A mixed hypergraph is a triple H = (X; C;D), where X is the vertex set, and each of C;D is a list of subsets of X. A strict t-coloring is a onto mapping from X to {1, 2,…,t} such that each c belongs to C contains two vertices have a common value and each d belongs to D has two vertices have distinct values. If H has a strict t-coloring, then t belongs to S(H), such S(H) is called the feasible set of H, and k is a gap if there are a value larger than k and a value less than k in the feasible set but k is not. We find the minimum and maximum gap of a mixed hypergraph with more than 5 vertices. Then we consider two special cases of the gap of mixed hypergraphs. First, if the mixed hypergraphs is spanned by a complete bipartite graph, then the gap is decided by the size of bipartition. Second, the (l,m)-uniform mixed hypergraphs has gaps if l > m/2 >2, and we prove that the minimum number of vertices of a (l,m)-uniform mixed hypergraph which has gaps is (m/2)( l -1) + m.

Chronic exposure to psychostimulants such as amphetamine (AMPH) can induce long-term disruptions in cognition via actions on prefrontal cortex dopamine. Previous work has shown that two types of executive functions, set shifting and working memory (WM), are disrupted by AMPH sensitization and that these cognitive domains are impaired in schizophrenics and stimulant abusers. We assessed the effects of AMPH sensitization on behavioural flexibility using a cross-maze set shifting task and a WM task using the delayed spatial win-shift (SWSh) task in Long Evans (LE) and Sprague Dawley (SD) rats. Rats were exposed to an AMPH sensitization regimen (15 AMPH or saline injections: 1-5 mg/kg every 2nd day, increasing the dose by 1 mg every 3rd injections) following habituation on the mazes. In experiment 1, LE and SD rats were initially trained on a visual cue discrimination. During the set shift, rats were required to shift from the previously acquired visual-cue-based strategy to a response strategy (e.g.; always turn left, ignore the visual cue). For the reversal, rats were trained to reverse their turn direction. AMPH treatment did not impair learning of the initial cue discrimination in either strain. However, AMPH treated rats learned the response discrimination faster than controls during the set shift and AMPH treated LE rats were faster than controls to reach acquisition criterion during the response reversal. AMPH treatment neither impaired nor improved reversal learning in SD rats. In experiment 2, rats were tested on the SWSh task in which spatial information acquired during a training phase was used 30 minutes later during the testing phase in order to retrieve food pellets on the maze. In this task, AMPH treated rats were faster to re-attain criterion than control rats. Correlational analysis further revealed that AMPH sensitized rats that required more days to reach criterion before AMPH treatment (i.e. slow learners) tended to make more errors during re-acquisition of the memory task. Viewed collectively, these results suggest that chronic AMPH treatment can enhance behavioural flexibility and WM assessed in this manner. However, repeated AMPH exposure may have exacerbated pre-existing cognitive deficits in slow learning rats.

Wireless Sensor Networks (WSNs), consisting of many small sensing devices working in concert, have the potential to revolutionise every aspect of our lives. Although the technology is still in its infancy offers an unlimited number of possible applications, ranging from military surveillance to environmental monitoring. These WSNs are prone to physical sensor failures due to environmental conditions such bio fouling and an adverse ambient environment, as well as threats that arise from their operation in an open environment. Consequently, reliability and fault-tolerance techniques become a critical aspect of the research associated with WSNs. In mission critical applications, such as the monitoring of enemy troops, unreliable or faulty information produced by WSNs could potentially lead to fatal outcomes. In such applications, it necessary to receive both a correct notification of event occurrences and uncorrupted data. Developing a fault-tolerance system for WSNs is a challenging task. New self-configuration, self-recognition and self-organisation techniques are needed due to unique aspects of the operation of WSNs. Our current understanding of WSNs leads to an immunologically inspired solution to the design of a fault-tolerant network. One of the main roles of the Natural Immune System(NIS) is the recognition of self and the elimination of non-self proteins. Hence, in order to have an immune system equivalent for a sensor network, we must have a clear and stable definition of what constitutes the Self and the Non-Self Sets in a sensor network. This thesis explores two different approaches to modelling, collection and representation of the Self-Set in distributed sensor networks. We approach this problem, of identifying what constitutes the Self-Set in terms of sensor readings, using pattern recognition techniques from the machine learning field that leverages a small number of past observations of sensor nodes. We have chosen Competitive Learning Neural Network (CLNN) for the construction of the Self-Set. We define and evaluate two approaches for the aggregation of the Self-Set across multiple sensors in a WSN. The first approach is the Graph Theory Based Aggregation (GTBA) which consists of two main parts, namely: classification of the sensor readings by means of CLNN, which provides the multimodal view data and GTBA of the CLNN output, which takes intersections of intervals produced by CLNN. In this thesis we define and evaluate two different interpretations of GTBA, namely: Midpoint Intersection (MPI): one that considers the midpoint of intervals. Midpoint Free Intersection (MFI): one that does not take the midpoints into account but assigns the confidence levels to each of the resulted intersections. We evaluated both interpretations on three different types of phenomena and have shown that the second interpretation, MFI, consistently produced more precise representations of the environment under observation. However, MFI produced a very strict representation of the phenomenon, which consequently led to a large number of systems' retraining. Hence, we defined and evaluated a technique which produced a more relaxed representation of the Self-Set and at the same time preserved the finer variation in the phenomenon. The second approach is based on unsupervised learning. We define and evaluate three related unsupervised learning procedures ?? Divergence and Merging (DMP), Suboptimal Clustering (SOC), and Simple Clustering (SC) for the collection of the Self-Set. We explore the design tradeoffs in unsupervised learning schemes with respect to the clustering quality. We implement and evaluate these related unsupervised learning procedures on a realworld data set. The outcome of these experiments show that, out of the three unsupervised learning procedures studied in this thesis, the Suboptimal Clustering procedure appears to be the most suitable for the classification of sensor readings, provided that the amount of free memory is large enough to store and recluster an entire training set. We evaluate aggregation of the Self-Set produced by means of the distributed implementation of the unsupervised learning procedures. The aggregation is based on extended unsupervised learning and we evaluate the possibilities of the autonomous retraining of the system. Our experiments show that, in a naturally slowly changing environment, 40% of nodes reporting deviations is a large enough number to reinitialise the retraining of the system. The final conclusion is that it is possible to have a distributed implementation of the unsupervised procedure that produces an almost identical representation of the environment, which makes unsupervised learning suitable for a large number of sensor network architectures.

