Global stability of fuzzy cognitive maps

Complex systems can be effectively modelled by fuzzy cognitive maps. Fuzzy cognitive maps (FCMs) are network-based models, where the connections in the network represent causal relations. The conclusion about the system is based on the limit of the iteratively applied updating process. This iteration may or may not reach an equilibrium state (fixed point). Moreover, if the model is globally asymptotically stable, then this fixed point is unique and the iteration converges to this point from every initial state. There are some FCM models, where global stability is the required property, but in many FCM applications, the preferred scenario is not global stability, but multiple fixed points. Global stability bounds are useful in both cases: they may give a hint about which parameter set should be preferred or avoided. In this article, we present novel conditions for the global asymptotical stability of FCMs, i.e. conditions under which the iteration leads to the same point from every initial vector. Furthermore, we show that the results presented here outperform the results known from the current literature.

The local formula of representation of a solution for a functional differential equation with the mixed initial condition considering perturbations of delays containing in the phase coordinates and in controls

For the perturbed controlled nonlinear delay functional differential equation with the mixed initial condition a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of main interval. In the formula the effects of perturbations of the delay parameters containing in the phase coordinates and controls, the initial vector, the initial and control functions are detected.

Development of a hash algorithm based on cellular automata and chaos theory

Information security, reliability of data transfer are today an important component of the globalization of information technology. Therefore, the proposed work is devoted to highlighting the results of the design and development of a hacking-resistant algorithm to ensure the integrity of information transfer via digital technology and computer engineering. To solve such problems, cryptographic hashing functions are used. In particular, elements of deterministic Chaos were introduced into the developed cyclic hashing algorithm. The investigation analyzes in detail the strengths and weaknesses of known hashing algorithms. They are shown to have disadvantages. The main ones are a large number of matches (Hamming (x, y) and the presence of a weak avalanche effect, which lead to a significant decrease in the reliability of the algorithm for hacking. The designed hashing algorithm uses an iterative Merkley-Damgard structure, augmented by the input message to a length multiple of 512 bits. Processing in blocks of 128-bit uses cellular automata with mixed rules of 30, 105 and 90, 150 and takes into account the dependence of the generation of the initial vector on the incoming message. This allows half of the 10,000 pairs of arbitrary messages to have an inverse Hamming distance of 0 to 2. The proposed algorithm is four times slower than the well-known family of "secure hash algorithms." However, computation speed is not a critical requirement for a hash function. Decreasing the sensitivity to the avalanche effect allows the generation time to be approximately halved. Optimization of the algorithm, as well as its testing was carried out using new technologies of the Java programming language (version 15). Suggestions and recommendations for improving this approach to data hashing are given also

4G Network Security Algorithms: Overview

<p class="0abstractCxSpFirst">Long Term Evolution (LTE) of (Universal Mobile Telecommunication System) is one of the modern steps in series of mobile telecommunications systems. That appears to be a strong technology that meets the requirements of fourth-generation (4G) mobile networks and supports authentication and encryption mechanisms between User Equipment (UE) and Message Management Entity (MME). This paper provides an overview of the three most important algorithms that are considered the heart of LTE cryptographic algorithms (SNOW3G, AES, and ZUC) and a comparison between cipher key length and initial vector length to generate keystream depending on the structure used for each algorithm as each algorithm has a time of complexity and space of complexity that differs from the other security algorithm.</p><p class="0abstractCxSpLast"><strong> </strong></p>

Time-dependent unbounded Hamiltonian simulation with vector norm scaling

The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable discretization, the norm of the Hamiltonian can be very large, which significantly increases the simulation cost. However, the operator norm measures the worst-case error of the quantum simulation, while practical simulation concerns the error with respect to a given initial vector at hand. We demonstrate that under suitable assumptions of the Hamiltonian and the initial vector, if the error is measured in terms of the vector norm, the computational cost may not increase at all as the norm of the Hamiltonian increases using Trotter type methods. In this sense, our result outperforms all previous error bounds in the quantum simulation literature. Our result extends that of [Jahnke, Lubich, BIT Numer. Math. 2000] to the time-dependent setting. We also clarify the existence and the importance of commutator scalings of Trotter and generalized Trotter methods for time-dependent Hamiltonian simulations.

