Minorities in a model for opinion formation

We study a model for social influence in which the agents' opinion is a continuous variable [G. Weisbuch et al., Complexity 2002, 7(2), 55]. The convergent opinion adjustment process takes place as a result of random binary encounters whenever the difference between agents' opinions is below a given threshold. The inhomogeneity in the dynamics gives rise to a complex steady state structure, which is also highly dependent on the threshold and on the convergence parameter of the model. © 2004 Wiley Periodicals, Inc. Complexity 9: 24–30, 2004     

A collective model for the formation of public opinion: An application to nuclear public acceptance

A collective model is proposed for the formation of public opinion and applied to the problem of public acceptance for nuclear energy in Japan. The selection of attitude for the people to a certain subject is assumed to be made depending on the sociopsychological pressure suffering from the surroundings, and on the quality and quantity of information on that subject released from the newsmedia. The reportorial stance of the newsmedia, on the other hand, is assumed to vary depending on, not only public opinion, but also the resultant of the mutual watch of the newsmedia to each other, concerning the state of information on the subject. Both an individual person and an individual medium are regarded as an interactive but structureless particle, and the interactions between the particles of the people and of media are described by introducing respective potentials of the type of molecular dynamics. Applying this model to the issue of electricity generation by nuclear energy, it was found to well reproduce the observed movement of public opinion in Japan. It also became clear that this sort of physical model is quite useful for understanding the status of socially collective phenomena in which nonlinearity and self-organization are strongly concerned.     

A hybrid algorithm for the manufacturing cell formation problem

In this paper we compare different heuristic methods for the manufacturing cell formation problem considering part process sequence: a GRASP algorithm, a reactive GRASP algorithm and a hybrid algorithm which combines reactive GRASP and tabu search. All algorithms are tested with a set of instances from the literature. The results from the GRASP algorithm are compared to those of the reactive GRASP in order to evaluate the advantages of automatically adjusting the parameter value within the randomized greedy procedure. Also the reactive GRASP results are compared to those of the hybrid algorithm to evaluate the contribution to solution quality of replacing the local search phase of the GRASP algorithm with tabu search.     

Consensus formation of two-level opinion dynamics

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1-α)d, where α ∈ (0,1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound d_c = 1/(4α) for the two-level opinion dynamics on ?. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold d_c increases with α but does not depend on p.     

A hybrid convex variational model for image restoration

We propose a new hybrid model for variational image restoration using an alternative diffusion switching non-quadratic function with a parameter. The parameter is chosen adaptively so as to minimize the smoothing near the edges and allow the diffusion to smooth away from the edges. This model belongs to a class of edge-preserving regularization methods proposed in the past, the ?-function formulation. This involves a minimizer to the associated energy functional. We study the existence and uniqueness of the energy functional of the model. Using real and synthetic images we show that the model is effective in image restoration.     

Clustering and asymptotic behavior in opinion formation

We investigate the long time behavior of models of opinion formation. We consider the case of compactly supported interactions between agents which are also non-symmetric, including for instance the so-called Krause model. Because of the finite range of interaction, convergence to a unique consensus is not expected in general. We are nevertheless able to prove the convergence to a final equilibrium state composed of possibly several local consensus. This result had so far only been conjectured through numerical evidence. Because of the non-symmetry in the model, the analysis is delicate and is performed in two steps: First using entropy estimates to prove the formation of stable clusters and then studying the evolution in each cluster. We study both discrete and continuous in time models and give rates of convergence when those are available.     

A variational model with hybrid Hyper-Laplacian priors for Retinex

Retinex aims at estimating real reflectance images by removing the effect of illumination. We propose a nonconvex variational model for Retinex with novel priors for reflectance and illumination. Based on the statistics of the gradients of reflectance and illumination, we use the hyper-Laplacian prior to characterize the gradients of reflectance, and the hybrid hyper-Laplacian and Tikhonov prior to characterize the gradients of illumination. An efficient alternating direction method of multipliers (ADMM) is developed to solve the proposed model. Extensive numerical experiments show that the proposed method is comparable to the state-of-the-art methods quantitatively and qualitatively.     

A hybrid model for selection of an outsourcing provider

Outsourcing is a good strategy for firms that need to reduce operating costs and improve competitiveness and it is important that firms scientifically select appropriate outsourcing providers. Some efforts have been made to find systematic ways to deal with outsourcing problems, but these efforts incorrectly assumed that the criteria used in the decision process are independent, which is not true in the real world. In this study, we propose a new hybrid multiple criteria decision-making (MCDM) model, which addresses the dependent relationships between the various criteria. The relations-structure among the criteria is built with the aid of the decision-making trial and evaluation laboratory (DEMATEL) method. Decision-makers tend to hold diverse opinions about their preferences due to incomplete information and knowledge, or inherent conflict between various departments. We further used the fuzzy preference programming and the analytic network process (ANP) to form a model for the selection of partners for outsourcing providers. The proposed model can help practitioners improve their decision making process, especially when criteria are numerous and inter-related. The method is demonstrated using data from a Taiwanese airline.     

A bivariate interval censorship model for partnership formation

We consider a statistical problem of estimating a bivariate age distribution of newly formed partnership. The study is motivated by a type of data that consist of uncensored, right-censored, left-censored, interval-censored and missing observations in the coordinates of a bivariate random vector. A model is proposed for formulating such type of data. A feasible algorithm to estimate the generalized MLE (GMLE) of the bivariate distribution function is also proposed. We establish asymptotic properties for the GMLE under a discrete assumption on the underlying distributions and apply the method to the data set.     

A hybrid inexact-stochastic water management model

An inexact-stochastic water management (ISWM) model is proposed and applied to a case study of water quality management within an agricultural system. The model is based on an inexact chance-constrained programming (ICCP) method, which improves upon the existing inexact and stochastic programming approaches by allowing both distribution information in B and uncertainties in A and C to be effectively incorporated within its optimization process. In its solution process, the ICCP model (under a given pi level) is first transformed into two deterministic submodels, which correspond to the upper and lower bounds for the desired objective function value. This transformation process is based on an interactive algorithm, which is different from normal interval analysis or best/worst case analysis. Interval solutions, which are feasible and stable in the given decision space, can then be obtained by solving the two submodels sequentially. Thus, decision alternatives can be generated by adjusting decision variable values within their solution intervals. The obtained ICCP solutions are also useful for decision makers to obtain insight regarding tradeoffs between environmental and economic objectives and between increased certainties and decreased safeties (or increased risks). Results of the case study indicate that useful solutions for the planning of agricultural activities in the water quality management system have been obtained. A number of decision alternatives have been generated and analyzed based on projected applicable conditions. Generally, some alternatives can be considered when water quality objective is given priority, while the others may provide compromises between environmental and economic considerations. The above alternatives represent various options between environmental and economic tradeoffs. Willingness to accept low agricultural income will guarantee meeting the water quality objectives. A strong desire to acquire high agricultural income will run into the risk of violating water quality constraints.     

A hybrid genetic model for the prediction of corporate failure

This study examines the potential of a neural network (NN) model, whose inputs and structure are automatically selected by means of a genetic algorithm (GA), for the prediction of corporate failure using information drawn from financial statements. The results of this model are compared with those of a linear discriminant analysis (LDA) model. Data from a matched sample of 178 publicly quoted, failed and non-failed, US firms, drawn from the period 1991 to 2000 is used to train and test the models. The best evolved neural network correctly classified 86.7 (76.6)% of the firms in the training set, one (three) year(s) prior to failure, and 80.7 (66.0)% in the out-of-sample validation set. The LDA model correctly categorised 81.7 (75.0)% and 76.0 (64.7)% respectively. The results provide support for a hypothesis that corporate failure can be anticipated, and that a hybrid GA/NN model can outperform an LDA model in this domain.MSC codes: 62M45, 68W10, 90B50, 91C20     

A hybrid evolutionary learning algorithm for TSK-type fuzzy model design

In this paper, a TSK-type fuzzy model (TFM) with a hybrid evolutionary learning algorithm (HELA) is proposed. The proposed HELA method combines the compact genetic algorithm (CGA) and the modified variable-length genetic algorithm (MVGA). Both the number of fuzzy rules and the adjustable parameters in the TFM are designed concurrently by the HELA method. In the proposed HELA method, individuals of the same length constitute the same group, and there are multiple groups in a population. Moreover, the proposed HELA adopts the compact genetic algorithm (CGA) to carry out the elite-based reproduction strategy. The CGA represents a population as a probability distribution over the set of solutions and is operationally equivalent to the order-one behavior of the simple GA. The evolution processes of a population consist of three major operations: group reproduction using the compact genetic algorithm, variable two-part individual crossover, and variable two-part mutation. Computer simulations have demonstrated that the proposed HELA method gives a better performance than some existing methods.     

A hybrid macroscopic-based model for traffic flow in road networks

Recently, the unquestionable growth of interest to increase the operational efficiency and capability of transportation systems led to the development of a large number of traffic modeling theories. One of the major operational issues when developing a transportation system management model lies in the selection of the appropriate methodological approach with respect to several decisions, such as the selection of the type of input and output data as well as the qualitative representation and the computational power of the model. Despite the considerable effort in the area, there is still not an approach which per se models effectively the various dynamically evolving features of traffic in road networks. The present paper addresses this issue by introducing a new hybrid approach which combines the complementary features and capabilities of both continuum mathematical models e.g. 1, 6, 23 and 26 and knowledge-based models e.g. 7, 22 and 28 in order to describe effectively traffic flow in road networks.     

A stick-slip/Rouse hybrid model for viscoelasticity in polymers

A Rouse model for polymer chains is incorporated into the linear continuous stick-slip molecular-based tube reptation ideas of Doi–Edwards and Johnson–Stacer. This treats the physically constrained (PC) molecular stretches as internal strain variables for the overall PC/chemically cross-linked (CC) system. It yields an explicit system of stress–strain equations for the system permitting simple calculations of complex stress–strain relations. The model that is developed here treats PC molecule as entrapped within a constraining tube, which is comprised of both CC and PC molecules. The model is compared with experimental data sets from the literature.     

A model of concept formation

At first we model the way an intelligence “I” constructs statements from phrases, and then how “I” interlocks these statements to form a string of statements to attain a concept. These strings of statements are called progressions. That is, starting with an initial stimulating relation between two phrases, we study how “I” forms the first statement of the progression and continues from this first statement to form the remaining statements in these progressions to construct a concept. We assume that “I” retains the progressions that it has constructed. Then we show how these retained progressions provide “I” with a platform to incrementally constructs more and more sophisticated conceptual structures. The reason for the construction of these conceptual structures is to achieve additional concepts. Choice plays a very important role in the progression and concept formation. We show that as “I” forms new concepts, it enriches its conceptual structure and makes further concepts attainable. This incremental attainment of concepts is a way in which we humans learn, and this paper studies the attainability of concepts from previously attained concepts. We also study the ability of “I” to apply its progressions and also the ability of “I” to electively manipulate its conceptual structure to achieve new concepts. Application and elective manipulation requires of “I” ingenuity and insight. We also show that as “I” attains new concepts, the conceptual structures change and circumstances arise where unanticipated conceptual discoveries are attainable. As the conceptual structure of “I” is developed, the logical and structural relationships between concepts embedded in this structure also develop. These relationships help “I” understand concepts in the context of other concepts and help “I₁” communicate to another “I₂” information and concept structures. The conceptual structures formed by “I” give rise to a directed web of statement paths which is called a convolution web. The convolution web provides “I” with the paths along which it can reason and obtain new concepts and alternative ways to attain a given concept.This paper is an extension of the ideas introduced in [1]. It is written to be self-contained and the required background is supplied as needed.     

A diffusion model for patch formation on cellular surfaces

A number of phenomena of interest in the biology of the cellular membrane can be modeled by a diffusion process which is undergone by certain objects on the cellular surface.We consider one such model and are led to the task of estimating the principal eigenvalue of an elliptic operator with homogeneous Dirichlet boundary conditions.The requested estimate is carried out by two different methods: one makes use of a Lyapunov-type technique and the other applies the Cameron—Martin—Girsanov formula. These methods apply to much more general situations than the specific one considered here.This work was carried out within the frame of a research program partially supported by C.N.R.-GNAFA (G.D.G.) and C.N.R.-GNFM (A.G., F.M.).     

A model for peak formation in the two-phase equations

We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.

     

A hybrid stochastic model of retinal angiogenesis

Understanding the biological principles that govern blood vessel growth in the retina has important clinical implications, for the prevention of possible retinopathies, which may eventually lead to blindness. The availability of a realistic mathematical model of the relevant phenomenon may support the medical community in both issues, diagnosis being related to inverse problems, and therapy to optimal control strategies. The mathematical modeling of retinal angiogenesis leads to an highly complex problem, because of dimension, nonlinearity, and intrinsic randomness. In this paper, we propose a reduced model which leads to numerical simulations that somehow reproduce normal vascularization and predict possible pathologies. We call our model hybrid because it includes the coupling of a fully stochastic model for the construction of a vessel network in the retina, with continuum underlying fields describing relevant factors, such as growth factors and oxygen. We perform numerical simulations of a stochastic particle system coupled with partial differential equations (PDEs)' so to obtain images of vessel structure resembling real retina vasculatures. We then derive a possible mean field approximation of the stochastic vessel network, so to obtain a fully deterministic PDE system for the evolution of the underlying fields. Actually, in order to reproduce the geometric structure of the retina vessel network, we have to keep a stochastic model (though simplified) for its construction. Future investigations may concern the use of such a mean field approximation in the numerical simulations of the retina vasculature. Inverse and optimal control problems being the final goal of our research plan.     

A model for stochastic hybrid systems with application to communication networks

We propose a model for stochastic hybrid systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for piecewise-deterministic Markov process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state.As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finite-dimensional model. This model shows that, for transfer-size distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms.     

Cluster formation in opinion dynamics: a qualitative analysis

In this paper we formulate a discrete version of the bounded confidence model (Deffuant et al. in Adv Complex Syst 3:87–98, 2000; Weisbuch et al. in Complexity 7:55–63, 2002), which is representable as a family of ordinary differential equation systems. Then, we analytically study these systems. We establish the existence of equilibria which correspond to opinion profiles displaying a finite number of isolated clusters. We prove the asymptotic stability of some of these equilibria and show that they represent the asymptotic trend of the solutions of the systems under consideration. For a particular case, we also characterize the initial profiles that lead to different cluster configurations.