Wireless Sensor Networks (WSNs), consisting of many small sensing devices working in concert, have the potential to revolutionise every aspect of our lives. Although the technology is still in its infancy offers an unlimited number of possible applications, ranging from military surveillance to environmental monitoring. These WSNs are prone to physical sensor failures due to environmental conditions such bio fouling and an adverse ambient environment, as well as threats that arise from their operation in an open environment. Consequently, reliability and fault-tolerance techniques become a critical aspect of the research associated with WSNs. In mission critical applications, such as the monitoring of enemy troops, unreliable or faulty information produced by WSNs could potentially lead to fatal outcomes. In such applications, it necessary to receive both a correct notification of event occurrences and uncorrupted data. Developing a fault-tolerance system for WSNs is a challenging task. New self-configuration, self-recognition and self-organisation techniques are needed due to unique aspects of the operation of WSNs. Our current understanding of WSNs leads to an immunologically inspired solution to the design of a fault-tolerant network. One of the main roles of the Natural Immune System(NIS) is the recognition of self and the elimination of non-self proteins. Hence, in order to have an immune system equivalent for a sensor network, we must have a clear and stable definition of what constitutes the Self and the Non-Self Sets in a sensor network. This thesis explores two different approaches to modelling, collection and representation of the Self-Set in distributed sensor networks. We approach this problem, of identifying what constitutes the Self-Set in terms of sensor readings, using pattern recognition techniques from the machine learning field that leverages a small number of past observations of sensor nodes. We have chosen Competitive Learning Neural Network (CLNN) for the construction of the Self-Set. We define and evaluate two approaches for the aggregation of the Self-Set across multiple sensors in a WSN. The first approach is the Graph Theory Based Aggregation (GTBA) which consists of two main parts, namely: classification of the sensor readings by means of CLNN, which provides the multimodal view data and GTBA of the CLNN output, which takes intersections of intervals produced by CLNN. In this thesis we define and evaluate two different interpretations of GTBA, namely: Midpoint Intersection (MPI): one that considers the midpoint of intervals. Midpoint Free Intersection (MFI): one that does not take the midpoints into account but assigns the confidence levels to each of the resulted intersections. We evaluated both interpretations on three different types of phenomena and have shown that the second interpretation, MFI, consistently produced more precise representations of the environment under observation. However, MFI produced a very strict representation of the phenomenon, which consequently led to a large number of systems' retraining. Hence, we defined and evaluated a technique which produced a more relaxed representation of the Self-Set and at the same time preserved the finer variation in the phenomenon. The second approach is based on unsupervised learning. We define and evaluate three related unsupervised learning procedures ?? Divergence and Merging (DMP), Suboptimal Clustering (SOC), and Simple Clustering (SC) for the collection of the Self-Set. We explore the design tradeoffs in unsupervised learning schemes with respect to the clustering quality. We implement and evaluate these related unsupervised learning procedures on a realworld data set. The outcome of these experiments show that, out of the three unsupervised learning procedures studied in this thesis, the Suboptimal Clustering procedure appears to be the most suitable for the classification of sensor readings, provided that the amount of free memory is large enough to store and recluster an entire training set. We evaluate aggregation of the Self-Set produced by means of the distributed implementation of the unsupervised learning procedures. The aggregation is based on extended unsupervised learning and we evaluate the possibilities of the autonomous retraining of the system. Our experiments show that, in a naturally slowly changing environment, 40% of nodes reporting deviations is a large enough number to reinitialise the retraining of the system. The final conclusion is that it is possible to have a distributed implementation of the unsupervised procedure that produces an almost identical representation of the environment, which makes unsupervised learning suitable for a large number of sensor network architectures.

