Transition Graph Research Articles

Synchronization of networks over finite fields

In this paper, the synchronization problem for networks over finite fields is investigated, which is a generalization of consensus and provides a new perspective for networks of agents with limited capacities of memory and communication. It is assumed that the states and communication weights can only attain values from a finite alphabet equipped with a prime number of integers, termed finite fields, and operations are processed relying on modular arithmetic. For this synchronization problem, necessary and sufficient conditions are derived based on the transition graph of the studied network. The large number of nodes in the transition graph, dependent on the numbers of integers in finite fields and the agents, may lead to high computational cost and difficulties in verifying synchronization. To avoid this, an equivalent condition for synchronization of networks is provided by the characteristic polynomial of the studied network matrix. Furthermore, in a synchronized network over finite fields, the periodic behavior can be determined by the network matrix and the initial state.

A Cayley graph description of the symmetry breaking associated with deformation and structural phase transitions in metallic materials

Deformation and structural phase transitions are typical physical processes, which can produce variety types of defects (e.g., twinning and dislocation) in metals and alloys. Those crystalline defects are critical in determining the mechanical and functional properties of materials. Theoretically, crystalline defects belong to the so-called topological defects, which are generated by symmetry breaking processes. In spite of the well-established group theory description of crystal symmetry (for an individual crystal), a theoretical framework to characterize multiple symmetry breaking processes (e.g., multiple transformation pathways between two crystals, multiple deformation twinning modes) is still lacking. In the literature, a graph method, phase transition graph, has been introduced to describe the pathway connectivity in specific martensitic transformations. However, a general framework capturing the coupling of deformation and phase transitions is unavailable, partially due to the lack of rigorous connection between group theory (description of crystal symmetry) and graph theory (description of deformation pathway connectivity). In this paper, a theoretical connection between crystal symmetry and pathway connectivity is rigorously established for the first time. By examining the broken and preserved symmetries during crystal deformation and structural phase transitions through group theory, we employ a Cayley graph method to analyze symmetry groups, which leads to a new theoretical description of symmetry breaking based on group theory and graph theory. Our graph approach establishes a mathematical foundation to investigate the symmetry breaking associated with deformation and structural phase transitions in crystals, which also provides a new insight into the physical origin of crystalline defects.

Aggregation-based minimization of finite state automata

We present a minimization algorithm for non-deterministic finite state automata that finds and merges bisimulation-equivalent states. The bisimulation relation is computed through partition aggregation, in contrast to existing algorithms that use partition refinement. The algorithm simultaneously generalises and simplifies an earlier one by Watson and Daciuk for deterministic devices. We show the algorithm to be correct and run in time O left( n^2 r^2 left| varSigma right| right) , where n is the number of states of the input automaton M, r is the maximal out-degree in the transition graph for any combination of state and input symbol, and left| varSigma right| is the size of the input alphabet. The algorithm has a higher time complexity than derivatives of Hopcroft’s partition-refinement algorithm, but represents a promising new solution approach that preserves language equivalence throughout the computation process. Furthermore, since the algorithm essentially computes the maximal model of a logical formula derived from M, optimisation techniques from the field of model checking become applicable.

Learning With Interpretable Structure From Gated RNN.

The interpretability of deep learning models has raised extended attention these years. It will be beneficial if we can learn an interpretable structure from deep learning models. In this article, we focus on recurrent neural networks (RNNs), especially gated RNNs whose inner mechanism is still not clearly understood. We find that finite-state automaton (FSA) that processes sequential data have a more interpretable inner mechanism according to the definition of interpretability and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. With the learned FSA and via experiments on artificial and real data sets, we find that FSA is more trustable than the RNN from which it learned, which gives FSA a chance to substitute RNNs in applications involving humans' lives or dangerous facilities. Besides, we analyze how the number of gates affects the performance of RNN. Our result suggests that gate in RNN is important but the less the better, which could be a guidance to design other RNNs. Finally, we observe that the FSA learned from RNN gives semantic aggregated states, and its transition graph shows us a very interesting vision of how RNNs intrinsically handle text classification tasks.

Automata for DNA Splicing Languages with Palindromic and Non-Palindromic Restriction Enzymes using Grammars

In DNA splicing system, DNA molecules are cut and recombined with the presence of restriction enzymes and a ligase. The splicing system is analyzed via formal language theory where the molecules resulting from the splicing system generate a language which is called a splicing language. In nature, DNA molecules can be read in two ways; forward and backward. A sequence of string that reads the same forward and backward is known as a palindrome. Palindromic and non-palindromic sequences can also be recognized in restriction enzymes. Research on splicing languages from DNA splicing systems with palindromic and non-palindromic restriction enzymes have been done previously. This research is motivated by the problem of DNA assembly to read millions of long DNA sequences where the concepts of automata and grammars are applied in DNA splicing systems to simplify the assembly in short-read sequences. The splicing languages generated from DNA splicing systems with palindromic and nonpalindromic restriction enzymes are deduced from the grammars which are visualised as automata diagrams, and presented by transition graphs where transition labels represent the language of DNA molecules resulting from the respective DNA splicing systems.

Trend Analysis as a Useful Tool for Monetary Policy in the Real Estate Market

Purpose of article: The primary purpose of this study consists in the research that focuses on developing various scenarios for central bank interest rate regulation and its impact on property prices. Partial areas include the specification of individual factors and the description of relationships between individual scenarios. Since the study is based on real data and purely numerical calculations and simple statistical methods might not cover the whole issue, the trend analysis was used. After determining the main factors, a model containing a series of scenarios will be built. Based on these scenarios and the individual relationships between them, the oriented transitional graph will be generated. The eight-dimensional model serves as an example to determine transitions between scenarios and to understand the resulting scenario map as a whole. Using this study, we can monitor current market developments and behavior both in the past, present and predict a possible sequence of events in the future. This study builds on the already explored issues and extends the state of scientific knowledge in order to build more advanced models in the future with current factors and new conclusions valid for the continuous progress in the property market. Methodology/methods: Solving with using statistical methods, correlation matrix, trend analysis. Scientific aim: It is to find the correlation that proves the possibility of finding ways to lower house prices through central bank rates. Findings: The central bank interest rate has a direct impact on the real estate market which can be observed in the onset of scenarios in the transition graph. Conclusions: The real estate bubble represented as the housing price index can be affected by the central bank interest rates with the impact on other significant variables on the market.

EXACT SOLUTION OF TASKS OF DYNAMIC MODELING OF PROCESSES IN SYSTEMS OF TRANSPORT LOGISTIC

The dynamic models of processes in transport logistics systems are considered. In the literature, such complex systems as the military transport logistics system or the combat vehicle support system are often modeled as a set of typical system states. These states are interconnected by a large number of transitions of a given intensity, which are carried out with given probabilities. Graphically, this is represented using the so-called graph of states and transitions, and the probabilities of the system being in a particular state are the subject of research in such a graph. The methods available in the literature for studying the dynamic characteristics of state graphs and transitions are analyzed. A description of the changes in probabilities as a function of time is made using systems of differential equations, usually linear. Based on practical requirements, approximate solutions to such systems are usually sought. One of the approximate methods is the decomposition method, in which, instead of a system of coupled equations, a set of independent equations is considered, the solution of which is not difficult. The results of the solution have an accuracy satisfactory from the point of view of practical use. The assumptions based on which the decomposition method can be used are analyzed. It is shown that the accuracy of the obtained results substantially depends on the given initial conditions and should increase over time, when this dependence weakens. A method is proposed for the exact solution of a system of differential equations, free of any assumptions. The use of operational calculus is substantiated, which reduces the solution of a system of linear differential equations to the solution of a system of linear algebraic equations for unknown images of the sought-for Laplace functions. The method is used to describe the process of technical support for the restoration of the transport flow of military logistics. The boundaries of the possibility of applying the results of a simpler approximate solution are established.

