Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Non-zero mean Gaussian process prior wind field models

This report outlines the derivation and application of a non-zero mean, polynomial-exponential covariance function based Gaussian process which forms the prior wind field model used in 'autonomous' disambiguation. It is principally used since the non-zero mean permits the computation of realistic local wind vector prior probabilities which are required when applying the scaled-likelihood trick, as the marginals of the full wind field prior. As the full prior is multi-variate normal, these marginals are very simple to compute.

Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems

MSC 2010: 26A33, 34D05, 37C25

On strongly regular graphs with m2 = qm3 and m3 = qm2

2010 Mathematics Subject Classification: 05C50.

Non -traded goods, product differentiation and integration of factor markets

This research sought to determine the implications of a non-traded differentiated commodity produced with increasing returns to scale, for the welfare of countries that allowed free international migration. We developed two- and three-country Ricardian models in which labor was the only factor of production. The countries traded freely in homogeneous goods produced with constant returns to scale. Each also had a non-traded differentiated good sector where production took place using increasing returns to scale technology. Then we allowed for free international migration between two of the countries and observed what happened to welfare in both countries as indicated by their per capita utilities in the new equilibrium relative to their pre-migration utilities. ^ Preferences of consumers were represented by a two-tier utility function [Dixit and Stiglitz 1977]. As migration took place it impacted utility in two ways. The expanding country enjoyed the positive effect of increased product diversity in the non-traded good sector. However, it also suffered adverse terms-of-trade as its production cost declined. The converse was true for the contracting country. To determine the net impact on welfare we derived indirect per capita utility functions of the countries algebraically and graphically. Then we juxtaposed the graphs of the utility functions to obtain possible general equilibria. These we used to observe the welfare outcomes. ^ We found that the most likely outcomes were either that both countries gained, or one country lost while the other gained. We were, however, able to generate cases where both countries lost as a result of allowing free inter-country migration. This was most likely to happen when the shares of income spent on each country's export good differed significantly. In the three country world when we allowed two of the countries to engage in preferential trading arrangements while imposing a prohibitive tariff on imports from the third country welfare of the partner countries declined. When inter-union migration was permitted welfare declined even further. This we showed was due to the presence of the non-traded good sector. ^

NON-FULL-TIME COLLEGE PROFESSORS: A NARRATIVE INQUIRY INTO THE NON-FULL-TIME FACULTY ROLE

The rate of non-full-time faculty members has increased rapidly over the last decade (Louis, 2009; MacKay, 2014; Meranze & Newfield, 2013), as the post-secondary landscape of fluctuating enrolment, fiscal and operational challenges, and the requirement to hire specialized skill sets have required institutions to rely heavily on this demographic. In the Ontario Colleges of Applied Arts and Technology (CAATs) system, institutions have tried to preserve and enhance educational quality with fewer resources through greater reliance on non-full-time faculty. The purpose of this study was to explore the perceptions and experiences of teaching and support of non-full-time faculty at one Eastern Ontario college. Employing a narrative inquiry methodology, data were collected from four participants through their writing three individual letters at the end of each month and participating in one interview at the end of the contract period. The data were analyzed and coded. This analysis revealed five themes: motivation, connection and engagement, compensation, teaching and development, and performance evaluation. Differences in the participants’ perceptions tended to reflect divergences across career stage: retired versus early career. The compensation package provided to non-full-time faculty was considered inadequate for those in the early career stage, especially comparing it to that of full-time faculty. In addition, the amount of previous teaching experience was an important indicator for the appropriate level of teaching resources and support provided by the institution. The newer faculty members required a higher level of support to combat feelings of role isolation. The temporary nature of the role made it difficult to establish a feeling of a strong connection to the institution and subsequently opportunities to engage further to deepen the relationship. Despite these differences across participants, autonomous motivators were consistent across all narratives, as participants expressed their desire to teach and share their knowledge to help students achieve their goals. Participants concluded their narratives by sharing future advice for faculty interested in pursuing the role. The narratives provided areas for improvement that would help increase the level of job satisfaction for non-full-time college faculty members: (a) establishing a more thorough performance evaluation process to align with institutional supports, (b) offering more diverse teaching resources to better prepare faculty and enhance teaching practices, (c) overhauling the compensation package to better recognize the amount of time and effort spent in the role and aligning with the compensation provided to full-time faculty, and (d) including rewards and incentives as part of the compensation package to enhance the level of commitment and availability for the role. These changes might well increase the job satisfaction and improve the retention of non-full-time faculty members.

