Nearly reducible finite Markov chains: theory and algorithms

Finite Markov chains are probabilistic network models that are commonly used as representations of dynamical processes in the physical sciences, biological sciences, economics, and elsewhere. Markov chains that appear in realistic modelling tasks are frequently observed to be nearly reducible, incorporating a mixture of fast and slow processes that leads to ill-conditioning of the underlying matrix of probabilities for transitions between states. Hence, the wealth of established theoretical results that makes Markov chains attractive and convenient models often cannot be used straightforwardly in practice, owing to numerical instability associated with the standard computational procedures to evaluate the expressions. This work is concerned with the development of theory, algorithms, and simulation methods for the efficient and numerically stable analysis of finite Markov chains, with a primary focus on exact approaches that are robust and therefore applicable to nearly reducible networks. New methodologies are presented to determine representative paths, identify the dominant transition mechanisms for a particular process of interest, and analyze the local states that have a strong influence on the characteristics of the global dynamics. The novel approaches yield new insights into the behaviour of Markovian networks, addressing and overcoming numerical challenges. The methodology is applied to example models that are relevant to current problems in chemical physics, including Markov chains representing a protein folding transition, and a configurational transition in an atomic cluster. Relevant classical theory of finite Markov chains and a description of existing robust algorithms for their numerical analysis is given in Chapter 1. The remainder of this thesis considers the problem of investigating a transition from an initial set of states in a Markovian network to an absorbing (target) macrostate. A formal approach to determine a finite set of representative transition paths is proposed in Chapter 2, based on exact pathwise decomposition of the total productive flux. This analysis allows for the importance of competing dynamical processes to be rigorously quantified. A robust state reduction algorithm to compute the expectation of any path property for a transition between two endpoint states is also described in Chapter 2. Chapter 3 reports further numerically stable state reduction algorithms to compute quantities that characterize the features of a transition at a statewise level of detail, allowing for identification of the local states that play a key role in modulating the slow dynamics. An expression is derived for the probability that a state is visited on a path that proceeds directly to the absorbing state without revisiting the initial state, which characterizes the dynamical relevance of an individual state to the overall transition process. In Chapter 4, an unsupervised strategy is proposed to utilize a highly efficient simulation algorithm for sampling paths on a Markov chain. The framework employs a scalable community detection algorithm to obtain an initial clustering of the network into metastable sets of states, which is subsequently refined by a variational optimization procedure. The optimized clustering is then used as the basis for simulating trajectory segments that necessarily escape from the metastable macrostates. The thesis is concluded with an overview of recent related advances that are beyond the scope of the current work (Chapter 5), and a discussion of potential applications where the novel methodology reported herein may be applied to perform insightful analyses that were previously intractable.Cambridge Commonwealth, European and International Trust Engineering and Physical Sciences Research Counci

Cats with thermal burn injuries from California wildfires show echocardiographic evidence of myocardial thickening and intracardiac thrombi.

Recent increases in the prevalence and severity of wildfires in some regions have resulted in an increased frequency of veterinary burn patients. Few studies exist regarding diagnostics and management of burn wounds in veterinary patients and current knowledge is extrapolated from human literature and research models. Post-burn cardiac injury is a common finding and predictor of mortality in human patients and echocardiography is an important tool in monitoring response to therapy and predicting outcome. We describe the notable findings from cats naturally exposed to California wildfires in 2017 and 2018. Domestic cats (n = 51) sustaining burn injuries from the Tubbs (2017) and Camp (2018) wildfires were prospectively enrolled and serial echocardiograms and cardiac troponin I evaluations were performed. Echocardiograms of affected cats revealed a high prevalence of myocardial thickening (18/51) and spontaneous echocardiographic contrast and thrombi formation (16/51). Forty-two cats survived to discharge and 6 died or were euthanized due to a possible cardiac cause. For the first time, we describe cardiovascular and coagulation effects of thermal burn and smoke inhalation in cats. Further studies in veterinary burn victims are warranted and serve as a translational research opportunity for uncovering novel disease mechanisms and therapies

