P. De Wilde

Performance analysis of the DCT-LMS adaptive filtering algorithm

Abstract This paper presents the convergence analysis result of the discrete cosine transform-least-mean-square (DCT-LMS) adaptive filtering algorithm which is based on a well-known interpretation of the variable stepsize algorithm. The time-varying stepsize of the DCT-LMS algorithm is implemented by the modified power estimator to redistribute the spread power after the DCT. The performance analysis is considerably simplified by the modification of a power estimator. First of all, the proposed DCT-LMS algorithm has a fast convergence rate when compared to the LMS, the normalised LMS (NLMS), the variable stepsize LMS (VSLMS) algorithm for a highly correlated input signal, whilst constraining the level of the misadjustment required by a specification. The main contribution of this paper is the statistical performance analysis in terms of the mean and mean-squared error of the weight error vector. In addition, the decorrelation property of the DCT-LMS is derived from the lower and upper bounds of the eigenvalue spread ratio, λ max / λ min . It is also shown that the shape of sidelobes affecting the decorrelation of the input signal is governed by the location of two zeros. Theoretical analysis results are validated by the Monte Carlo simulation. The proposed algorithm is also applied in the system identification and the inverse modelling for a channel equalisation in order to verify its applicability.

Fuzzy utility and equilibria

A decision maker is frequently confronted with fuzzy constraints, fuzzy utility maximization, and fuzziness about the state of competitors. In this paper we present a framework for fuzzy decision-making, using techniques from fuzzy logic, game theory, and micro-economics. In the first part, we study the rationality of fuzzy choice. We introduce fuzzy constraints, and show that this can easily be combined with maximizing a fuzzy utility. The second part of the paper analyzes games with uncertainty about the state of the competitors. We implement fuzzy Cournot adjustment, define equilibria, and study their stability. Finally, we show how a play progresses where the players have uncertainty about the state of the other players, and about their utility. For a likely procedure of utility maximization, the equilibria are the same as for the game without utility maximization.

Stability of multi-agent systems

This work attempts to shed light on the fundamental concepts behind the stability of multi-agent systems. We view the system as a discrete time Markov chain with a potentially unknown transitional probability distribution. The system will be considered to be stable when its state has converged to an equilibrium distribution. Faced with the non-trivial task of establishing the convergence to such a distribution, we propose a hypothesis testing approach according to which we test whether the convergence of a particular system metric has occurred. We describe some artificial multi-agent ecosystems that were developed and we present results based on these systems which confirm that this approach qualitatively agrees with our intuition.

The magnitude of the diagonal elements in neural networks

Abstract The weights of completely connected neural networks are usually derived from the sum-of-outerproducts rule, with zero diagonal in the weight matrix. In this paper, we calculate what the magnitude of the diagonal elements should be in order to obtain a capacity that is linear in the number of neurons, with the proportionality factor chosen by the user of the network. The theoretical results are verified with simulations. We also show how to obtain the optimal magnitude for the diagonal elements and we investigate the number of spurious patterns. We assume several statistical independence conditions. The theoretical calculations are valid in the limit for an infinite number of neurons. The simulations provide results for networks of a finite size.

Simulation of a trading multi-agent system

In a trading scenario agents interact with each other, selling and buying resources. In order to control the behavior of the trading scenario, the interactions must be coordinated. We present a brief discussion of communication types and coordination models applicable in multi-agent systems. We find a programmable tuple space more appropriate to manage and rule the interactions between the trading agents. We discuss the advantages of a trading agent model that deals with the trading strategy, concentrating on what to buy or sell. This relieves the agent from the task of coordinating the negotiations and their revoking or acceptances. This is the task of the programmable tuple space.

The Emergence of Knowledge Exchange: An Agent-Based Model of a Software Market

We investigate knowledge exchange among commercial organizations, the rationale behind it, and its effects on the market. Knowledge exchange is known to be beneficial for industry, but in order to explain it, authors have used high-level concepts like network effects, reputation, and trust. We attempt to formalize a plausible and elegant explanation of how and why companies adopt information exchange and why it benefits the market as a whole when this happens. This explanation is based on a multiagent model that simulates a market of software providers. Even though the model does not include any high-level concepts, information exchange naturally emerges during simulations as a successful profitable behavior. The conclusions reached by this agent-based analysis are twofold: 1) a straightforward set of assumptions is enough to give rise to exchange in a software market, and 2) knowledge exchange is shown to increase the efficiency of the market.

Fuzzy constraints, choice, and utility

We revisit the notion of fuzzy revealed preference, with the intention of using it in decision making. A decision making agent manages resources that are priced, and it has a certain wealth. We review proposed fuzzifications of preference relations. Although they are well founded, they cannot deal well with decision making under fuzzy constraints. We introduce the fuzzy budget set as a general model of fuzzy constraints on resources. We then show that a general condition for rationality, the fuzzy axiom of revealed preference should not be an axiom anymore, but just a statement that is true to a certain degree. We show how to calculate this degree of truth. We define a fuzzy utility function, and show how it can be maximised, subject to fuzzy budget constraints. Keywords— fuzzy choice, fuzzy utility, fuzzy budget, qualitative reasoning I. Fuzzy choice and intelligent agents ELECTRONIC commerce allows buyers and sellers to use increasingly complicated decision procedures. Large amounts of information are available, and computers can process this to advise the economic agent in the choice of an alternative. The information gathered, over the web for example, is often inconsistent. If it is to be used in decision making, the decision making process will have to be able to deal with uncertainty. Humans deal with uncertainty in a natural way, via generalization. Automatic procedures use either probability theory or fuzzy logic. We prefer fuzzy logic because it deals with linguistic variables in a more intuitive way that probability theory. The linguistic variables are classes that have evolved over time, in a certain application domain, to be effective in generalization. Linguistic variables are the method adopted by humans to indicate choice and preference. Many intelligent agents aim to capture the preferences of their human owner. If decisions are to be made by a computer agent in e-commerce, it is essential that the computer agent agrees with the human owner. Should we study psychology before implementing a shop-bot? This would create problems, as a psychological analysis of economical behaviour returns results that are difficult to implement in a computer algorithm. Most economists hold that their theory, micro-economics based on game theory, gives an accurate description of human economical behaviour. They even have applied the microeconomic paradigm to areas such as social interactions, and irrational behaviour in households and firms [1]. For the management of resources, a core economic activity, the micro-economic approach is prevailing. This is what e-commerce is mostly about: buying and selling quantifiable resources. If we can allow the quantities to be fuzzy, e-commerce and e-management of resources will be even more widely applied than it is now. E-commerce and e-management of resources can operate automatically using intelligent software agents. To achieve this, we need to re-formulate micro-economy so that it can deal with fuzzy choice and preferences. The Orlovsky choice function is often used as the basis for fuzzy choice [2], [3]. We will start from an entirely different starting point, immediately taking into account prices of resources that affect the choice among alternatives. Another approach, ranking based on pairwise comparisons is described in [4]. Choice among attributes that have multiple attributes is reviewed in [5]. The attributes of our alternatives will be the prices of goods in the consumption bundle. This will allow us to have more specific procedures for ranking than in [5], [4]. Once a basic concept, such as the Orlovsky choice function is proposed and adopted, scientists usually start refining and generalizing it. This happened to fuzzy choice functions, just as it happened to Nash equilibrium, expert systems, etc. Much of the current theory about fuzzy choice has become so abstract that it is impossible to implement in an e-commerce agent. The refined theory of choice can certainly be used to model particular user’s decisions very accurately, but this matching of theory and user requires extensive human intervention. If the e-commerce agent has to implement fuzzy choice automatically for a large class of users, we have to turn back, and use a more intuitive theory. Kulshreshtha and Shekar [6] have recently attempted to present an intuitive perspective on fuzzy preference. It becomes clear from this paper that there is an array of possible choice functions, with no clear criteria as to which ones to prefer. There are even some intuitive contradictions. The authors point out the need to conduct experiments to find the most appropriate fuzzy preference relations for real life situations. We will not conduct experiments, but consider the crisp theory of preference closer to the application (resource management), before fuzzifying it. II. Two weak axioms of fuzzy revealed

Fast tracking conjugate gradient algorithm

This paper describes a novel Conjugate Gradient (CG) algorithm utilizing a noise-immunized forgetting factor in order to boost the tracking capability for time-varying parameters. The new algorithm is based on re-initializing the forgetting factor when it encounters an unexpected parameter change and has a noise-immunity property due to the counter logic function. Fast tracking and low parametric error variance properties are verified through computer simulation in a system identification problem. In addition, the convergence property is analyzed by a Chebyshev polynomial approximation. It is shown that the convergence of the CG algorithm is speeded up by an acceleration term when compared to the Steepest Descent (SD) algorithm.

Ontological Stratification in an Ecology of Infohabitants

This paper reports progress from the EEII research project where ontological stratification is applied in the study of openness. We explain a stratification approach to reduce the overall complexity of conceptual models, and to enhance their modularity. A distinction is made between ontological and epistemological stratification. The application of the stratification approach to agent system design is explained and illustrated. A preliminary characterization of the relevant strata is given. The wider relevance of this result for information infrastructure design is addressed: ontological stratification will be key to the model management and semantic interoperability in a ubiquitous and model driven information infrastructure.

A neural network model of a communication network with information servers

This paper models information flow in a communication network. The network consists of nodes that communicate with each other, and information servers that have a predominantly one-way communication to their customers. A neural network is used as a model for the communication network. The existence of multiple equilibria in the communication network is established. The network operator observes only one equilibrium, but if he knows the other equilibria, he can influence the free parameters, for example by providing extra bandwidth, so that the network settles in another equilibrium that is more profitable for the operator. The influence of several network parameters on the dynamics is studied both by simulation and by theoretical methods.