Construction of Almost Disjunct Matrices for Group Testing

In a \emph{group testing} scheme, a set of tests is designed to identify a small number $t$ of defective items among a large set (of size $N$) of items. In the non-adaptive scenario the set of tests has to be designed in one-shot. In this setting, designing a testing scheme is equivalent to the construction of a \emph{disjunct matrix}, an $M \times N$ matrix where the union of supports of any $t$ columns does not contain the support of any other column. In principle, one wants to have such a matrix with minimum possible number $M$ of rows (tests). One of the main ways of constructing disjunct matrices relies on \emph{constant weight error-correcting codes} and their \emph{minimum distance}. In this paper, we consider a relaxed definition of a disjunct matrix known as \emph{almost disjunct matrix}. This concept is also studied under the name of \emph{weakly separated design} in the literature. The relaxed definition allows one to come up with group testing schemes where a close-to-one fraction of all possible sets of defective items are identifiable. Our main contribution is twofold. First, we go beyond the minimum distance analysis and connect the \emph{average distance} of a constant weight code to the parameters of an almost disjunct matrix constructed from it. Our second contribution is to explicitly construct almost disjunct matrices based on our average distance analysis, that have much smaller number of rows than any previous explicit construction of disjunct matrices. The parameters of our construction can be varied to cover a large range of relations for $t$ and $N$.Comment: 15 Page

Locating and Detecting Arrays for Interaction Faults

The identification of interaction faults in component-based systems has focused on indicating the presence of faults, rather than their location and magnitude. While this is a valuable step in screening a system for interaction faults prior to its release, it provides little information to assist in the correction of such faults. Consequently tests to reveal the location of interaction faults are of interest. The problem of nonadaptive location of interaction faults is formalized under the hypothesis that the system contains (at most) some number d of faults, each involving (at most) some number t of interacting factors. Restrictions on the number and size of the putative faults lead to numerous variants of the basic problem. The relationships between this class of problems and interaction testing using covering arrays to indicate the presence of faults, designed experiments to measure and model faults, and combinatorial group testing to locate faults in a more general testing scenario, are all examined. While each has some definite similarities with the fault location problems for component-based systems, each has some striking differences as well. In this paper, we formulate the combinatorial problems for locating and detecting arrays to undertake interaction fault location. Necessary conditions for existence are established, and using a close connection to covering arrays, asymptotic bounds on the size of minimal locating and detecting arrays are established. A final version of this paper appears in J Comb Optim (2008) 15: 17-48

Preemptive mobile code protection using spy agents

This thesis introduces 'spy agents' as a new security paradigm for evaluating trust in remote hosts in mobile code scenarios. In this security paradigm, a spy agent, i.e. a mobile agent which circulates amongst a number of remote hosts, can employ a variety of techniques in order to both appear 'normal' and suggest to a malicious host that it can 'misuse' the agent's data or code without being held accountable. A framework for the operation and deployment of such spy agents is described. Subsequently, a number of aspects of the operation of such agents within this framework are analysed in greater detail. The set of spy agent routes needs to be constructed in a manner that enables hosts to be identified from a set of detectable agent-specific outcomes. The construction of route sets that both reduce the probability of spy agent detection and support identification of the origin of a malicious act is analysed in the context of combinatorial group testing theory. Solutions to the route set design problem are proposed. A number of spy agent application scenarios are introduced and analysed, including: a) the implementation of a mobile code email honeypot system for identifying email privacy infringers, b) the design of sets of agent routes that enable malicious host detection even when hosts collude, and c) the evaluation of the credibility of host classification results in the presence of inconsistent host behaviour. Spy agents can be used in a wide range of applications, and it appears that each application creates challenging new research problems, notably in the design of appropriate agent route sets

Computation in Complex Networks

Complex networks are one of the most challenging research focuses of disciplines, including physics, mathematics, biology, medicine, engineering, and computer science, among others. The interest in complex networks is increasingly growing, due to their ability to model several daily life systems, such as technology networks, the Internet, and communication, chemical, neural, social, political and financial networks. The Special Issue “Computation in Complex Networks" of Entropy offers a multidisciplinary view on how some complex systems behave, providing a collection of original and high-quality papers within the research fields of: • Community detection • Complex network modelling • Complex network analysis • Node classification • Information spreading and control • Network robustness • Social networks • Network medicin

