Spatial discretization of discrete dynamical systems

Investigates what can go wrong when dynamical systems are modelled with a computer. Number theoretic techniques were used to detail the effects "discretization" errors caused by computer round-off had on characteristics of a system. In particular, a relationship was established between the occurrence of long cycles in a system and the classical result known as Artin's conjecture. Algorithms were then developed which eliminated discretization errors.

Understanding feedback report uptake: process evaluation findings from a 13-month feedback intervention in long-term care settings

BACKGROUND: Long-term care settings provide care to a large proportion of predominantly older, highly disabled adults across the United States and Canada. Managing and improving quality of care is challenging, in part because staffing is highly dependent on relatively non-professional health care aides and resources are limited. Feedback interventions in these settings are relatively rare, and there has been little published information about the process of feedback intervention. Our objectives were to describe the key components of uptake of the feedback reports, as well as other indicators of participant response to the intervention. METHODS: We conducted this project in nine long-term care units in four facilities in Edmonton, Canada. We used mixed methods, including observations during a 13-month feedback report intervention with nine post-feedback survey cycles, to conduct a process evaluation of a feedback report intervention in these units. We included all facility-based direct care providers (staff) in the feedback report distribution and survey administration. We conducted descriptive analyses of the data from observations and surveys, presenting this in tabular and graphic form. We constructed a short scale to measure uptake of the feedback reports. Our analysis evaluated feedback report uptake by provider type over the 13 months of the intervention. RESULTS: We received a total of 1,080 survey responses over the period of the intervention, which varied by type of provider, facility, and survey month. Total number of reports distributed ranged from 103 in cycle 12 to 229 in cycle 3, although the method of delivery varied widely across the period, from 12% to 65% delivered directly to individuals and 15% to 84% left for later distribution. The key elements of feedback uptake, including receiving, reading, understanding, discussing, and reporting a perception that the reports were useful, varied by survey cycle and provider type, as well as by facility. Uptake, as we measured it, was consistently high overall, but varied widely by provider type and time period. CONCLUSIONS: We report detailed process data describing the aspects of uptake of a feedback report during an intensive, longitudinal feedback intervention in long-term care facilities. Uptake is a complex process for which we used multiple measures. We demonstrate the feasibility of conducting a complex longitudinal feedback intervention in relatively resource-poor long-term care facilities to a wider range of provider types than have been included in prior feedback interventions.

Loss of periodicity in breeding success of waders links to changes in lemming cycles in Arctic ecosystems

Lemming population cycles in the Arctic have an important impact on the Arctic food web, indirectly also affecting breeding success in Arctic-nesting birds through shared predators. Over the last two decades lemming cycles have changed in amplitude and even disappeared in parts of the Arctic. To examine the large scale effect of these recent changes we re-analysed published data from the East Atlantic Flyway (EAF), where a relationship between lemming cycles and wader breeding success was earlier found, and new data on breeding success of waders in the East Asian-Australasian Flyway (EAAF). We found that 1) any long-term periodicities in wader breeding success existed only until the year 2000 in the EAAF and until the 1980s in the EAF; 2) studying these patterns at a smaller spatial scale, where the Siberian-Alaskan breeding grounds were divided into five geographical units largely based on landscape features, breeding success of waders from the EAAF was not correlated to an index of predation pressure, but positively correlated to Arctic summer temperatures in some species. We argue that fading out of lemming cycles in some parts of the Arctic is responsible for faltering periodicity in wader breeding success along both flyways. These changed conditions have not yet resulted in any marked changing trends in breeding success across years, and declining numbers of waders along the EAAF are therefore more likely a result of changing conditions at stop-over and wintering sites.

