Homomorphic Mapping Research Articles

The L-Fuzzy Prime Filter Degrees on Lattices and Its Induced L-Fuzzy Convex Structure

The aim of this paper is to examine the L-fuzzy prime filter degrees on lattices and their induced L-fuzzy convex structure. Firstly, the notion of L-fuzzy prime filter degrees on lattices is established using the implication operator when L is a completely distributive lattice. Secondly, an equivalent characterization of L-fuzzy prime filter degrees on lattices is provided. The equivalence relation, through the definitions of reflexivity, symmetry, and transitivity, provides a method for partitioning subsets within a lattice that possesses the prime filter property. Finally, the L-fuzzy convex structure induced by the L-fuzzy prime filter degrees on lattices is examined. Simultaneously, the properties of L-fuzzy prime filter degrees on lattices in relation to images and preimages under homomorphic mappings are discussed.

Topology reconstruction for asymmetric systems by homomorphic mapping or perturbation approximation

Topology reconstruction for asymmetric systems by homomorphic mapping or perturbation approximation

HierCGRA: A Novel Framework for Large-scale CGRA with Hierarchical Modeling and Automated Design Space Exploration

Coarse-grained reconfigurable arrays (CGRAs) are promising design choices in computation-intensive domains, since they can strike a balance between energy efficiency and flexibility. A typical CGRA comprises processing elements (PEs) that can execute operations in applications and interconnections between them. Nevertheless, most CGRAs suffer from the ineffectiveness of supporting flexible architecture design and solving large-scale mapping problems. To address these challenges, we introduce HierCGRA, a novel framework that integrates hierarchical CGRA modeling, Chisel-based Verilog generation, LLVM-based data flow graph (DFG) generation, DFG mapping, and design space exploration (DSE). With the graph homomorphism (GH) mapping algorithm, HierCGRA achieves a faster mapping speed and higher PE utilization rate compared with the existing state-of-the-art CGRA frameworks. The proposed hierarchical mapping strategy achieves 41× speedup on average compared with the ILP mapping algorithm in CGRA-ME. Furthermore, the automated DSE based on Bayesian optimization achieves a significant performance improvement by the heterogeneity of PEs and interconnections. With these features, HierCGRA enables the agile development for large-scale CGRA and accelerates the process of finding a better CGRA architecture.

Estimating Acceleration from a Single Uniform Linear Motion-Blurred Image using Homomorphic Mapping and Machine Learning

Context: Vision-based measurement (VBM) systems are becoming popular as an affordable and suitable alternative for scientific and engineering applications. When cameras are used as instruments, motion blur usually emerges as a recurrent and undesirable image degradation, which in fact contains kinematic information that is usually dismissed. Method: This paper introduces an alternative approach to measure relative acceleration from a real invariant uniformly accelerated linear motion-blurred image. This is done by using homomorphic mapping to extract the characteristic Point Spread Function (PSF) of the blurred image, as well as machine learning regression. A total of 125 uniformly accelerated motion-blurred pictures were taken in a light- and distance-controlled environment, at five different accelerations ranging between 0,64 and 2,4 m/s2. This study evaluated 19 variants such as tree ensembles, Gaussian processes (GPR), and linear, support vector machine (SVM), and tree regression. Results: The best RMSE result corresponds to GPR (Matern 5/2), with 0,2547 m/s2 and a prediction speed of 530 observations per second (obs/s). Additionally, some novel deep learning methods were used to obtain the best RMSE value (0,4639 m/s2 for Inception ResNet v2, with a prediction speed of 11 obs/s. Conclusions: The proposed method (homomorphic mapping and machine learning) is a valid alternative for calculating acceleration from invariant motion blur in real-time applications when additive noise is not dominant, even surpassing the deep learning techniques evaluated.