Wireless Sensor Networks (WSNs), consisting of many small sensing devices working in concert, have the potential to revolutionise every aspect of our lives. Although the technology is still in its infancy offers an unlimited number of possible applications, ranging from military surveillance to environmental monitoring. These WSNs are prone to physical sensor failures due to environmental conditions such bio fouling and an adverse ambient environment, as well as threats that arise from their operation in an open environment. Consequently, reliability and fault-tolerance techniques become a critical aspect of the research associated with WSNs. In mission critical applications, such as the monitoring of enemy troops, unreliable or faulty information produced by WSNs could potentially lead to fatal outcomes. In such applications, it necessary to receive both a correct notification of event occurrences and uncorrupted data. Developing a fault-tolerance system for WSNs is a challenging task. New self-configuration, self-recognition and self-organisation techniques are needed due to unique aspects of the operation of WSNs. Our current understanding of WSNs leads to an immunologically inspired solution to the design of a fault-tolerant network. One of the main roles of the Natural Immune System(NIS) is the recognition of self and the elimination of non-self proteins. Hence, in order to have an immune system equivalent for a sensor network, we must have a clear and stable definition of what constitutes the Self and the Non-Self Sets in a sensor network. This thesis explores two different approaches to modelling, collection and representation of the Self-Set in distributed sensor networks. We approach this problem, of identifying what constitutes the Self-Set in terms of sensor readings, using pattern recognition techniques from the machine learning field that leverages a small number of past observations of sensor nodes. We have chosen Competitive Learning Neural Network (CLNN) for the construction of the Self-Set. We define and evaluate two approaches for the aggregation of the Self-Set across multiple sensors in a WSN. The first approach is the Graph Theory Based Aggregation (GTBA) which consists of two main parts, namely: classification of the sensor readings by means of CLNN, which provides the multimodal view data and GTBA of the CLNN output, which takes intersections of intervals produced by CLNN. In this thesis we define and evaluate two different interpretations of GTBA, namely: Midpoint Intersection (MPI): one that considers the midpoint of intervals. Midpoint Free Intersection (MFI): one that does not take the midpoints into account but assigns the confidence levels to each of the resulted intersections. We evaluated both interpretations on three different types of phenomena and have shown that the second interpretation, MFI, consistently produced more precise representations of the environment under observation. However, MFI produced a very strict representation of the phenomenon, which consequently led to a large number of systems' retraining. Hence, we defined and evaluated a technique which produced a more relaxed representation of the Self-Set and at the same time preserved the finer variation in the phenomenon. The second approach is based on unsupervised learning. We define and evaluate three related unsupervised learning procedures ?? Divergence and Merging (DMP), Suboptimal Clustering (SOC), and Simple Clustering (SC) for the collection of the Self-Set. We explore the design tradeoffs in unsupervised learning schemes with respect to the clustering quality. We implement and evaluate these related unsupervised learning procedures on a realworld data set. The outcome of these experiments show that, out of the three unsupervised learning procedures studied in this thesis, the Suboptimal Clustering procedure appears to be the most suitable for the classification of sensor readings, provided that the amount of free memory is large enough to store and recluster an entire training set. We evaluate aggregation of the Self-Set produced by means of the distributed implementation of the unsupervised learning procedures. The aggregation is based on extended unsupervised learning and we evaluate the possibilities of the autonomous retraining of the system. Our experiments show that, in a naturally slowly changing environment, 40% of nodes reporting deviations is a large enough number to reinitialise the retraining of the system. The final conclusion is that it is possible to have a distributed implementation of the unsupervised procedure that produces an almost identical representation of the environment, which makes unsupervised learning suitable for a large number of sensor network architectures.

Doctor of Philosphy (PhD) / The term boset was coined by Patrick Jordan, both as an abbreviation of biordered set, and as a generalisation of poset, itself an abbreviation of partially ordered set. A boset is a set equipped with a partial multiplication and two intertwining reflexive and transitive arrow relations which satisfy certain axioms. When the arrow relations coincide the boset becomes a poset. Bosets were invented by Nambooripad (in the 1970s) who developed his own version of the theory of fundamental regular semigroups, including the classical theory of fundamental inverse semigroups using semilattices, due to Munn (in the 1960s). A semigroup is fundamental if it cannot be shrunk homomorphically without collapsing its skeleton of idempotents, which is a boset. Nambooripad constructed the maximum fundamental regular semigroup with a given boset of idempotents. Fundamental semigroups and bosets are natural candidates for basic building blocks in semigroup theory because every semigroup is a coextension of a fundamental semigroup in which the boset of idempotents is undisturbed. Recently Jordan reproved Nambooripad's results using a new construction based on arbitrary bosets. In this thesis we prove that this construction is always fundamental, which was previously known only for regular bosets, and also that it possesses a certain maximality property with respect to semigroups which are generated by regular elements. For nonregular bosets this constuction may be regular or nonregular. We introduce a class of bosets, called sawtooth bosets, which contain many regular and nonregular examples, and correct a criterion of Jordan's for the regularity of this construction for sawtooth bosets with two teeth. We also introduce a subclass, called cyclic sawtooth bosets, also containing many regular and nonregular examples, for which the construction is always regular.

Thesis (M.Sc.). / Written for the School of Computer Science. Title from title page of PDF (viewed 2008/01/15). Includes bibliographical references.

Thesis (doctoral)--Universität Breslau.

Thesis (doctoral)--Universität Breslau.

Thesis (M.S.)--University of Wisconsin--Madison, 1967. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.