Actin droplet machine

The actin droplet machine is a computer model of a three-dimensional network of actin bundles developed in a droplet of a physiological solution, which implements mappings of sets of binary strings. The actin bundle network is conductive to travelling excitations, i.e. impulses. The machine is interfaced with an arbitrary selected set of k electrodes through which stimuli, binary strings of length k represented by impulses generated on the electrodes, are applied and responses are recorded. The responses are recorded in a form of impulses and then converted to binary strings. The machine’s state is a binary string of length k: if there is an impulse recorded on the ith electrode, there is a ‘1’ in the ith position of the string, and ‘0’ otherwise. We present a design of the machine and analyse its state transition graphs. We envisage that actin droplet machines could form an elementary processor of future massive parallel computers made from biopolymers.

Visual analysis of the opinion flow among multiple social groups

Journalists, government agency and the public may hold different opinions about the same event; these opinions flow within and across multiple social groups. Understanding opinion flow in multiple social groups is conducive to have a quick grasp of the information on social media. Our study aims to explore the opinion flow within or across the pre-defined social groups and the mutual influence of these groups’ views about the same event. First of all, to depict the opinion flow, we propose a topic transition model, and for expressing the interaction of groups’ opinion, we propose a quantitative approach. Secondly, according to 4Ws, we design a visual analytic system to let users analyze public opinion events through our system. The visual interface is tightly coupled with the analytical methods to present a concise summary of the opinion flow of events. A novel forwarding-network slicing diagram is designed to depict the forwarding process. To describe the result of the topic transition model, we also propose a topic transition graph to characterize the opinion flow. And a novel glyph is designed to visualize the characteristic of the influence. Our system provides a variety of interactions to assist users in exploring data, and we demonstrate the functionality of the system through two case studies.

A Cayley Graph Description of the Symmetry Breaking Associated with Deformation and Structural Phase Transitions in Metallic Materials

Deformation and structural phase transitions are typical physical processes, which can produce variety types of defects (e.g., twinning and dislocation) in metals and alloys. Those crystalline defects are critical in determining the mechanical and functional properties of materials. Theoretically, crystalline defects belong to the so-called topological defects, which are generated by symmetry breaking processes. In spite of the well-established group theory description of crystal symmetry (for an individual crystal), a theoretical framework to characterize multiple symmetry breaking processes (e.g., multiple transformation pathways between two crystals, multiple deformation twinning modes) is still lacking. In the literature, a graph method, phase transition graph, has been introduced to describe the pathway connectivity in specific martensitic transformations. However, a general framework capturing the coupling of deformation and phase transitions is unavailable, partially due to the lack of rigorous connection between group theory (description of crystal symmetry) and graph theory (description of deformation pathway connectivity). In this paper, a theoretical connection between crystal symmetry and pathway connectivity is rigorously established for the first time. By examining the broken and preserved symmetries during crystal deformation and structural phase transitions through group theory, we employ a Cayley graph method to analyze symmetry groups, which leads to a new theoretical description of symmetry breaking based on group theory and graph theory. Our graph approach establishes a mathematical foundation to investigate the symmetry breaking associated with deformation and structural phase transitions in crystals, which also provides a new insight into the physical origin of crystalline defects.

METHODS MODELING SYSTEMS FOR THE IMPROVEMENT OF THEIR RELIABILITY


 
 
 
 The method of Markov’s processes for the analysis of systems with constant bounce and recovery intensities considered. The article presents calculations of the failure probability of the system for describing the various cases of redundancy of its components using Markov’s models. Expressions obtained for calculating the approximate value of the failure probability of the system and analyzed of failures to improve the reliability of the system. The Markov’s graph of transitions in the reservation of the system, which reflects its behavior, described. Analysis of the results of numerical solution of systems shows that when loaded with redundancy, the probability of failure is higher than with partially loaded, and with partially loaded - higher than with unloaded backup. A tree of errors for the system of cooling and clearing of flue gas at the reservation made by replacing "2 of 3", which has seven minimum bounce cross sections. Calculated the probability of system failure. The obtained calculations allow to analyze failures of technical systems in order to increase the reliability of their functioning.
 