Dual quaternion operations for rigid body motion and their application to the hand–eye calibration

The dual quaternion plays an advantageous role in the field of robotic kinematics and dynamics due to its compact expression. It is well known that quaternion can be easily implemented as algebraic operations on vectors through matrix operators. Similarly, the dual matrix operators can convert dual quaternion operations to matrix operations. However, it has not received adequate attention, and thus there are very few applications at present. With the dual matrix operators of dual quaternion, this paper re-verifies the equivalency between the conjugate formula of unit dual quaternion and dual Euler–Rodrigues formula. To combine this equivalence with the homomorphic mapping of Lie groups, a theoretical correlation of the current hand-eye calibration methods is established. Motivated by the attempt to establish a more complete scheme for hand-eye calibration, a new simultaneous method based on the conjugate formula of dual quaternion is proposed. The method verifies that the rotation problem can be extended to the rigid-body transformation problem via the dual algebra. Finally, the simulation and experimental validations for the hand–eye calibration method are given.

Maps Preserving Zero ∗-Products on ℬ(ℋ)

The conventional research topic in operator algebras involves exploring the structure of algebras and using homomorphic mappings to study the classification of algebras. In this study, a new invariant is developed based on the characteristics of the operator using the linear preserving method. The results show that the isomorphic mapping is used for preserving this invariant, which provides the classification information of operator algebra from a new perspective. Let H and K be Hilbert spaces with dimensions greater than two, and let B(H) and B(K) be the set of all bounded linear operators on H and K, respectively. For A,B∈B(H), the ∗, ∗-Lie, and ∗-Jordan products are defined by A∗B, A∗B−B∗A, and A∗B+B∗A, respectively. Let Φ:B(H)→B(K) be an additive unital surjective map. It is confirmed that if Φ preserves zero ∗, ∗-Lie, and ∗-Jordan products, then Φ is unitary or conjugate unitary isomorphisms.

Families of homomorphic mappings in the polydisk

We study classes of locally biholomorphic mappings defined in the polydisk P n that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations, and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order is Lipschitz continuous with respect to the bound on the Schwarzian, and use this to estimate the order of the original classes.

Кількісна оцінка рівня ризику збільшення витрат на розробку зразків космі-чної техніки

The goal of this work is to develop a methodological approach to quantitative estimation of the risk of an increase in the cost of space hardware prototyping. The paper considers a technology and mathematical models for quantitative estimation of the risk of an increase in the cost of a developmental work on space hardware prototyping. The main cause of the risk of development cost increase is that data used in expected cost estimation are incomplete and inaccurate. The risk level is estimated as the probability of the possible cost of an R&D project exceeding a critical (for the investor) value. The risk estimation technology is constructed on the basis of the Monte Carlo method embedded in a simulation model. The Monte Carlo method is based on an analytico-probabilistic model (a deterministic mathematical model and a probabilistic model with known distribution functions (laws)). The uniqueness, novelty, and technical complexity of space hardware prototypes do not allow one to construct any analytico-probabilistic model. This paper presents a mathematical model equivalent to an analytico-probabilistic one. The paper substantiates the appropriateness of a homomorphic mapping of a possibilistic space of random variables into a probabilistic space; i.e. in this case the proposed model is equivalent to an analytico-probabilistic one. The key component of the simulation model is the mathematical model of the development cost of a space hardware prototype. The cost model is based on a component-by-component analogy for relatively simple components of the space hardware prototype, moving (upward) along the weighted oriented tree graph that models the engineering structure of the space hardware prototype, and fuzzy methods. The proposed methodological approach may be used in the construction of a simulation model for quantitative estimation vc of the risk of a decrease in the efficiency of use of the prototype under development. To do this, it will be sufficient to replace the mathematical model of development cost with a mathematical model of expected efficiency.

Neurophenomenal structuralism. A philosophical agenda for a structuralist neuroscience of consciousness.

The program of “neurophenomenal structuralism” is presented as an agenda for a genuine structuralist neuroscience of consciousness that seeks to understand specific phenomenal experiences as strictly relational affairs. The paper covers a broad range of topics. It starts from considerations about neural change detection and relational coding that motivate a solution of the Newman problem of the brain in terms of spatiotemporal relations. Next, phenomenal quality spaces and their Q-structures are discussed. Neurophenomenal structuralism proclaims a homomorphic mapping of the structures of self-organized neural maps in the brain onto Q-structures, and it will be demonstrated how this leads to a new and special version of structural representationalism about phenomenal content. A methodological implication of neurophenomenal structuralism is that it proposes measurement procedures that focus on the relationships between different stimuli (as, for instance, similarity ratings or representational geometry methods). Finally, it will be shown that neurophenomenal structuralism also has strong philosophical implications, as it leads to holism about phenomenal experiences and serves to reject inverted qualia scenarios.