Infinite Series of Singularities in the Correlated Random Matrices Product

We consider the product of a large number of two 2 × 2 matrices chosen randomly (with some correlation): at any round there are transition probabilities for the matrix type, depending on the choice at previous round. Previously, a functional equation has been derived to calculate such a random product of matrices. Here, we identify the phase structure of the problem with exact expressions for the transition points separating “localized” and “ergodic” regimes. We demonstrate that the latter regime develops through a formation of an infinite series of singularities in the steady-state distribution of vectors that results from the action of the random product of matrices on an initial vector.

Automatic construction of academic profile: A case of information science domain

To provide junior researchers with domain-specific concepts efficiently, an automatic approach for academic profiling is needed. First, to obtain personal records of a given scholar, typical supervised approaches often utilise structured data like infobox in Wikipedia as training dataset, but it may lead to a severe mis-labelling problem when they are utilised to train a model directly. To address this problem, a new relation embedding method is proposed for fine-grained entity typing, in which the initial vector of entities and a new penalty scheme are considered, based on the semantic distance of entities and relations. Also, to highlight critical concepts relevant to renowned scholars, scholars’ selective bibliographies which contain massive academic terms are analysed by a newly proposed extraction method based on logistic regression, AdaBoost algorithm and learning-to-rank techniques. It bridges the gap that conventional supervised methods only return binary classification results and fail to help researchers understand the relative importance of selected concepts. Categories of experiments on academic profiling and corresponding benchmark datasets demonstrate that proposed approaches outperform existing methods notably. The proposed techniques provide an automatic way for junior researchers to obtain organised knowledge in a specific domain, including scholars’ background information and domain-specific concepts.

TRUST MODELING: A PROBABILITY APPROACH

The work is devoted to describing an application of the DeGroot model in the following analysis: is it possible to establish a consensus of opinions of members in a social group (a society). This model describes the process of changing the agents’ opinion about a certain event or statement, factoring in the effect of interpersonal trust between agents, which is modelled by Markov chains. Agents’ opinions are represented by the probability of them showing their support to a given statement (event). The interpretation of the DeGroot model is quite broad. It includes, in particular, the study of economic decision-making, the influence of public opinion on people and the fact of achieving a consensus. The paper considers the conditions under which the process of updating the opinions of agents, belonging to a social group (network), converges to a certain limit value - a consensus, i.e. a case when all agents in a social group have the same opinion on a particular issue. We also show some generalizations of the DeGroot model, namely those that concern adding time dependency to the rules of updating the opinions of agents. To test the DeGroot model, we implemented the two-dimensional case as a dynamic Microsoft Excel workbook. The paper describes 2 types of problems related to reaching a consensus, solved with the model. The first kind of problem constitutes an analysis of possibilities of obtaining the desired consensus with a given matrix of trust (interpersonal trust of agents), whilst changing the initial group members’ opinions vector about an event (statement). We also discuss a solution of the inverse problem: find the trust matrix such that the iterative opinion update process converges to the desired consensus with a given initial vector of opinions. The results we obtained may be used for analyzing the process of managing public (collective) opinion concerning certain economic decisions in a social group (network).

Solving Kepler’s equation with CORDIC double iterations

ABSTRACT In previous work, we developed the idea to solve Kepler’s equation with a CORDIC-like algorithm, which does not require any division, but still requires multiplications in each iteration. Here we overcome this major shortcoming and solve Kepler’s equation using only bitshifts, additions and one initial multiplication. We prescale the initial vector with the eccentricity and the scale correction factor. The rotation direction is decided without correction for the changing scale. We find that double CORDIC iterations are self-correcting and compensate for possible wrong rotations in subsequent iterations. The algorithm needs 75 per cent more iterations and delivers the eccentric anomaly and its sine and cosine terms times the eccentricity. The algorithm can also be adopted for the hyperbolic case. The new shift-and-add algorithm brings Kepler’s equation close to hardware and allows it to be solved with cheap and simple hardware components.

The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition

For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula, the effects of perturbations of the delay parameter, the initial vector, the initial and control functions are detected.