Unary Operation Research Articles

Varieties of unary-determined distributive $\ell$-magmas and bunched implication algebras

A distributive lattice-ordered magma ($d\ell$-magma) $(A,\wedge,\vee,\cdot)$ is a distributive lattice with a binary operation $\cdot$ that preserves joins in both arguments, and when $\cdot$ is associative then $(A,\vee,\cdot)$ is an idempotent semiring. A $d\ell$-magma with a top $\top$ is unary-determined if $x{\cdot} y=(x{\cdot}\!\top\wedge y)$ $\vee(x\wedge \top\!{\cdot}y)$. These algebras are term-equivalent to a subvariety of distributive lattices with $\top$ and two join-preserving unary operations $\mathsf p,\mathsf q$. We obtain simple conditions on $\mathsf p,\mathsf q$ such that $x{\cdot} y=(\mathsf px\wedge y)\vee(x\wedge \mathsf qy)$ is associative, commutative, idempotent and/or has an identity element. This generalizes previous results on the structure of doubly idempotent semirings and, in the case when the distributive lattice is a Heyting algebra, it provides structural insight into unary-determined algebraic models of bunched implication logic. We also provide Kripke semantics for the algebras under consideration, which leads to more efficient algorithms for constructing finite models. We find all subdirectly irreducible algebras up to cardinality eight in which $\mathsf p=\mathsf q$ is a closure operator, as well as all finite unary-determined bunched implication chains and map out the poset of join-irreducible varieties generated by them.

The impacts of the transmission line length in an interconnected micro-grid on its performance and protection at different fault levels

Power systems, in recent years, have been experiencing a dynamic rise in the amount of power obtained from distributed renewable energy sources leading to the concept of microgrids to address the distributed power grid integration issues. Microgrids, a promising means of facilitating the green transformation of power systems, allow the union operation of distributed energy resources (DER) such as combined heat and power (CHP), renewables like photovoltaic (PV), wind and fuel cells (FC), energy storage systems, diesel generators, and controllable loads, either individually or in combination. The protection of DERs within microgrids can be considered as one of the main challenges associated with such phenomenon. Short and Long power transmission lines, in case of a fault, both have particular impacts on system parameters and may result into subsequent events threatening the microgrid and renewable generation units. On the other hand, The high penetration of microgrids not only can change the power flow within the power network, but it can also affect the fault current levels and may lead to their islanding in case of a fault. Before investing in microgrids, especially those in far places, this paper develops a tool to be used in investigating the influence of the interconnecting transmission line length as well as the type/severity of fault on the microgrid performance. The toolbox was developed using MATLAB/Simulink Toolbox. The developed tool was then validated on a case study microgrid and results show that the length of the interconnecting transmission line and the fault severity directly impact the microgrid performance (i.e. voltage and power deviations). In that case, interconnection or islanded mode is contingent upon the decision of the utility operator which also depends on the sensitivity of the equipment used in the microgrid.

Decidability of the Satisfiability Problem for Boolean Set Theory with the Unordered Cartesian Product Operator

We give a positive solution to the decidability problem for the fragment of set theory, dubbed BST ⊗, consisting of quantifier-free formulae involving the Boolean set operators of union, intersection, and set difference, along with the unordered Cartesian product operator ⊗ (where \(s \otimes t := \big \lbrace \lbrace u,v\rbrace \,\texttt {|}\:u \in s \wedge v \in t \big \rbrace\) ), and the equality predicate, but no membership. Specifically, we provide nondeterministic exponential decision procedures for both the ordinary and the finite satisfiability problems for BST ⊗. We expect that these decision procedures can be adapted for the standard Cartesian product and, with added technicalities, to the cases involving membership, providing a solution to a longstanding problem in computable set theory.

RESEARCH ON FRACTAL DIMENSIONS AND THE HÖLDER CONTINUITY OF FRACTAL FUNCTIONS UNDER OPERATIONS

Based on the previous studies, we make further research on how fractal dimensions of graphs of fractal continuous functions under operations change and obtain a series of new results in this paper. Initially, it has been proven that a positive continuous function under unary operations of any nonzero real power and the logarithm taking any positive real number that is not equal to one as the base number can keep the fractal dimension invariable. Then, a general method to calculate the Box dimension of two continuous functions under binary operations has been proposed. Using this method, the lower and upper Box dimensions of the product and the quotient of continuous functions without zero points have been investigated. On this basis, these conclusions will be generalized to the ring of rational functions. Furthermore, we discuss the Hölder continuity of continuous functions under operations and then prove that a Lipschitz function can be absorbed by any other continuous functions under certain binary operations in the sense of fractal dimensions. Some elementary results for vector-valued continuous functions have also been given.