Final Project Report for Bricks from Recyclables

The Bricks from Recyclables team is dedicated to designing and constructing an eco-friendly concrete brick that incorporates plastic to tackle the issue of plastic waste in the environment. The sponsor, Samadhi Yoga Retreat, plans to use this innovative product as a building material on-site to recycle and repurpose plastic, thereby eliminating the impracticality of transporting plastic waste to a recycling center in the remote location. The team conducted tests on four essential subsystems: shredder, mixer, mold, and brick. The shredder tests involved evaluating the shredder\u27s capability and speed. The capability test demonstrated that the shredder could process both PET and HDPE plastic effectively into appropriate sizes, with HDPE producing slightly more of the targeted size. The speed test demonstrated that the shredder could process five bottles of both plastic types in under five minutes. These tests showed that the shredder adhered to the shredder functionality working criteria. The mixer test evaluated whether the mixture could produce a visually uniform blend in less than five minutes. All mixtures created in the mixer successfully met the criteria. However, the team recommends using a larger mixer for producing full-size bricks. The mold functionality test evaluated the effectiveness of the molds utilized to fabricate the coupons. The 3-D printed molds demonstrated excellent performance, with easy ejection of coupons and convenient cleaning and reusability. However, the melamine coupon mold proved less efficient due to being hand-manufactured and requiring the application of messy silicone for sealing. To accommodate the size limitations of the 3-D printers available to the team, the full-size mold comprises a combination of melamine and 3-D printed components. This test showed that the 3D printed mold adhered to the mold functionality working criteria. The brick tests included a compression test to determine the optimum plastic-concrete formulation and a weather resistance test to assess the brick\u27s water resistance. The compression test showed that pure Quikrete achieved a compressive strength of over 1900 psi for water ratios ranging from 7-7.5%. The team selected 7.5% water as it retained plastic particles more effectively. PET outperformed HDPE in compression tests. However, none of the coupons with plastic ratios ranging from 1 to 15 percent plastic on a mass basis, or 1.54 to 23.11 percent on a volume basis, met the 1900 psi requirement mandated by ASTM C90 [1]. The team recommends longer curing times as a way to increase compressive strength. The final phase of compression testing was anisotropic tests, which tested the bricks\u27 performance in a more consistent orientation with how full-size bricks will be loaded. The results indicated that an increase in plastic particle size resulted in an increase in compressive strength. The rough surfaces of the coupons, caused by molds designed for testing in the other orientation, led to some of the lower fatigue stresses. This test demonstrated that modifying the mold\u27s orientation could increase the compressive strength and potentially lead to a formulation that meets the 1900 psi requirement. The team recommends further research and testing on the anisotropic orientation. The weather resistance test evaluated the water absorption capacity and the formation of salt deposits as the bricks/coupons dried. All specimens underwent both tests and successfully passed. To meet the requirements of the absorption test, the bricks/coupons needed to absorb less than 20% of their original weight. The full-size ASTM C90 bricks performed better, with a range of 6-7%, compared to the coupons, which had a range of 8.8-14.9%

The Clinchfield and Unicoi County: Documenting the Oral History and Traditions of a Railroad Community

The panel will focus on the oral history and traditions of the Clinchfield from those that were there, as passengers, employees, landowners, and various other stakeholders of the railroad and Unicoi County

Analysis of the African coelacanth genome sheds light on tetrapod evolution

It was a zoological sensation when a living specimen of the coelacanth was first discovered in 1938, as this lineage of lobe-finned fish was thought to have gone extinct 70 million years ago. The modern coelacanth looks remarkably similar to many of its ancient relatives, and its evolutionary proximity to our own fish ancestors provides a glimpse of the fish that first walked on land. Here we report the genome sequence of the African coelacanth, Latimeria chalumnae. Through a phylogenomic analysis, we conclude that the lungfish, and not the coelacanth, is the closest living relative of tetrapods. Coelacanth protein-coding genes are significantly more slowly evolving than those of tetrapods, unlike other genomic features . Analyses of changes in genes and regulatory elements during the vertebrate adaptation to land highlight genes involved in immunity, nitrogen excretion and the development of fins, tail, ear, eye, brain, and olfaction. Functional assays of enhancers involved in the fin-to-limb transition and in the emergence of extra-embryonic tissues demonstrate the importance of the coelacanth genome as a blueprint for understanding tetrapod evolution

Dealing with femtorisks in international relations

The contemporary global community is increasingly interdependent and confronted with systemic risks posed by the actions and interactions of actors existing beneath the level of formal institutions, often operating outside effective governance structures. Frequently, these actors are human agents, such as rogue traders or aggressive financial innovators, terrorists, groups of dissidents, or unauthorized sources of sensitive or secret information about government or private sector activities. In other instances, influential .actors. take the form of climate change, communications technologies, or socioeconomic globalization. Although these individual forces may be small relative to state governments or international institutions, or may operate on long time scales, the changes they catalyze can pose significant challenges to the analysis and practice of international relations through the operation of complex feedbacks and interactions of individual agents and interconnected systems. We call these challenges "femtorisks," and emphasize their importance for two reasons. First, in isolation, they may be inconsequential and semiautonomous; but when embedded in complex adaptive systems, characterized by individual agents able to change, learn from experience, and pursue their own agendas, the strategic interaction between actors can propel systems down paths of increasing, even global, instability. Second, because their influence stems from complex interactions at interfaces of multiple systems (e.g., social, financial, political, technological, ecological, etc.), femtorisks challenge standard approaches to risk assessment, as higher-order consequences cascade across the boundaries of socially constructed complex systems. We argue that new approaches to assessing and managing systemic risk in international relations are required, inspired by principles of evolutionary theory and development of resilient ecological systems

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead