A category-theoretic proof of the ergodic decomposition theorem

The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms of string diagrams, using the formalism of Markov categories. We recover the usual measure-theoretic statement by instantiating our result in the category of stochastic kernels. Along the way we give a conceptual treatment of several concepts in the theory of deterministic and stochastic dynamical systems. In particular, - ergodic measures appear very naturally as particular cones of deterministic morphisms (in the sense of Markov categories); - the invariant $\sigma$-algebra of a dynamical system can be seen as a colimit in the category of Markov kernels. In line with other uses of category theory, once the necessary structures are in place, our proof of the main theorem is much simpler than traditional approaches. In particular, it does not use any quantitative limiting arguments, and it does not rely on the cardinality of the group or monoid indexing the dynamics. We hope that this result paves the way for further applications of category theory to dynamical systems, ergodic theory, and information theory.Comment: 29 page

A late-Holocene record of coastal wetland development and fire regimes in tropical northern Australia

This study presents three records of environmental change during the late-Holocene from wetlands across Bentinck Island in the South Wellesley Islands, northern Australia. Radiometric dating provided ages for sediment cores with the longest chronology spanning the last 1250 cal. yr BP. Palynological results show the diverse mangrove community transitioned to woodland- and wetland-dominated vegetation over the last 850 years on the southeast coast. The key driver of this landscape change was likely late-Holocene sea level regression and coastal progradation in the Gulf of Carpentaria. This study found freshwater wetlands expanded across Bentick Island over the last 500 years, with sedges and rushes peaking in the last 350 years. Macroscopic and microscopic charcoal records, coupled with archaeological evidence, highlights the spatial and temporal variation in fire regimes across the island, reflecting the traditional fire management practices of the Kaiadilt people during the late-Holocene. This study finds a significant increase in charcoal accumulation in the 1900s when Kaiadilt fire practices were disrupted and the South Wellesley Islands were abandoned. The pollen record reflects little change in the vegetation despite the shifting fire regime, highlighting the importance of multi-proxy approaches to reconstructing past environments in tropical northern Australia where vegetation is adapted to fire

Recursion and Sequentiality in Categories of Sheaves

We present a fully abstract model of a call-by-value language with higher-order functions, recursion and natural numbers, as an exponential ideal in a topos. Our model is inspired by the fully abstract models of O'Hearn, Riecke and Sandholm, and Marz and Streicher. In contrast with semantics based on cpo's, we treat recursion as just one feature in a model built by combining a choice of modular components

Implementing Organizational Change in a Multidimensional Community College District: A Case Study

Implementing organizational change within complex organizations involves responding to external forces that impact business operations. Leaders guide their organizations through planned change processes by implementing strategic initiatives that affect the entire organization, impact business operations, and influence organizational values (Nadler & Tushman, 1989; Tushman & Nadler, 2012). Community colleges implement change initiatives on behalf of historically, non-dominant students to address systemic issues through developing more inclusive higher education practices (Harris & Wood, 2016; Tate IV, 2008). The following study investigated a matrix-structured community college district located in the Pacific Northwest that implemented change across multiple dimensions to improve student success outcomes for systemically minoritized populations. The purpose of the study was to investigate perceptions held by leaders and staff associated with change management implementation within a multidimensional higher education organization with a focus on Black male student outcomes. Through a qualitative, case study approach, the study analyzed data collected within six focus group interviews with 12 participants. Analysis of RQ1 established four major themes including high turnover/attrition, effectiveness of change, effectiveness of communication, and cross-functional teams; and RQ2 established three major themes including heightened awareness of opportunity gaps, shared vision, and cross-functional teams. Findings produced primary recommendations (integrate Achieving the Dream (ATD) into the formal structure of the district, clarifying decision-making and processes, improve transparency and communication, and thoughtful collaboration) and recommendations for future research (1) contributes to emerging literature on multidimensional higher education institutions; (2) improving educational experiences for Black male community college students; and (3) understanding organizational change processes on community college campuses

The Dialectica Models of Type Theory

This thesis studies some constructions for building new models of Martin-Löf type theory out of old. We refer to the main techniques as gluing and idempotent splitting. For each we give general conditions under which type constructors exist in the resulting model. These techniques are used to construct some examples of Dialectica models of type theory. The name is chosen by analogy with de Paiva's Dialectica categories, which semantically embody Gödel's Dialectica functional interpretation and its variants. This continues a programme initiated by von Glehn with the construction of the polynomial model of type theory. We complete the analogy between this model and Gödel's original Dialectica by using our techniques to construct a two-level version of this model, equipping the original objects with an extra layer of predicates. In order to do this we have to carefully build up the theory of finite sum types in a display map category. We construct two other notable models. The first is a model analogous to the Diller-Nahm variant, which requires a detailed study of biproducts in categories of algebras. To make clear the generalization from the categories studied by de Paiva, we illustrate the construction of the Diller-Nahm category in terms of gluing an indexed system of types together with a system of predicates. Following this we develop the general techniques needed for the type-theoretic case. The second notable model is analogous to the Dialectica category associated to the error monad as studied by Biering. This model has only weak dependent products. In order to get a model with full dependent products we use the idempotent splitting construction, which generalizes the Karoubi envelope of a category. Making sense of the Karoubi envelope in the type-theoretic case requires us to face up to issues of coherence in our models. We choose the route of making sure all of the constructions we use preserve strict coherence, rather than applying a general coherence theorem to produce a strict model afterwards. Our chosen method preserves more detailed information in the final model.EPSRC studentshi

Robust local vegetation records from dense archaeological shell matrixes: a palynological analysis of the Thundiy shell deposit, Bentinck Island, Gulf of Carpentaria, Australia

This study investigates the palynological remains (both fossil pollen and charcoal) recovered from the Thundiy shell midden deposit, Bentinck Island, Gulf of Carpentaria, northern Australia, to provide a vegetation and fire record for this site, which sheds light on human occupation of the southern Wellesley Archipelago over the late Holocene. Results show that the development of a high-density shell deposit by human activities was directly responsible for pollen preservation, possibly through the creation of a moist, anaerobic environment that reduces oxidation of pollen grains. The presence of recoverable pollen from a shell midden deposit from Bentinck Island provides a valuable new proxy to provide greater context for archaeological records, particularly in terms of local vegetation information and potential insight into human land management practices

Probabilistic Programming Interfaces for Random Graphs::Markov Categories, Graphons, and Nominal Sets

We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programming language corresponds to a graphon, and conversely, every graphon arises in this way.We provide three constructions for showing that every graphon arises from an equational theory. The first is an abstract construction, using Markov categories and monoidal indeterminates. The second and third are more concrete. The second is in terms of traditional measure theoretic probability, which covers 'black-and-white' graphons. The third is in terms of probability monads on the nominal sets of Gabbay and Pitts. Specifically, we use a variation of nominal sets induced by the theory of graphs, which covers Erdős-Rényi graphons. In this way, we build new models of graph probabilistic programming from graphons

Fever in a returning traveler: A case and literature review of melioidosis

Burkholderia pseudomallei is an aerobic, motile, non-spore-forming gram-negative bacillus found in tropical endemic environments that causes the disease melioidosis. Melioidosis displays a diversity of clinical presentations ranging from septic shock to chronic latent infection, often with characteristic abscesses in multiple organs. Melioidosis is an opportunistic infection, with risk factors, including diabetes, alcohol use, chronic lung disease, and chronic renal disease, and these risk factors increase the severity of disease (Wiersinga et al., 2006) [1]. In this case report, we illustrate a case of a 32 year old man with several risk factors and recent travel to an endemic region presenting with melioidosis. Our case demonstrates the challenges in obtaining a diagnosis in a non-endemic location, highlights a complex presentation of this disease, and describes the multifaceted clinical management required to care for this patient. As global travel increases, there is an increased need for clinician awareness of this disease in non-endemic regions

Increased prevalence of the pfdhfr/phdhps quintuple mutant and rapid emergence of pfdhps resistance mutations at codons 581 and 613 in Kisumu, Kenya

<p>Abstract</p> <p>Background</p> <p>Anti-malarial drug resistance in Kenya prompted two drug policy changes within a decade: sulphadoxine-pyrimethamine (SP) replaced chloroquine (CQ) as the first-line anti-malarial in 1998 and artemether-lumefantrine (AL) replaced SP in 2004. Two cross-sectional studies were conducted to monitor changes in the prevalence of molecular markers of drug resistance over the period in which SP was used as the first-line anti-malarial. The baseline study was carried out from 1999-2000, shortly after implementation of SP, and the follow-up study occurred from 2003-2005, during the transition to AL.</p> <p>Materials and methods</p> <p>Blood was collected from malaria smear-positive, symptomatic patients presenting to outpatient centers in Kisumu, Kenya, during the baseline and follow-up studies. Isolates were genotyped at codons associated with SP and CQ resistance. <it>In vitro </it>IC₅₀values for antifolates and quinolones were determined for isolates from the follow-up study.</p> <p>Results</p> <p>The prevalence of isolates containing the <it>pfdhfr </it>N51I/C59R/S108N/<it>pfdhps </it>A437G/K540E quintuple mutant associated with SP-resistance rose from 21% in the baseline study to 53% in the follow-up study (p < 0.001). Isolates containing the <it>pfdhfr </it>I164L mutation were absent from both studies. The <it>pfdhps </it>mutations A581G and A613S/T were absent from the baseline study but were present in 85% and 61%, respectively, of isolates from the follow-up study. At follow-up, parasites with mutations at five <it>pfdhps </it>codons, 436, 437, 540, 581, and 613, accounted for 39% of isolates. The CQ resistance-associated mutations <it>pfcrt </it>K76T and <it>pfmdr1 </it>N86Y rose from 82% to 97% (p = 0.001) and 44% to 76% (p < 0.001), respectively, from baseline to follow-up.</p> <p>Conclusions</p> <p>During the period in which SP was the first-line anti-malarial in Kenya, highly SP-resistant parasites emerged, including isolates harboring <it>pfdhps </it>mutations not previously observed there. SP continues to be widely used in Kenya; however, given the highly resistant genotypes observed in this study, its use as a first-line anti-malarial should be discouraged, particularly for populations without acquired immunity to malaria. The increase in the <it>pfcrt </it>K76T prevalence, despite efforts to reduce CQ use, suggests that either these efforts are not adequate to alleviate CQ pressure in Kisumu, or that drug pressure is derived from another source, such as the second-line anti-malarial amodiaquine.</p

Extended residence times for foraminifera in a marine-influenced terrestrial archaeological deposit and implications for palaeoenvironmental reconstruction

Accelerator Mass Spectrometry (AMS) radiocarbon dating and taphonomic grading was undertaken on foraminifera preserved in the archaeological shell matrix site of Thundiy, Bentinck Island, southern Gulf of Carpentaria, Australia. Foraminifera were assigned to one of six taphonomic grades ranging from pristine to severely abraded. AMS dating demonstrates a weak relationship between preservation status and age. Foraminifera ages are inconsistent with multiple ages on marine shell from the same deposit implying significant sediment transport system residence ages (the time between death of the organism and final deposition) for foraminifera in the deposit. Results demonstrate that foraminifera cannot be assumed to be contemporary with other components of the sedimentary context in which they occur, indicating that caution is required in interpreting chronologies and palaeoenvironmental records based on foraminifera recovered from highly dynamic depositional settings. Findings point to the potential of foraminifera AMS dating of coastal archaeological deposits to contribute to evaluations of site integrity and chrono-stratigraphic analyses