A Control-Oriented Notion of Finite State Approximation

We consider the problem of approximating discrete-time plants with finite-valued sensors and actu- ators by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. Building on ideas from robust control, we propose a control-oriented notion of finite state approximation for these systems, demonstrate its relevance to the control synthesis problem, and discuss its key features.Comment: IEEE Transactions on Automatic Control, to appea

Finite Alphabet Control of Logistic Networks with Discrete Uncertainty

We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative examples

Solving Commutative Relaxations of Word Problems

We present an algebraic characterization of the standard commutative relaxation of the word problem in terms of a polynomial equality. We then consider a variant of the commutative word problem, referred to as the “Zero-to-All reachability” problem. We show that this problem is equivalent to a finite number of commutative word problems, and we use this insight to derive necessary conditions for Zero-to-All reachability. We conclude with a set of illustrative examples

Understanding Workplace Incivility Experiences and the Moderating Role of Mindfulness

Rude treatment at work can lead to many negative consequences, as evidenced by the wealth of research available. This dissertation, addressed two important questions that have yet to receive adequate attention. First, how does an employee experience incivility, and second, what is a practical and cost-effective way of mitigating the negative outcomes associated with incivility and promoting positive ones? Incivility research has mainly employed quantitative methods to understand incivility experiences. Using qualitative methods however, would complement the knowledge and potentially move the field of inquiry in new directions. As such, the goal of Study One was to obtain a narrative description of workplace incivility experiences. I took a descriptive phenomenological approach as this allowed me to best capture the events through the employees’ eyes. The interviews involved discussions about an uncivil event and their thoughts, feelings, and behaviour during and after the event. Interview findings revealed several novel elements of the incivility incident such as the importance of communication and the almost certain deterioration of the relationship between perpetrator and victim. The interview findings also identified vulnerability factors that intensified the negative experience. For example, newcomers to the organization were more likely to experience feelings of anger, hate, and anxiety than more tenured employees. In Study Two, I explored the role of three mindfulness facets (non-reactivity, non-judging, and acting with awareness) as regulatory factors by examining whether they mitigated the negative relationship between incivility and well-being and promoted forgiveness via decreased rumination and negative affect. Overall, results showed that when using the Perceived Victimization Measure, non-judging and acting with awareness buffered against stress and promoted forgiveness via deceased negative affect, but not rumination. These results were not replicated when using the Workplace Incivility Scale. Theoretical and practical implications are discussed, along with directions for future research

Taking a Closer Look at Workplace Incivility: Dimensionality and Source Effects

The purpose of this thesis was twofold. First, it sought to investigate whether taking a multi-foci approach to the study of workplace incivility would result in differential relations with affective commitment, job satisfaction, and turnover intentions. In general, the results were supported. When the source of incivility was measured jointly, relations between incivility and organizational outcomes were overestimated. Measuring incivility from a supervisor and a co-worker separately showed that incivility from a supervisor was more strongly associated with job satisfaction and turnover intentions. Co-worker incivility was more strongly associated with affective commitment. Second, this thesis critically assessed the dimensionality of the scale commonly used to measure workplace incivility. The Workplace Incivility Scale (Cortina, Magley, Williams, & Langhout, 2001) revealed two factors – covert and overt incivility. Covert incivility had stronger relationships with organizational outcomes than overt incivility. I draw on relational considerations to explain these findings and to discuss avenues for future research

On the graph of trees

We consider an ldquon-graph of treesrdquo whose nodes are the set of trees of fixed order n, and in which two nodes are adjacent if one tree can be derived from the other through a single application of a local edge transformation rule. We derive an exact formula for the length of the shortest path from any node to any ldquocanonicalrdquo node in the n-graph of trees. We use this result to derive upper and lower bounds on the diameter of the n-graph of trees. We then propose a coordinate system that is convenient for studying the structure of the n-graph of trees, and in which trees having the same degree sequence are projected onto a single point