 
 

On the fastest finite Markov processes

Consider a finite state irreducible Markov process with transition graph G and invariant probability distribution π. Its inverse communication speed is defined as the expectation of the time to go from x to y when x,y are sampled independently according to π. We study this in the context of both discrete and continuous time. One of our goals is to show (under a suitable normalization condition on the transition rates for the continuous time case) that the shortest inverse communication speed among all Markov processes compatible with G and π is attained on those whose successive positions follow a Hamiltonian cycle, assuming one exists, and that π is close enough to the uniform distribution υ. This result is no longer true when π is sufficiently different from υ. Another purpose of the paper is to prove that when the invariance with respect to π is dropped and the inverse communication speed is replaced by the unweighted sum of the hitting times, then the Hamiltonian cycles, when they exist, are still the minimizers over all processes compatible with the prescribed directed graph G of permitted transitions, not only Markov processes, thus extending some previous results.

The Labeling Graphs of Definite Automata

Au algorithm of labeling a directed graph so that the obtained transition graph represents a definite automaton is described.

Optimal in-field routing for full and partial field coverage with arbitrary non-convex fields and multiple obstacle areas

Within the context of optimising the logistics in agriculture this paper relates to optimal in-field routing for full and partial field coverage with arbitrary non-convex fields and multiple obstacle areas. It is distinguished between nine different in-field routing tasks: two for full-field coverage, seven for partial-field coverage and one for shortest path planning between any two vertices of the transition graph. It differentiates between equal or different start and end vertices for a task, coverage of only a subset of vertices, and a subset of edges or combinations. The proposed methods are developed primarily for applying sprays and fertilisers with larger operating widths and with fields where there is unique headland path. Partial field coverage where, e.g., only a specific subset of edges has to be covered is relevant for precision agriculture and also for optimised logistical operation of smaller-sized machinery with limited loading capacities. The result of this research is the proposition of two compatible algorithms for optimal full and partial field coverage path planning, respectively. These are evaluated on three real-world fields to demonstrate their characteristics and computational efficiency.

Karnaugh Maps of Logical Systems and Applications in Digital Circuit Design

This paper extends the concept of Karnaugh map from a logical function to a logical system, thereby allowing both the state transition graph and state transition matrix of a logical system, as well as a digital circuit, to be constructed directly. It is found that the Karnaugh map of a logical system is actually a two-dimensional state transition table or, equivalently, a table-like state transition graph and is also a grid-type state transition matrix. For constructing the state transition graph and state transition matrix of a logical system, the computational complexities of the methods based on the proposed Karnaugh map are exponentially lower than those of the existing methods. The Karnaugh maps of logical systems are then used in the analysis and design of clocked sequential circuits and in the simplification of multioutput gate circuits. Some illustrative examples and simulations are presented to demonstrate the results and their applications.

Learning and distinguishing time series dynamics via ordinal patterns transition graphs

Strategies based on the extraction of measures from ordinal patterns transformation, such as probability distributions and transition graphs, have reached relevant advancements in distinguishing different time series dynamics. However, the reliability of such measures depends on the appropriate selection of parameters and the need for large time series. In this paper we present a method for the characterization of distinct time series behaviors based on the probability of self-transitions, a measure extracted from their transformation onto ordinal patterns transition graphs. We validate our method by investigating the main characteristics of periodic, random, and chaotic time series. By the application of learning strategies, we precisely classify different randomness levels in time series, reaching 100% in accuracy, and advances in performing the hard task of distinguishing random noises from chaotic time series, correctly distinguishing 96.61% of the cases. Furthermore, we show that this strategy is well suitable to be used by many applications, even for short time series, and does not depend on the selection of parameters.