1834년 신빈민법의 이데올로기적 양면성과 그 실제

This paper seeks to trace the ideological trends surrounding the enactment of the New Poor Law and explore the essence of the act itself and the changes it brought about. The Swing Riots of 1830 sparked a substantial demand for reforming poor laws, resulting in the organisation of the Royal Commission into the Operation of the Poor Laws. Edwin Chadwick, a Benthamite, and Nassau Senior, a liberal political economist, played key roles in leading the compilation of the final report of the commission that served as the foundational material for the New Poor Law. Their divergent ideological orientations translated into the dual nature of the act. Utilitarian Benthamites prioritised expanding government functions, the growth of bureaucracy, and the restructuring and rationalisation of administrative structures as needed. On the other hand, advocates of classical liberalism, who championed laissez-faire, emphasized minimizing government intervention, local autonomy, and economic individualism. The specific legal provisions of the New Poor Law and the socio-economic changes following its enactment were an exquisite compromise between these two ideologies. According to the act, a central authority specialising in poor administration was established. Locally, the parish-based Old Poor Law system was dismantled, and poor law unions took the place of parishes, establishing large joint workhouses. These structural changes clearly aligned with the direction pursued by the Benthamites. At the same time, in specific matters, the New Poor Law, however, embodied elements of classical liberalism. The newly established central authority performed only a passive supervisory role, and the operation of local unions still remained under the influence of local elites. The ultimate goal of the union workhouses was not the expected rehabilitation of or care for the poor but rather a deterrent effect. In conclusion, the 19th-century New Poor Law system encapsulated elements of classical liberalism within the Benthamite framework.

Relación de la Derivada de Cantor-Bendixson con el Álgebra de Conjuntos

This article provides a detailed analysis of the relationship between the Cantor-Bendixson derivative and set containment, as well as the standard set operations of union and intersection. In particular, it is shown that the Cantor-Bendixson derivative is increasing with respect to set containment and, under suitable hypotheses, generates a decreasing family of sets. On the other hand, we study both the derivative of a union and the derivative of an intersection, under different restrictions on the cardinality of the family of sets being operated on, while taking into account the order of derivative being performed.

Post-processing feature-mapping topology optimisation designs towards feature-based CAD processing

Feature-mapping (FM) optimisation frameworks have received much attention for structural topology optimisation with explicit geometric parameters. This paper presents a methodology for constructing parametric feature-based CAD models from designs generated using Moving Morphable Components (MMC). Emphasis is placed on constructing feature-based CAD models that conform to conventional modelling practices, where individual parameterised features are modelled using feature templates and united through Boolean union operations. This involves the use of algorithms to facilitate feature clean-up and identify connexions between features. The progression through several examples demonstrates how the developed algorithms can realise a feature-based CAD model from the results of an FM optimisation. Integration with a commercial CAD system provides a wide range of modelling capabilities to the designer for downstream design tasks.

Some Properties of Operations in the Collection of Intuitionistic Fuzzy Sets : A Novel Approach

In this paper, we introduce collection of intuitionistic fuzzy sets as a new concept of intuitionistic fuzzy sets. In ordinary, universal set in intuitionistic fuzzy sets is classical set. So in this paper, we generalize the universal set as a collection or family of intuitionistic fuzzy sets. We also present intersection and union operation on collection of of intuitionistic fuzzy sets and show that the operations hold commutative, assosiative, idempotent, and De Morgan’s laws properties.

A representation of a class of quasi-arithmetic means using a unary modifier operator

In this short communication, we will show that a quasi-arithmetic mean induced by an additive generator of a strict t-norm (strict t-conorm, respectively) can be represented by the composition of a unary operator (called the tau function) and the strict t-norm (strict t-conorm, respectively), both induced by the same generator function as the quasi arithmetic mean. Here, we will also state a connection between the idempotency of a transformed strict t-norm (strict t-conorm, respectively) and the tau function.

A New Soft Set Operation: Complementary Soft Binary Piecewise Intersection (∩) Operation

The soft set theory developed by Molodtsov has been applied both theoretically and practically in many fields. It is a useful piece of mathematics for handling uncertainty. Numerous variations of soft set operations have been described and used since its introduction. In this paper, we define a new soft set operation, called complementary soft binary piecewise intersection operation, a unique soft set operation, and examine its basic algebraic properties. Additionally, we aim to contribute to the literature on soft sets by illuminating the relationships between this new soft set operation and other kinds of soft set operations by researching the distribution of this new soft set operation over other soft set operations. Moreover, we prove that the set of all the soft sets with a fixed parameter set together with the complementary soft binary piecewise intersection operation and the soft binary piecewise union operation is a zero-symmetric near-semiring and hemiring.

Linking Phenotypes and Genotypes with Matrix Factorizations.

We linked phenotypes and genotypes by PheGe-Net, a unified operation frame. Genotype refers to the general name of all gene combinations of an individual. It reflects the genetic composition of organisms. Phenotype refers to the macroscopic characteristics of an organism that can be observed. Identifying the phenotype-genotype association assists in the explanation of the pathogenesis and the progress of genomic medicine. PheGe-Net exploited the similarity net of phenotypes and genotypes and recognized phenotype-genotype relationships to discover their hidden interactions. By conducting experiments with a real-world dataset, the validity of our PheGe-Net is verified. Our method outperformed the second-best one by around 3% on Accuracy and NMI when clustering the phenotype/genotype; it also successfully detected phenotype-genotype associations, for example, the association for obesity (OMIM ID: 601665) was analyzed, and among the top ten scored genes, two known ones were assigned with scores more than 0.75, and other eight predicted ones are also explainable. PheGe-Net is not only able to discover latent phenotype or genotype clusters but also can uncover the hidden relationships among them, as long as there are known similarity networks of phenotype, genotype, and acknowledged pheno-genotype relationships.

A power/energy-efficient, process-variation-resilient multiplier using graphene nanoribbon technology and ternary logic

In consideration of the difficulties related to interconnectivity and energy usage in binary logic, designers have felt compelled to explore ternary logic as a viable alternative. The most effective approach for implementing circuits based on ternary logic involves the use of the multi-threshold voltage (Vth) technique. In the case of field-effect transistors (FETs) that utilize graphene nanoribbons (GNRs), known as GNRFETs, the value of Vth relies on the GNR’s width, which can be adjusted by altering the dimer lines number. GNRFET shows potential as a replacement for CMOS technology due to the remarkable properties of GNR that help address scaling issues and short-channel effects. However, for real-time applications like portable electronic devices, power and energy efficiency are the primary concerns. Consequently, this paper presents a power and energy-efficient ternary multiplier based on 32-nm GNRFET technology. HSPICE simulation results obtained at 0.9 V demonstrate that the suggested circuit can achieve a minimum of 36.72% improvement in power and 28.17% enhancement in energy efficiency. This is accomplished through the utilization of distinct methods such as specific transistor configurations, unary operators, and dual power sources. Moreover, Monte-Carlo simulation results confirm the variation tolerance of the proposed circuit.

Logical Multilateralism

In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives.

An unbalanced ternary multiplier cell based on graphene nanoribbon field-effect transistors for PVT-tolerant low-energy portable applications

The potential benefits of using multiple-valued logic (MVL), especially ternary logic, which includes less interconnections, quicker response times, and smaller chip sizes, has gained the interest of designers of digital systems. A practical solution for achieving circuits with multiple thresholds in an efficient manner is through using graphene nanoribbon field-effect transistors (GNRFETs) that have modifiable threshold voltage values by adjusting the width of graphene nanoribbon. This article leverages the unique characteristics of GNRFETs and proposes a new design for a single-trit ternary multiplier (TMUL) circuit. The proposed TMUL uses two supply voltages to block direct current paths from high-to-low voltage levels, resulting in power and energy savings. Additionally, unary operators such as negative and positive ternary inverters and the complement of decisive literal are used to reduce transistor count and improve circuit performance. To thoroughly evaluate the performance of the proposed GNRFET-based TMUL circuit, extensive simulations are performed using Synopsis HSPICE tool and 32-nm channel length GNRFET devices, while taking into account the influences of process-voltage-temperature variations (PVT). The simulation results confirm the robustness and reliability of the proposed design, exhibiting reductions in power consumption by 71.18% to 76.36%, and energy consumption by 67.78% to 86.54%, when compared to other state-of-the-art TMUL circuits available in literature. Moreover, Monte-Carlo simulations have been performed to demonstrate that the suggested design exhibits reduced sensitivity towards significant process variations. As a result, the presented TMUL design can be a good choice for use in low-energy battery-operated portable multimedia device.

Semantical investigations on non-classical logics with recovery operators: negation

Abstract We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to ‘recover’ the properties of classical logic in a controlled manner. These structures are known as topological Boolean algebras, which are Boolean algebras extended with additional operations subject to specific conditions of a topological nature. In this study, we focus on the paradigmatic case of negation. We demonstrate how these algebras are well-suited to provide a semantics for some families of paraconsistent Logics of Formal Inconsistency and paracomplete Logics of Formal Undeterminedness. These logics feature recovery operators used to earmark propositions that behave ‘classically’ when interacting with non-classical negations. Unlike traditional semantical investigations, which are carried out in natural language (extended with mathematical shorthand), our formal meta-language is a system of higher-order logic (HOL) for which automated reasoning tools exist. In our approach, topological Boolean algebras are encoded as algebras of sets via their Stone-type representation. We use our higher-order meta-logic to define and interrelate several transformations on unary set operations, which naturally give rise to a topological cube of opposition. Additionally, our approach enables a uniform characterization of propositional, first-order and higher-order quantification, including restrictions to constant and varying domains. With this work, we aim to make a case for the utilization of automated theorem proving technology for conducting computer-supported research in non-classical logics. All the results presented in this paper have been formally verified, and in many cases obtained, using the Isabelle/HOL proof assistant.

Approach for Detecting Attacks on IoT Networks Based on Ensemble Feature Selection and Deep Learning Models.

The Internet of Things (IoT) has transformed our interaction with technology and introduced security challenges. The growing number of IoT attacks poses a significant threat to organizations and individuals. This paper proposes an approach for detecting attacks on IoT networks using ensemble feature selection and deep learning models. Ensemble feature selection combines filter techniques such as variance threshold, mutual information, Chi-square, ANOVA, and L1-based methods. By leveraging the strengths of each technique, the ensemble is formed by the union of selected features. However, this union operation may overlook redundancy and irrelevance, potentially leading to a larger feature set. To address this, a wrapper algorithm called Recursive Feature Elimination (RFE) is applied to refine the feature selection. The impact of the selected feature set on the performance of Deep Learning (DL) models (CNN, RNN, GRU, and LSTM) is evaluated using the IoT-Botnet 2020 dataset, considering detection accuracy, precision, recall, F1-measure, and False Positive Rate (FPR). All DL models achieved the highest detection accuracy, precision, recall, and F1 measure values, ranging from 97.05% to 97.87%, 96.99% to 97.95%, 99.80% to 99.95%, and 98.45% to 98.87%, respectively.

FDF-HybridFS: Towards design of a failure detection framework using hybrid feature selection method for IP core networks that connect 5G core in NFV-based test environment

With the advancement of recent technologies, high-speed and secure internet connectivity is required for 5th-generation mobile networks. A massive number of smart devices connected to the networks generate a large amount of data. Consequently, increasing traffic has generated more strain on networks and devices. Therefore, to handle the huge amount of data generated by the various devices and to detect network and device failures, automation is expected to play an important role. Hence, these requirements have accelerated the necessity of automation. This study presents a novel hybrid feature-selection technique for detecting network and device failure in IP core networks that connect 5 G core networks for internet connectivity. This approach first performs feature ranking using the MI (Mutual information), CC (Correlation coefficient), and GI (Gini index) to get the three different feature sets. Subsequently, in order to acquire a single optimized feature set, features are combined using a union operation. This optimized feature set is fed to the wrapper-based Boruta feature selection algorithm. In addition, to handle the data imbalance problem, we have applied the SMOTETomek method. Finally, obtained optimized feature set is fed to the three most popular ensemble approaches, Random forest, LGBM (Light gradient boosting machine), and xGBoost for the detection of failure. The proposed detection system's performance is evaluated using the KDDI dataset provided by KDDI Corporation. The effectiveness of the proposed FDF-HybridFS is tested and compared with several recent state-of-the-art methods cited in the related work in terms of detection rate, precision, accuracy, and F1 score. An analysis of the proposed failure detection framework's performance on the KDDI dataset shows that it outperforms state-of-the-art methods in terms of both detection rate and detection accuracy.

Nondeterministic operational complexity in subregular languages

We study the nondeterministic state complexity of basic regular operations on subregular language families. In particular, we focus on the classes of combinational, singleton, finite, finitely generated left ideal, symmetric definite, group, star, comet, two-sided comet, ordered, and power-separating languages, and consider the operations of intersection, union, concatenation, power, Kleene star, reversal, and complementation. We get the exact complexity in all cases, except for complementation of singleton languages where we only have a lower bound n and an upper bound n. The complexity of all operations on combinational languages is given by a constant function, except for the k-th power where it is k+1. For all considered operations, the known upper bounds for left ideals are met by finitely generated left ideal languages, and the known lower bound 2n−1 for complementation on left ideals is tight also for symmetric definite languages. The complexity of intersection on singleton languages is min⁡{m,n}, and for all other operations, except for complementation, the known upper bounds for finite languages are met by singleton languages. The nondeterministic state complexity of the k-th power, star, and reversal on star languages is n, and the nondeterministic state complexity of complementation on group languages is max⁡{n,(n−1⌊n/2⌋)}. In all the remaining cases, the nondeterministic state complexity of all considered operations is the same as in the regular case, although sometimes we need to use a larger alphabet to describe the corresponding witnesses.

An efficient GNRFET-based circuit design of ternary half-adder

Attaining low energy consumption in digital circuits design is a main task for designers because emerging applications are based on batteries and face limited-energy. Designing digital circuits with application to multiple-valued logic (MVL) and graphene nanoribbon field-effect transistor (GNRFET) provides a huge improvement in energy consumption. In this regard, this paper presents a novel ternary Half-Adder (THA) implemented with metal-oxide semiconductor (MOS)-type GNRFET. In the proposed THA, the Sum circuit is based on a combination of 3:1 ternary multiplexer, unary operators, and two supply voltages (dual-VDD), and the Carry circuit is based on unary operators, pass-transistor logic, and dual-VDD. The proposed THA is simulated using the 32-nm MOS-type GNRFET technology node at 0.9 V supply voltage in the HSPICE simulator. The proposed THA reduces the transistors count by 5.71–26.67% compared to the previously published THA circuits available in the literature, which are similar to the proposed THA from the design approach point of view. It is concluded from the simulation results that the proposed THA improves the power and energy consumptions by 83.33–91.41% and 66.38–82.27%, respectively. Moreover, the proposed THA is also designed and simulated using the Stanford 32-nm carbon nanotube field-effect transistor (CNTFET) technology. The proposed MOS-type GNRFET-based THA reduces the power and energy consumptions by 84.79% and 68.03%, respectively, and increases the delay by 2.12 × compared to its CNTFET-based counterpart. Moreover, the proposed CNTFET-based THA offers the second-lowest delay and power and the third-lowest energy compared to other existing CNTFET-based THA circuits.

An Adaptive Subinterval Finite Element Method Based on Dynamic Sensitivity Analysis for Structures with Uncertain-but-Bounded Parameters

To overcome computational inefficiency of the traditional subinterval finite element method, a novel adaptive subinterval finite element method based on dynamic sensitivity analysis is proposed to evaluate static response bounds of structures with uncertain-but-bounded parameters. Firstly, the original interval is divided into subintervals, and expansion routes for each displacement component are constructed based on dynamic sensitivity analysis. Then, the structural response bounds are analysed using a modified interval finite element method within each subinterval on the expansion route. Finally, the bounds of all displacement components are obtained via the interval union operation. To determine the appropriate number of subintervals, an adaptive convergence mechanism is proposed. The proposed method has accuracy and efficiency advantages over traditional subinterval finite element methods. The accuracy and effectiveness of this method are verified via numerical calculations of a nine-bar truss and an impeller.