Graph-Based Information Processing:Scaling Laws and Applications

We live in a world characterized by massive information transfer and real-time communication. The demand for efficient yet low-complexity algorithms is widespread across different fields, including machine learning, signal processing and communications. Most of the problems that we encounter across these disciplines involves a large number of modules interacting with each other. It is therefore natural to represent these interactions and the flow of information between the modules in terms of a graph. This leads to the study of graph-based information processing framework. This framework can be used to gain insight into the development of algorithms for a diverse set of applications. We investigate the behaviour of large-scale networks (ranging from wireless sensor networks to social networks) as a function of underlying parameters. In particular, we study the scaling laws and applications of graph-based information processing in sensor networks/arrays, sparsity pattern recovery and interactive content search. In the first part of this thesis, we explore location estimation from incomplete information, a problem that arises often in wireless sensor networks and ultrasound tomography devices. In such applications, the data gathered by the sensors is only useful if we can pinpoint their positions with reasonable accuracy. This problem is particularly challenging when we need to infer the positions based on basic information/interaction such as proximity or incomplete (and often noisy) pairwise distances. As the sensors deployed in a sensor network are often of low quality and unreliable, we need to devise a mechanism to single out those that do not work properly. In the second part, we frame the network tomography problem as a well-studied inverse problem in statistics, called group testing. Group testing involves detecting a small set of defective items in a large population by grouping a subset of items into different pools. The result of each pool is a binary output depending on whether the pool contains a defective item or not. Motivated by the network tomography application, we consider the general framework of group testing with graph constraints. As opposed to conventional group testing where any subset of items can be grouped, here a test is admissible if it induces a connected subgraph. Given this constraint, we are interested in bounding the number of pools required to identify the defective items. Once the positions of sensors are known and the defective sensors are identified, we investigate another important feature of networks, namely, navigability or how fast nodes can deliver a message from one end to another by means of local operations. In the final part, we consider navigating through a database of objects utilizing comparisons. Contrary to traditional databases, users do not submit queries that are subsequently matched to objects. Instead, at each step, the database presents two objects to the user, who then selects among the pair the object closest to the target that she has in mind. This process continues until, based on the user’s answers, the database can identify the target she has in mind. The search through comparisons amounts to determining which pairs should be presented to the user in order to find the target object as quickly as possible. Interestingly, this problem has a natural connection with the navigability property studied in the second part, which enables us to develop efficient algorithms

Linguistic meta-theory the formal and empirical conditions of acceptability of linguistic theories and descriptions

Most linguists acknowledge, explicitly or implicitly, the relevance of epistemological questions in linguistics but relatively few have given more than a cursory, ad hoc or incomplete consideration to them. The work of one of those few, Jan Mulder, forms the starting point for much of the present discussion. Epistemological considerations arise in many contexts in linguistics and in many guises. It is an epistemological matter whenever we test the adequacy of a description or the acceptability of a theory. Epistemological considerations are latent whenever we discuss the form or the content of linguistic theories and descriptions or their interrelations. The comparison of different approaches to linguistics inevitably raises epistemological questions concerning our approach to linguistics or our presuppositions about it. These questions are of a general nature and transcend questions about particular linguistic theories and descriptions. These epistemological questions force us to consider what we take linguistics to be. In considering questions of the type mentioned we are forced, for example, to analyse what we mean by a "linguistic theory", a "linguistic description" and what phenomena we are aiming to understand. We are, furthermore, forced to analyse the constraints which a scientific attitude places upon linguistic theorising and description-building. It is these questions concerning the acceptability of linguistic theories and descriptions which we call linguistic meta-theory. This thesis falls into five main parts. Firstly, in Chapter One, we consider the nature and scope of linguistic meta-theory. Secondly, in Chapter Two, we look at a number of previous approaches to the subject. Other important contributions are discussed as they arise in the text. Thirdly, in Chapters Three and Four, we consider in detail the major meta-theoretical distinctions in linguistics and their consequences. In particular, we distinguish linguistic theories from linguistic descriptions and discuss the nature of linguistic phenomena. The view is put forward that linguistics is a scientific subject. The meaning of this assertion is analysed and the interrelations of linguistic theories, descriptions and phenomena are considered in the light of this analysis. The main epistemological requirement that is put forward and defended is that of the empiricism of linguistics. Certain changes in our view of the philosophy of science and in our view of the form of linguistic theories and descriptions follow from the conjunction of these major meta-theoretical positions. Fourthly, we consider the main meta-theoretical considerations concerning theories (Chapter Five) and reject a widespread view of linguistic theory as a non-empirical study (Chapter Six) and we consider the main meta-theoretical conditions relating to linguistic descriptions and some practical examples of description -building consonant with the general positions adopted in Chapter Seven. In Chapter Eight, we look at a concrete example of theory-building in the light of the meta-theoretical conditions of acceptability previously set up. We are especially concerned to show how a theory can meet the condition of being "applicable" or "indirectly scientific" through the establishment of acceptable empirical descriptions consonant with the meta-theoretical conditions on descriptions considered earlier. The view that linguistics is a science implies that we must be concerned with the empirical testing of descriptions and, so, the fifth part of the work is devoted to methodology. In Chapter Nine, we defend the role and necessity of methodology in linguistics and set up the logical framework of relations between the methodology and theory descriptions and phenomena. In Chapter Ten, we examine two of the known types of empirical testing and their shortcomings. Finally, in Chapter Eleven, we give an example of the successful and correct application of a methodology in order to bring out the nature of empirical testing and to demonstrate its feasibility within a scientific linguistics of the sort we imagine