Bittorio revisited: structural coupling in the Game of Life

The notion of structural coupling plays a central role in Maturana and Varela’s biology of cognition framework and strongly influenced Varela’s subsequent enactive elaboration of this framework. Building upon previous work using a glider in the Game of Life (GoL) cellular automaton as a toy model of a minimal autopoietic system with which to concretely explore these theoretical frameworks, this article presents an analysis of structural coupling between a glider and its environment. Specifically, for sufficiently small GoL universes, we completely characterize the nonautonomous dynamics of both a glider and its environment in terms of interaction graphs, derive the set of possible glider lives determined by the mutual constraints between these interaction graphs, and show how such lives are embedded in the state transition graph of the entire GoL universe.

Automatic construction and evaluation of macro-actions in reinforcement learning

In this paper, we propose a new subgoal-based method for automatic construction of useful macro-actions modeled with option framework. We propose a new community detection algorithm to provide an appropriate partitioning of the agent’ transition graph. Subgoals are considered as the border states of the transition graph communities and options are constructed for taking the agent from one community to other communities. Despite the importance of considering the effect of each macro-action on learning speed, there is no generic known mechanism for evaluating macro-actions in the literature. We show that using all of the detected macro-actions are not useful and even in a simple environment, the augmentation of the action space with useless or wrong macro-actions may easily worsen learning performance. We propose four different heuristics for evaluating options. We identify, in this way, inappropriate options and discard them from the agent choices. Experimental results show significant improvements in the speed of learning after pruning options.

Finite-Time Stability of Probabilistic Logical Networks: A Topological Sorting Approach

This brief presents some further results on the finite-time stability of probabilistic logical networks (PLNs). By semi-tensor product technique routinely, the dynamic behavior of a PLN is characterized by its corresponding state transition graph (STG). Then, an irradiative result is found. That is, a PLN is globally stable within finite time, if and only if, its STG is acyclic, except for the self loop at the pre-designated vertex. Based on this observation, some properties of STG, which is associated with a finite-time stable PLN, are formulated. The most significant finding is that the determinant of its anti-adjacency matrix is compactly related to the existence of a Hamilton path and is only equal to 0 or 1. Afterwards, the topological sort of all the vertices in STG is defined. As a consequence, two topological sorting algorithms are presented to analyze the stability of PLNs applicably and efficiently. Finally, a simulation example is employed to illustrate the applicability of the obtained results.

Моделирование сети связи для управления действиями пожарных подразделений при тушении пожаров различной сложности

Introduction. The organization of radio communication at the fire, as an important part of the fire units operating management, should be given a considerable attention. The effectiveness of fire units operating management depends largely on thesteady of the radio network operation, in which, depending on the complexity of the situation, can work different officials who control the process of extinguishing the fire. Methods. Modelling of radio network operation is based on Queuing theory methods. A list of n States in which the communication network and the corresponding transition graph can is compiled. Taking into account the generally accepted assumptions on the basis of the transition graph, a system of n differential equations connecting the probabilities of States and the intensity of the transition to these States is compiled. The stationary case is considered. Based upon the obtained solutions the efficiency of the radio network is estimated. Results. The article presents three variants for which the possible States are described, graphs are constructed and systems of equations are composed. In the first variant, three officials interact inside the radio network, in the second, four officials interact. In the third variant the option of interaction between four fire units operating management with other hierarchy of management is considered. In the first two cases, analytical solutions for the States probabilities are obtained, for the third case, a solution using numerical methods is proposed. For each case, the critical States affecting the control stability are determined. The obtained solutions are followed by examples. Conclusion. The possibility of modeling the radio communication network at the fire, as an important element of controlling of fire departments operating is demonstrated. Three variants of interaction between officials with use of a radio communication network are given. The mathematical models developed for the under consideration cases allow to estimate the probably characteristics of the radio network functioning. It allows us to assess the possibility of the probably of critical modes appearance that affect the effectiveness of the fire units operating management and the success his implementation.