Representation in the (Artificial) Immune System

Much of contemporary research in Artificial Immune Systems (AIS) has partitioned into either algorithmic machine learning and optimisation, or, modelling biologically plausible dynamical systems, with little overlap between. We propose that this dichotomy is somewhat to blame for the lack of significant advancement of the field in either direction and demonstrate how a simplistic interpretation of Perelson’s shape-space formalism may have largely contributed to this dichotomy. In this paper, we motivate and derive an alternative representational abstraction. To do so we consider the validity of shape-space from both the biological and machine learning perspectives. We then take steps towards formally integrating these perspectives into a coherent computational model of notions such as life-long learning, degeneracy, constructive representations and contextual recognition—rhetoric that has long inspired work in AIS, while remaining largely devoid of operational definition.     

A Recommender System based on Idiotypic Artificial Immune Networks

The immune system is a complex biological system with a highly distributed, adaptive and self-organising nature. This paper presents an Artificial Immune System (AIS) that exploits some of these characteristics and is applied to the task of film recommendation by Collaborative Filtering (CF). Natural evolution and in particular the immune system have not been designed for classical optimisation. However, for this problem, we are not interested in finding a single optimum. Rather we intend to identify a sub-set of good matches on which recommendations can be based. It is our hypothesis that an AIS built on two central aspects of the biological immune system will be an ideal candidate to achieve this: Antigen–antibody interaction for matching and idiotypic antibody–antibody interaction for diversity. Computational results are presented in support of this conjecture and compared to those found by other CF techniques.Mathematics Subject Classifications (2000) 68Rxx, 68Txx, 90Bxx.     

Multi-objective Bayesian Artificial Immune System: Empirical Evaluation and Comparative Analyses

Recently, we have proposed a Multi-Objective Bayesian Artificial Immune System (MOBAIS) to deal effectively with building blocks (high-quality partial solutions coded in the solution vector) in combinatorial multi-objective problems. By replacing the mutation and cloning operators with a probabilistic model, more specifically a Bayesian network representing the joint distribution of promising solutions, MOBAIS takes into account the relationships among the variables of the problem, avoiding the disruption of already obtained high-quality partial solutions. The preliminary results have indicated that our proposal is able to properly build the Pareto front. Motivated by this scenario, this paper better formalizes the proposal and investigates its usefulness on more challenging problems. In addition, an important enhancement regarding the Bayesian network learning was incorporated into the algorithm in order to speed up its execution. To conclude, we compare MOBAIS with state-of-the-art algorithms taking into account quantitative aspects of the Pareto front found by the algorithms. MOBAIS outperforms the contenders in terms of the quality of the obtained solutions and requires an amount of computational resource inferior or compatible with the contenders.     

On the Kernel Rule for Function Classification

Let X be a random variable taking values in a function space , and let Y be a discrete random label with values 0 and 1. We investigate asymptotic properties of the moving window classification rule based on independent copies of the pair (X,Y). Contrary to the finite dimensional case, it is shown that the moving window classifier is not universally consistent in the sense that its probability of error may not converge to the Bayes risk for some distributions of (X,Y). Sufficient conditions both on the space and the distribution of X are then given to ensure consistency.     

An evolutionary artificial immune system for multi-objective optimization

In this paper, an evolutionary artificial immune system for multi-objective optimization which combines the global search ability of evolutionary algorithms and immune learning of artificial immune systems is proposed. A new selection strategy is developed based upon the concept of clonal selection principle to maintain the balance between exploration and exploitation. In order to maintain a diverse repertoire of antibodies, an information-theoretic based density preservation mechanism is also presented. In addition, the performances of various multi-objective evolutionary algorithms as well as the effectiveness of the proposed features are examined based upon seven benchmark problems characterized by different difficulties in local optimality, non-uniformity, discontinuity, non-convexity, high-dimensionality and constraints. The comparative study shows the effectiveness of the proposed algorithm, which produces solution sets that are highly competitive in terms of convergence, diversity and distribution. Investigations also demonstrate the contribution and robustness of the proposed features.     

FCM聚类算法中模糊加权指数m的优选方法

模糊c-均值(FCM)聚类算法是一种通过目标函数的极小化来获得数据集模糊划分的方法。其中,模糊加权指数m对FCM算法的分类性能有着重要的影响,而调用FCM算法进行模糊聚类分析时又必须给m赋值。因此,模糊加权指数m的优选研究就变得很有意义。基于模糊决策的方法本文给出了一种对m的优选方法,实验结果表明该方法是有效的。     

An Artificial Boundary Condition for the Vortex Movements in Two Dimensions

1 Motion of vortices and cloud in cell method The motion of incompressible inviscid ?ow in two dimensions can be described by the equations ?u ?t (u ?) ρ1 ?P = f (1) ?u = 0 , (2) where u = (u, v), ρ, P , and f = (f1, f2) denote ?uid velocity, densit…     

支持向量分类方法理论基础的改进

支持向量机是通过求解对偶问题来解决原始问题的.针对线性决策函数f(x)=(w·x)+b,我们指出了其原有的逻辑系统中的错误,并通过严格的证明,对其理论基础作了改进.而且,对于阈值b,我们给出了一个新的简洁计算公式.     

An improved artificial bee colony algorithm for directing orbits of chaotic systems

Artificial bee colony algorithm (ABC) is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in ABC regarding its solution search equation, which is good at exploration but poor at exploitation. To address this concerning issue, we propose an improved ABC (IABC) by using a modified search strategy to generate a new food source in order that the exploration and exploitation can be well balanced and satisfactory optimization performances can be achieved. In addition, to enhance the global convergence, when producing the initial population, both opposition-based learning method and chaotic maps are employed. In this paper, the proposed algorithm is applied to control and synchronization of discrete chaotic systems which can be formulated as both multimodal numerical optimization problems with high dimension. Numerical simulation and comparisons with some typical existing algorithms demonstrate the effectiveness and robustness of the proposed approach.     

Signal Decoupling with Preview in the Geometric Context: Exact Solution for Nonminimum-Phase Systems

The problem of making the output of a discrete-time linear system totally insensitive to an exogenous input signal known with preview is tackled in the geometric approach context. A necessary and sufficient condition for exact decoupling with stability in the presence of finite preview is introduced, where the structural aspects and the stabilizability aspects are considered separately. On the assumption that structural decoupling is feasible, internal stabilizability of the minimal self-bounded controlled invariant satisfying the structural constraint guarantees the stability of the dynamic feedforward compensator. However, if the structural decoupling is feasible, but is not internally stabilizable, exact decoupling is nonetheless achievable with a stable feedforward compensator on the sole assumption that has no unassignable internal eigenvalues on the unit circle, provided that the signal to be rejected is known with infinite preview. An algorithmic framework based on steering-along-zeros techniques, completely devised in the time domain, shows how to compute the convolution profile of the feedforward compensator in each case. Communicated by G. Leitmann     

An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method

Outranking methods constitute an important class of multicriteria classification models. Often, however, their implementation is cumbersome, due to the large number of parameters that the decision maker must specify. Past studies tried to address this issue using linear and nonlinear programming, to elicit the necessary preferential information from assignment examples. In this study, an evolutionary approach, based on the differential evolution algorithm, is proposed in the context of the ELECTRE TRI method. Computational results are given to test the effectiveness of the methodology and the quality of the obtained models.     

Finding the Number of Normal Groups in Model-Based Clustering via Constrained Likelihoods

Deciding the number of clusters k is one of the most difficult problems in cluster analysis. For this purpose, complexity-penalized likelihood approaches have been introduced in model-based clustering, such as the well-known Bayesian information criterion and integrated complete likelihood criteria. However, the classification/mixture likelihoods considered in these approaches are unbounded without any constraint on the cluster scatter matrices. Constraints also prevent traditional EM and CEM algorithms from being trapped in (spurious) local maxima. Controlling the maximal ratio between the eigenvalues of the scatter matrices to be smaller than a fixed constant c ? 1 is a sensible idea for setting such constraints. A new penalized likelihood criterion which takes into account the higher model complexity that a higher value of c entails is proposed. Based on this criterion, a novel and fully automated procedure, leading to a small ranked list of optimal (k, c) couples is provided. A new plot called “car-bike,” which provides a concise summary of the solutions, is introduced. The performance of the procedure is assessed both in empirical examples and through a simulation study as a function of cluster overlap. Supplementary materials for the article are available online.     

模糊聚类方法在高校分类中的应用

在对教学、科研两方面分别进行综合评价的基础上,先按教育部对学科门的划分及大学各学科门的比例对高校进行分类,再利用模糊聚类方法从教学、科研两方面分别进行聚型,当阈值降至黄金分割位0 .61 8附近时,刚好分成了四个型,称之为:教学 Ⅰ、Ⅱ、Ⅲ、Ⅳ、型和科研Ⅰ、Ⅱ、Ⅲ、Ⅳ型,然后根据每个学校的类和教学、科研两方面的型给出他们的类型结果,这样对高校进行定位比较客观、合理.     

An Age-structured Mathematical Model for the Within Host Dynamics of Malaria and the Immune System

In the paper, we use a mathematical model to study the population dyna mics of replicating malaria parasites and their interaction with the immune cells within a human host. The model is formulated as a system of age-structured partial differential equations that are then integrated over age to obtain a system of nonlinear delay differential equations. Our model incorporates an intracellular time delay between the infection of the red blood cells by the merozoites that grow and replicate within the infected cells to produce new merozoites. The infected red blood cells burst approximately every 48 h releasing daughter parasites to renew the cycle. The dynamical processes of the parasites within the human host are subjected to pressures exerted by the human immunological responses. The system is then solved using a first-order, finite difference method to give a discrete system. Numerical simulations carried out to illustrate stability of the system reveal that the populations undergo damped oscillations that stabilise to steady states.      

A General Theorem of the Alternative in the Context of Set-Valued Function

1.IntroductionTheclassicalworkOiltheoremsofthealternativeforsingle-valuedfunctionbyG..d..II]andMotzkin[2]wereextendbymanyresearchersinvariousways(suchasJeyakumar['l'],Lily],andTamminen[6]),whereconditionsofconvexityaremoreorlessrelaxed.Met's..rk[:]givesemphasistotheoremsofthealternativeinthesettingofset-valuedfunctionwhereconditionofconvexityissettobecone-convex.Thispaperaimsatprovidinganunifiedextensionoftheabove-mentionedtheorems,andgivesoutageneraltheoremofthealternativeinthecontextofset…     

Classification and refined singularity of positive solutions for nonlinear Maxwell equations arising in mesoscopic electromagnetism

This paper is a continuation of [13], where we studied the existence and other analytic properties of positive radial solutions for a system of nonlinear Maxwell equations in the plane R²${\mathbb{R}}^2$, which arises in the modelling of mesoscopic scale electromagnetic phenomena. In this paper we derive local estimates of singular positive solutions, based on which a classification theorem of general positive solutions is established. The refined singularity of general positive solutions is also investigated by employing the theory of infinite dimensional dynamical systems.     

Strategies for detecting fraudulent claims in the automobile insurance industry

Some property and casualty insurers use automated detection systems to help to decide whether or not to investigate claims suspected of fraud. Claim screening systems benefit from the coded experience of previously investigated claims. The embedded detection models typically consist of scoring devices relating fraud indicators to some measure of suspicion of fraud. In practice these scoring models often focus on minimizing the error rate rather than on the cost of (mis)classification. We show that focusing on cost is a profitable approach. We analyse the effects of taking into account information on damages and audit costs early on in the screening process. We discuss several scenarios using real-life data. The findings suggest that with claim amount information available at screening time detection rules can be accommodated to increase expected profits. Our results show the value of cost-sensitive claim fraud screening and provide guidance on how to render this strategy operational.     

An affine model for the actions in an integrable system with monodromy

We give a standard model for the flat affine geometry defined by the local action variables of a completely integrable system. We are primarily interested in the affine structure in the neighborhood of a critical value with nontrivial monodromy.      

Receding-Horizon Control Method for the Stabilization of an Unpredictably Changing Discrete-Time Uncertain System

The paper is concerned with the applicability of the receding-horizon control method for stabilizing a discrete-time uncertain system with a time-varying linear nominal part. The specific feature of the problem is that the nominal system is supposed to be known only up to the actual time. The effectiveness of the method is illustrated by an example.     

An iterative substructuring method for the p-version of the boundary element method for hypersingular integral operators in three dimensions

Summary. We study preconditioners for the -version of the boundary element method for hypersingular integral equations in three dimensions. The preconditioners are based on iterative substructuring of the underlying ansatz spaces which are constructed by using discretely harmonic basis functions. We consider a so-called wire basket preconditioner and a non-overlapping additive Schwarz method based on the complete natural splitting, i.e. with respect to the nodal, edge and interior functions, as well as an almost diagonal preconditioner. In any case we add the space of piecewise bilinear functions which eliminate the dependence of the condition numbers on the mesh size. For all these methods we prove that the resulting condition numbers are bounded by . Here, is the polynomial degree of the ansatz functions and is a constant which is independent of and the mesh size of the underlying boundary element mesh. Numerical experiments supporting these results are reported. Received July 8, 1996 / Revised version received January 8, 1997