Synthesis of a porous sheet-like V₂O₅-CNT nanocomposite using an ice-templating 'bricks-and-mortar' assembly approach as a high-capacity, long cyclelife cathode material for lithium-ion batteries

Tailoring the nanostructures of electrode materials is an effective way to enhance their electrochemical performance for energy storage. Herein, an ice-templating "bricks-and-mortar" assembly approach is reported to make ribbon-like V2O5 nanoparticles and CNTs integrated into a two-dimensional (2D) porous sheet-like V2O5-CNT nanocomposite. The obtained sheet-like V2O5-CNT nanocomposite possesses unique structural characteristics, including a hierarchical porous structure, 2D morphology, large specific surface area and internal conducting networks, which lead to superior electrochemical performances in terms of long-term cyclability and significantly enhanced rate capability when used as a cathode material for LIBs. The sheet-like V2O5-CNT nanocomposite can charge/discharge at high rates of 5C, 10C and 20C, with discharge capacities of approximately 240 mA h g-1, 180 mA h g-1, and 160 mA h g-1, respectively. It also retains 71% of the initial discharge capacity after 300 cycles at a high rate of 5C, with only 0.097% capacity loss per cycle. The rate capability and cycling performance of the sheet-like V2O5-CNT nanocomposite are significantly better than those of commercial V2O5 and most of the reported V2O5 nanocomposite.

Polyhedral results for the Cardinality Constrained Multi-cycle Problem (CCMcP) and the Cardinality Constrained Cycles and Chains Problem (CCCCP)

In recent years, there has been studies on the cardinality constrained multi-cycle problems on directed graphs, some of which considered chains co-existing on the same digraph whilst others did not. These studies were inspired by the optimal matching of kidneys known as the Kidney Exchange Problem (KEP). In a KEP, a vertex on the digraph represents a donor-patient pair who are related, though the kidney of the donor is incompatible to the patient. When there are multiple such incompatible pairs in the kidney exchange pool, the kidney of the donor of one incompatible pair may in fact be compatible to the patient of another incompatible pair. If Donor A’s kidney is suitable for Patient B, and vice versa, then there will be arcs in both directions between Vertex A to Vertex B. Such exchanges form a 2-cycle. There may also be cycles involving 3 or more vertices. As all exchanges in a kidney exchange cycle must take place simultaneously, (otherwise a donor can drop out from the program once his/her partner has received a kidney from another donor), due to logistic and human resource reasons, only a limited number of kidney exchanges can occur simultaneously, hence the cardinality of these cycles are constrained. In recent years, kidney exchange programs around the world have altruistic donors in the pool. A sequence of exchanges that starts from an altruistic donor forms a chain instead of a cycle. We therefore have two underlying combinatorial optimization problems: Cardinality Constrained Multi-cycle Problem (CCMcP) and the Cardinality Constrained Cycles and Chains Problem (CCCCP). The objective of the KEP is either to maximize the number of kidney matches, or to maximize a certain weighted function of kidney matches. In a CCMcP, a vertex can be in at most one cycle whereas in a CCCCP, a vertex can be part of (but in no more than) a cycle or a chain. The cardinality of the cycles are constrained in all studies. The cardinality of the chains, however, are considered unconstrained in some studies, constrained but larger than that of cycles, or the same as that of cycles in others. Although the CCMcP has some similarities to the ATSP- and VRP-family of problems, there is a major difference: strong subtour elimination constraints are mostly invalid for the CCMcP, as we do allow smaller subtours as long as they do not exceed the size limit. The CCCCP has its distinctive feature that allows chains as well as cycles on the same directed graph. Hence, both the CCMcP and the CCCCP are interesting and challenging combinatorial optimization problems in their own rights. Most existing studies focused on solution methodologies, and as far as we aware, there is no polyhedral studies so far. In this paper, we will study the polyhedral structure of the natural arc-based integer programming models of the CCMcP and the CCCCP, both containing exponentially many constraints. We do so to pave the way for studying strong valid cuts we have found that can be applied in a Lagrangean relaxation-based branch-and-bound framework where at each node of the branch-and-bound tree, we may be able to obtain a relaxation that can be solved in polynomial time, with strong valid cuts dualized into the objective function and the dual multipliers optimised by subgradient optimisation.