Building autonomous sensitive artificial listeners (Extended abstract)

This paper describes a substantial effort to build a real-time interactive multimodal dialogue system with a focus on emotional and non-verbal interaction capabilities. The work is motivated by the aim to provide technology with competences in perceiving and producing the emotional and non-verbal behaviours required to sustain a conversational dialogue. We present the Sensitive Artificial Listener (SAL) scenario as a setting which seems particularly suited for the study of emotional and non-verbal behaviour, since it requires only very limited verbal understanding on the part of the machine. This scenario allows us to concentrate on non-verbal capabilities without having to address at the same time the challenges of spoken language understanding, task modeling etc. We first summarise three prototype versions of the SAL scenario, in which the behaviour of the Sensitive Artificial Listener characters was determined by a human operator. These prototypes served the purpose of verifying the effectiveness of the SAL scenario and allowed us to collect data required for building system components for analysing and synthesising the respective behaviours. We then describe the fully autonomous integrated real-time system we created, which combines incremental analysis of user behaviour, dialogue management, and synthesis of speaker and listener behaviour of a SAL character displayed as a virtual agent. We discuss principles that should underlie the evaluation of SAL-type systems. Since the system is designed for modularity and reuse, and since it is publicly available, the SAL system has potential as a joint research tool in the affective computing research community.

Introduction: dispersed minorities and non-territorial autonomy

The concept of non-territorial autonomy gives rise to at least two important questions: the range of functional areas over which autonomy extends, and the extent to which this autonomy is indeed non-territorial. A widely used early description significantly labelled this ‘national cultural autonomy’, implying that its focus is mainly on cultural matters, such as language, religion, education and family law. In many of the cases that are commonly cited, ‘autonomy’ may not even extend this far: its most visible expression is the existence of separate electoral registers or quotas for the various groups. Part of the dilemma lies in the difficulty of devolving substantial power on a non-territorial basis: to the extent that devolved institutions are state-like, they ideally require a defined territory. Ethnic groups, however, vary in the extent to which they are territorially concentrated, and therefore in the degree to which any autonomous arrangements for them are territorial or non-territorial. This article explores the dilemma generated by this tension between ethnic geography (pattern of ethnic settlement) and political autonomy (degree of selfrule), and introduces a set of case studies where the relationship between these two features is discussed further: the Ottoman empire and its successor states, the Habsburg monarchy, the Jewish minorities of Europe, interwar Estonia, contemporary Belgium, and two indigenous peoples, the Sa´mi in Norway and the Maori in New Zealand.

Conclusion: patterns of non-territorial autonomy

This article seeks to generalise about the significance of non-territorial autonomy as a mechanism for the management of ethnic conflict on the basis of a set of case studies covering the Ottoman empire and its successor states, the Habsburg monarchy, the Jewish minorities of Europe, interwar Estonia, contemporary Belgium, and two indigenous peoples, the Sami in Norway and Maori in New Zealand. It begins by assessing the extent to which the spatial distribution of ethnonational communities determined the range of autonomy options available—whether these might be territorial or whether only non-territorial autonomy would be realistic. The article continues with an assessment of the significance of ‘autonomy’ in circumstances where the institutions with which it is associated enjoy a non-territorial rather than a territorial writ. It concludes by suggesting that in almost all cases where autonomy is extended to a minority within a state this is exercised on a territorial basis, and that in many cases of non-territorial autonomy, or national–cultural autonomy, the powers assumed by the ‘autonomous’ institutions are substantially symbolic. It argues that notwithstanding the limited empirical evidence for the existence of non-territorial autonomy, this device should not be written off at a normative level.

Garbage collection optimization for non uniform memory access architectures

Cache-coherent non uniform memory access (ccNUMA) architecture is a standard design pattern for contemporary multicore processors, and future generations of architectures are likely to be NUMA. NUMA architectures create new challenges for managed runtime systems. Memory-intensive applications use the system’s distributed memory banks to allocate data, and the automatic memory manager collects garbage left in these memory banks. The garbage collector may need to access remote memory banks, which entails access latency overhead and potential bandwidth saturation for the interconnection between memory banks. This dissertation makes five significant contributions to garbage collection on NUMA systems, with a case study implementation using the Hotspot Java Virtual Machine. It empirically studies data locality for a Stop-The-World garbage collector when tracing connected objects in NUMA heaps. First, it identifies a locality richness which exists naturally in connected objects that contain a root object and its reachable set— ‘rooted sub-graphs’. Second, this dissertation leverages the locality characteristic of rooted sub-graphs to develop a new NUMA-aware garbage collection mechanism. A garbage collector thread processes a local root and its reachable set, which is likely to have a large number of objects in the same NUMA node. Third, a garbage collector thread steals references from sibling threads that run on the same NUMA node to improve data locality. This research evaluates the new NUMA-aware garbage collector using seven benchmarks of an established real-world DaCapo benchmark suite. In addition, evaluation involves a widely used SPECjbb benchmark and Neo4J graph database Java benchmark, as well as an artificial benchmark. The results of the NUMA-aware garbage collector on a multi-hop NUMA architecture show an average of 15% performance improvement. Furthermore, this performance gain is shown to be as a result of an improved NUMA memory access in a ccNUMA system. Fourth, the existing Hotspot JVM adaptive policy for configuring the number of garbage collection threads is shown to be suboptimal for current NUMA machines. The policy uses outdated assumptions and it generates a constant thread count. In fact, the Hotspot JVM still uses this policy in the production version. This research shows that the optimal number of garbage collection threads is application-specific and configuring the optimal number of garbage collection threads yields better collection throughput than the default policy. Fifth, this dissertation designs and implements a runtime technique, which involves heuristics from dynamic collection behavior to calculate an optimal number of garbage collector threads for each collection cycle. The results show an average of 21% improvements to the garbage collection performance for DaCapo benchmarks.

Exploring coordination-driven self-assembly with autonomous chemical robots

The work presented herein focused on the automation of coordination-driven self assembly, exploring methods that allow syntheses to be followed more closely while forming new ligands, as part of the fundamental study of the digitization of chemical synthesis and discovery. Whilst the control and understanding of the principle of pre-organization and self-sorting under non-equilibrium conditions remains a key goal, a clear gap has been identified in the absence of approaches that can permit fast screening and real-time observation of the reaction process under different conditions. A firm emphasis was thus placed on the realization of an autonomous chemical robot, which can not only monitor and manipulate coordination chemistry in real-time, but can also allow the exploration of a large chemical parameter space defined by the ligand building blocks and the metal to coordinate. The self-assembly of imine ligands with copper and nickel cations has been studied in a multi-step approach using a self-built flow system capable of automatically controlling the liquid-handling and collecting data in real-time using a benchtop MS and NMR spectrometer. This study led to the identification of a transient Cu(I) species in situ which allows for the formation of dimeric and trimeric carbonato bridged Cu(II) assemblies. Furthermore, new Ni(II) complexes and more remarkably also a new binuclear Cu(I) complex, which usually requires long and laborious inert conditions, could be isolated. The study was then expanded to the autonomous optimization of the ligand synthesis by enabling feedback control on the chemical system via benchtop NMR. The synthesis of new polydentate ligands has emerged as a result of the study aiming to enhance the complexity of the chemical system to accelerate the discovery of new complexes. This type of ligand consists of 1-pyridinyl-4-imino-1,2,3-triazole units, which can coordinate with different metal salts. The studies to test for the CuAAC synthesis via microwave lead to the discovery of four new Cu complexes, one of them being a coordination polymer obtained from a solvent dependent crystallization technique. With the goal of easier integration into an automated system, copper tubing has been exploited as the chemical reactor for the synthesis of this ligand, as it efficiently enhances the rate of the triazole formation and consequently promotes the formation of the full ligand in high yields within two hours. Lastly, the digitization of coordination-driven self-assembly has been realized for the first time using an in-house autonomous chemical robot, herein named the ‘Finder’. The chemical parameter space to explore was defined by the selection of six variables, which consist of the ligand precursors necessary to form complex ligands (aldehydes, alkineamines and azides), of the metal salt solutions and of other reaction parameters – duration, temperature and reagent volumes. The platform was assembled using rounded bottom flasks, flow syringe pumps, copper tubing, as an active reactor, and in-line analytics – a pH meter probe, a UV-vis flow cell and a benchtop MS. The control over the system was then obtained with an algorithm capable of autonomously focusing the experiments on the most reactive region (by avoiding areas of low interest) of the chemical parameter space to explore. This study led to interesting observations, such as metal exchange phenomena, and also to the autonomous discovery of self assembled structures in solution and solid state – such as 1-pyridinyl-4-imino-1,2,3-triazole based Fe complexes and two helicates based on the same ligand coordination motif.

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre.