryptographic systems using GPUs and additional algorithms to quicken fundamental computations. Looking ahead, the presented framework can be further developed to accommodate more complex, real-world applications.

Predecessor on the Ultra-Wide Word RAM

We consider the predecessor problem on the ultra-wide word RAM model of computation, which extends the word RAM model with ultrawords consisting of w2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$w^2$$\\end{document} bits (TAMC, 2015). The model supports arithmetic and boolean operations on ultrawords, in addition to scattered memory operations that access or modify w (potentially non-contiguous) memory addresses simultaneously. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures. Our main result is a simple, linear space data structure that supports predecessor in constant time and updates in amortized, expected constant time. This improves the space of the previous constant time solution that uses space in the order of the size of the universe. Our result holds even in a weaker model where ultrawords consist of w1+ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$w^{1+\\epsilon }$$\\end{document} bits for any ϵ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon > 0 $$\\end{document}. It is based on a new implementation of the classic x-fast trie data structure of Willard (Inform Process Lett 17(2):81–84, https://doi.org/10.1016/0020-0190(83)90075-3, 1983) combined with a new dictionary data structure that supports fast parallel lookups.

Spin orbit magnetic random access memory based binary CNN in-memory accelerator (BIMA) with sense amplifier

The research tends to suggest a spin-orbit torque magnetic random access memory (SOT-MRAM)-based Binary CNN In-Memory Accelerator (BIMA) to minimize power utilization and suggests an In-Memory Computing (IMC) for AdderNet-based BIMA to further enhance performance by fully utilizing the benefits of IMC as well as a low current consumption configuration employing SOT-MRAM. And recommended an IMC-friendly computation pipeline for AdderNet convolution at the algorithm level. Additionally, the suggested sense amplifier is not only capable of the addition operation but also typical Boolean operations including subtraction etc. The architecture suggested in this research consumes less power than its spin-orbit torque (STT) MRAM and resistive random access memory (ReRAM)-based counterparts in the Modified National Institute of Standards and Technology (MNIST) data set, according to simulation results. Based to evaluation outcomes, the pre-sented strategy outperforms the in-memory accelerator in terms of speedup and energy efficiency by 17.13× and 18.20×, respectively.

Development of Karawo Motif Design System Based on Philosophical Values of Gorontalo Regional Culture

Karawo is a traditional embroidered cloth for the people of the Gorontalo region. Currently karawo has been widely used by the surrounding community and the outside community in the form of souvenirs or other things. On the one hand, the Gorontalo Region is an area that has many cultures and customs. We need to protect and preserve this culture so that this culture does not quickly become extinct. The lack of karawo motif designs that have a Gorontalo regional cultural philosophy causes karawo craftsmen to lack ideas to design karawo motifs in various design variations. This can be overcome by creating a system that can make several variations of the karawo motif design with the help of computer algorithms. The development of this karawo motif design uses several object or image transformation functions, namely rotation, translation, mirror, flip and zoom functions. To enrich the object so that it looks varied, arithmetic operations and boolean operations are also used to value the color component of each point in the image. The usability measurement results show that the eligibility value of usefulness is 85.71%, ease of use is 100%, ease of learning is 85.71% and satisfaction is 92.86%. The average of all dimensions is 91.07% or it is included in the very satisfied category.

Drawing the Linkage Between Women's Reproductive Health, Climate Change, Natural Disaster, and Climate-driven Migration: Focusing on Low- and Middle-income Countries - A Systematic Overview.

One of the most important aspects of women's well-being and welfare is RSH (reproductive and sexual health). Reproductive health is not an exception to the threat that CCC (climate change and climate crisis) poses to numerous facets of public health. Firstly, the present review seeks to identify the influence of climatic changes, natural disasters, and climate-driven migration on RSH. Secondly, to identify knowledge gaps regarding the same. Two databases (Scopus and PubMed) were scanned using Boolean operation. The literature search aimed to find records pertaining to topics of RSH and climate change. Using the PRISMA-ScR method, records were screened and shortlisted based on established inclusion criteria. This literature search was carried out in November 2022. In the shortlisted records, preference for the comprehensive review articles was given. The present review is based on 38 records that collectively revealed that climate crisis and natural disasters have many negative impacts on female reproductive health. These effects are observed in different phases of life, ranging from teenage to menopause. The unique strength of the present review is that it draws a relationship between female reproductive health and the direct as well as indirect effects of the CCC. The available literature about LMICs is predominantly confined to drought, flood, and earthquake. Disasters like tsunamis, cyclones, and avalanches remain unexplored. From the available literature, it is quite evident that CCC has an adverse effect on a woman's reproductive life as well as a bearing on future generations' health. Filling these knowledge gaps is pivotal for designing more effective disaster and health policies. Policymakers should take into consideration these detrimental effects while designing health schemes and policies for females.