A Novel Concept of Fuzzy Subsemigroup (Ideal)

This paper focuses on a generalized definition of fuzzy subsemigroup (ideal) on semigroup. Let L be a completely distributive lattice; we introduce the definition of L‐fuzzy ideal and also the novel concept of subsemigroup (ideal) on semigroup. Then, we discuss the necessary and sufficient conditions of L‐fuzzy subsemigroup (ideal) measure using the four level cuts of an L‐fuzzy set. Moreover, we study the properties of L‐fuzzy subsemigroup (ideal) measure. As an application of L‐fuzzy subsemigroup (ideal) measure, we obtain the L‐fuzzy convexities on a semigroup and bijective semigroup homomorphic mapping is an L‐fuzzy isomorphism.

Research on the Properties of Lattice-Valued Finite State Machines in Computer Technology

In this paper, we discuss some algebraic properties of Lattice valued finite state machine and prove that if there are homomorphic mapping satisfying certain conditions between two Lattice valued finite state machines, the first one is strongly connected (cycle), then then the second one is the same. And if the homomorphism is strongly homomorphic, one of the Lattice valued finite state machines is complete if and only if another Lattice valued finite state machine is complete. Discuss the completeness, strong connectivity, circulation and exchange capacity between the product of a Lattice valued finite state machine and the original Lattice valued finite state machine and get some results.

Game Theory in Practice, on the (Non) Discovery of Social Equilibria

What follows is an attempt to view (elementary) game theory through the prism of recent developments in philosophy of mathematics. In particular, if a model (in the sense of model theory)on an appropriate domain can be constructed from a formal theory and it can be established that homomorphic mappings between model structures are possible then such a maneuver undermines the Realistic case for solution concepts since it makes the denotation of such concepts problematic since the denotation ceases to be unique. This creates philosophical problems within the Philosophy of mathematics which affects communities of mathematicians working in particular mathematical areas. (Groups, Rings, Vector Spaces, Graphs and so on) However when it comes to game theory, problematic denotation affects not only Professionals (mathematicians, economists, game theorists) but also ‘ordinary’ people in the real world who interact with each other in social contexts amenable to game theoretic analysis I note briefly that Game theory has difficulties, still, with equilibrium selection and simple 2X2 games fail to predict and these problems have triggered extensive debates. I do not specify any specific causal connection between referential failure and any given issue within game theory I do however suggest that there is clearly a need to supplement the semantics of equilibrium concepts (here the minimax theorem) and I note that even simple 2X2 games typically come with labels, prisoner, husband-wife, hawk and so on. These perhaps provide hooks into more comprehensive semantics. I also briefly discuss conventions as an additional mechanism. Finally I suggest that if this analysis is on the right lines it might be extended to include more complex social equilibrium mechanisms like Nash equilibrium or general economic equilibrium in micro economics. The style is deliberately informal.

The noncommutative values of quantum observables

We discuss the notion of representing the values of physical quantities by the real numbers, and its limits to describe the nature to be understood in the relation to our appreciation that the quantum theory is a better theory of natural phenomena than its classical analog. Getting from the algebra of physical observables to their values for a fixed state is, at least for classical physics, really a homomorphic map from the algebra into the real number algebra. The limitation of the latter to represent the values of quantum observables with noncommutative algebraic relation is obvious. We introduce and discuss the idea of the noncommutative values of quantum observables and its feasibility, arguing that at least in terms of the representation of such a value as an infinite set of complex numbers, the idea makes reasonable sense theoretically as well as practically.

Further research on exponential stability for quaternion-valued neural networks with mixed delays

This paper addresses the global exponential stability of a class of quaternion-valued neural networks (QVNNs) with mixed delays including time-varying delays and infinite distributed delays. Because of the noncommutativity of quaternion multiplication, the concerned quaternion-valued models separated into four real-valued parts to form the equivalent real-valued systems. Based on M-matrix properties and homomorphism mapping theories, some sufficient conditions are derived to guarantee the existence and uniqueness of the equilibrium point of the system. Conditions for ensuring the global exponential stability of the equilibrium point of the system are obtained on the basis of the vector Lyapunov function method instead of the linear matrix inequality method. Using a similar method, the mixed-delay QVNNs with parameter uncertainties are also studied, and the conditions for ensuring the global robust exponential stability of the system are established directly. The adopted approach and the obtained results in this paper complement already the existing ones. Finally, three numerical examples are provided to illustrate the feasibility and the less level conservatism of the main results.

HOMOMORPHIC AGGREGATE SIGNATURE SCHEME WITH OUTSOURCING ALGORITHM BASED PRIVACY PRESERVING IN VANETS

One of the important paradigms of recent technological development has known to be Vehicular Ad-hoc Networks (VANETs) due to its current intelligent transportation network. Moreover, leakage of communication information or sensitive data in VANETs can leads to vulnerable attacks that may affect many properties and lives. For this reason, VANET systems need to have high-level security aspects. In addition, devices with less computing resources expected for fast computation power. Several researchers have analysed various privacy preserving models for VANETs to protect from different attacks, which is not enough to prevent from new attackers. In this research, a Homomorphic Aggregate Signature (HAS) scheme proposed for achieving unforgeable message attacks without having random oracle and new outsourcing algorithm is designed efficiently for exponential operations to reduce the computational cost in which matrices conjugate operation based on homomorphic mapping is used for achieving the security of both base and exponent numbers. In addition, a protocol based on privacy preserving is constructed for VANETs by using the proposed HAS scheme and outsourcing computing, in which the authentication is processed by presenting a proxy re-signature scheme. In this proposed protocol, RSU will act as an agent when TA authorizes it and OBU’s signatures are converted to TA’s signature by using RSU. Real-identity of OBU is traced by TA using its secret key when an unknown/malicious message is detected then the proposed protocol will provide traceability, privacy, and anonymity. Furthermore, pairing and exponential operations are not needed by the proposed scheme as ` complexity of calculations is reduced significantly for VANET system.

Global Mittag-Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays

This paper investigates the stability of impulsive fractional-order complex-valued BAM neural networks with time varying delays. As the extension of fractional-order real-valued BAM neural networks, fractional-order complex-valued BAM neural networks have complex-valued states, synaptic weights, and the activation functions. Two different kinds of activation functions are considered, along with popular bounded and Lipschitz-kind activation functions. By using Lyapunov function and Homomorphic mapping theorem, sufficient conditions for the existence of unique equilibrium and global asymptotic stability of complex-valued systems are derived. In derivation we separated nonlinear complex-valued activation functions into real and imaginary parts. Moreover, Mittag-Leffler stability for BAM neural networks(BAMNNs) have been proposed when the nonlinear complex activation functions are bounded. Simulation results are presented to prove the efficiency of the obtained methods.

Integrating computation into the mechanistic hierarchy in the cognitive and neural sciences

It is generally accepted that, in the cognitive and neural sciences, there are both computational and mechanistic explanations. We ask how computational explanations can integrate into the mechanistic hierarchy. The problem stems from the fact that implementation and mechanistic relations have different forms. The implementation relation, from the states of an abstract computational system (e.g., an automaton) to the physical, implementing states is a homomorphism mapping relation. The mechanistic relation, however, is that of part/whole; the explaining features in a mechanistic explanation are the components of the explanandum phenomenon and their causal organization. Moreover, each component in one level of mechanism is constituted and explained by components of an underlying level of mechanism. Hence, it seems, computational variables and functions cannot be mechanistically explained by the medium-dependent states and properties that implement them. How then, do the computational and the implementational integrate to create the mechanistic hierarchy? After explicating the general problem (Sect. 2), we further demonstrate it through a concrete example, of reinforcement learning, in the cognitive and neural sciences (Sects. 3 and 4). We then examine two possible solutions (Sect. 5). On one solution, the mechanistic hierarchy embeds at the same levels computational and implementational properties. This picture fits with the view that computational explanations are mechanistic sketches. On the other solution, there are two separate hierarchies, one computational and another implementational, which are related by the implementation relation. This picture fits with the view that computational explanations are functional and autonomous explanations. It is less clear how these solutions fit with the view that computational explanations are full-fledged mechanistic explanations. Finally, we argue that both pictures are consistent with the reinforcement learning example, but that scientific practice does not align with the view that computational models are merely mechanistic sketches (Sect. 6).

Enhanced Homomorphic Unsharp Masking method for intensity inhomogeneity correction in brain MR images

ABSTRACTMRI is a powerful diagnostic tool providing excellent soft tissue contrast and high spatial resolution. However, imperfections arising in the radio frequency field and scanner-related intensity artefacts in MRI produce intensity inhomogeneity. These intensity variations pose major challenges for subsequent image processing and analysis techniques. Therefore, a robust means of correcting intensity inhomogeneity is essential for any accurate and efficient processing technique. Homomorphic filtering based techniques are commonly used for intensity correction in brain MR images, but the halo effect induced by these methods limit their performance in the presence of a tumour. To mitigate the halo effect, a novel Enhanced Homomorphic Unsharp Masking (EHUM) intensity correction algorithm is proposed in this paper. The proposed method first determines the ROI to overcome the halo effect between foreground and background regions. Then, the intensity correction is carried out using homomorphic filtering and linear grey scale mapping. The quantitative and qualitative evaluation results show the efficiency of the proposed method in overcoming the intensity inhomogeneity in both normal and abnormal brain MR images.

Foundation of Interval‐Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

The intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. However, the interval‐valued IFC (IVIFC), based on the basic operational laws of interval‐valued IFNs (IVIFNs), is only in the original stage. To further develop the theory of the IVIFC and make it be rigorous, the primary task is to systematically investigate the characteristics of the limits and differentials, which is a foundation of the IVIFC. Moreover, there is quite a lot of literature on IVIFNs; however, the scholars did not reveal the relationships between IFNs and the IVIFNs. To do that, we first investigate the limit of interval‐valued intuitionistic fuzzy sequences, and then, we focus on investigating the limit, the continuity, and the differential of IVIFFs in detail and reveal their relationships. After that, due to the fact that the IFC and the IVIFC are based on the basic operational laws of IFNs and IVIFNs, respectively, we reveal the relationships between the IFNs and the IVIFNs via some homomorphic mappings. Finally, a case study about continuous data of IVIFNs is provided to illustrate the advantages of continuous data.

A Lightweight Privacy-Preserving Protocol for VANETs Based on Secure Outsourcing Computing

In the VANET systems, the leakage of some sensitive data or communication information will cause heavy losses for life and property. Then, a higher security level is required in the VANET systems. Meanwhile, fast computation powers are needed by devices with limited computing resources. Thus, a secure and lightweight privacy-preserving protocol for VANETs is urgent. In this paper, we first propose an identity-based signature that achieves unforgeability against chosen-message attack without random oracle. In order to reduce the computational cost, we design two secure and efficient outsourcing algorithms for the exponential operations, where a homomorphic mapping based on matrices conjugate operation is used to achieve the security of both exponent and base numbers. Furthermore, we construct a privacy-preserving protocol for VANETs by using outsourcing computing and the proposed IBS, where a proxy re-signature scheme is presented for authentications. In the VANET privacy-preserving protocol, TA authorizes RSU to act as an agent and RUS converts OBU's signature into TA's signature, which effectively hides the real identity of vehicle OBU. Meanwhile, TA has access to trace the real identity of OBU using its secret key when malicious messages are found. Then, the protocol provides anonymity, traceability, and privacy. In addition, with respect to the efficiency, our scheme does not need pairing operations and exponential operations. Thus, the calculation burdens for the VANET system can be significantly reduced.