Order of magnitude time-reversible Markov chains and characterization of clustering processes

We introduce the notion of order of magnitude reversibility (OM-reversibility) in Markov chains that are parametrized by a positive parameter \ep. OM-reversibility is a weaker condition than reversibility, and requires only the knowledge of order of magnitude of the transition probabilities. For an irreducible, OM-reversible Markov chain on a finite state space, we prove that the stationary distribution satisfies order of magnitude detailed balance (analog of detailed balance in reversible Markov chains). The result characterizes the states with positive probability in the limit of the stationary distribution as \ep \to 0, which finds an important application in the case of singularly perturbed Markov chains that are reducible for \ep=0. We show that OM-reversibility occurs naturally in macroscopic systems, involving many interacting particles. Clustering is a common phenomenon in biological systems, in which particles or molecules aggregate at one location. We give a simple condition on the transition probabilities in an interacting particle Markov chain that characterizes clustering. We show that such clustering processes are OM-reversible, and we find explicitly the order of magnitude of the stationary distribution. Further, we show that the single pole states, in which all particles are at a single vertex, are the only states with positive probability in the limit of the stationary distribution as the rate of diffusion goes to zero.Comment: 22 pages, 3 figure

A survey of methods for deciding whether a reaction network is multistationary

Which reaction networks, when taken with mass-action kinetics, have the capacity for multiple steady states? There is no complete answer to this question, but over the last 40 years various criteria have been developed that can answer this question in certain cases. This work surveys these developments, with an emphasis on recent results that connect the capacity for multistationarity of one network to that of another. In this latter setting, we consider a network $N$ that is embedded in a larger network $G$, which means that $N$ is obtained from $G$ by removing some subsets of chemical species and reactions. This embedding relation is a significant generalization of the subnetwork relation. For arbitrary networks, it is not true that if $N$ is embedded in $G$, then the steady states of $N$ lift to $G$. Nonetheless, this does hold for certain classes of networks; one such class is that of fully open networks. This motivates the search for embedding-minimal multistationary networks: those networks which admit multiple steady states but no proper, embedded networks admit multiple steady states. We present results about such minimal networks, including several new constructions of infinite families of these networks

An SSE approach to reusability

The SSE project has engineering analysis and design efforts under way for the development of the SSE reusability library management system. An ad hoc committee on reuse has been meeting for several months identifying design considerations and learning about Ruben Prieto-Diaz faceted classification, CAMP domain analysis, SPC activities, SEI activities, and SPS activities. A standard format was developed for the Ada prologue for reusable components (both specification and body). The SSE reusability process can be viewed as a transformation process with minimized losses and difficulties

Open Vocabulary Learning on Source Code with a Graph-Structured Cache

Machine learning models that take computer program source code as input typically use Natural Language Processing (NLP) techniques. However, a major challenge is that code is written using an open, rapidly changing vocabulary due to, e.g., the coinage of new variable and method names. Reasoning over such a vocabulary is not something for which most NLP methods are designed. We introduce a Graph-Structured Cache to address this problem; this cache contains a node for each new word the model encounters with edges connecting each word to its occurrences in the code. We find that combining this graph-structured cache strategy with recent Graph-Neural-Network-based models for supervised learning on code improves the models' performance on a code completion task and a variable naming task --- with over $100\%$ relative improvement on the latter --- at the cost of a moderate increase in computation time.Comment: Published in the International Conference on Machine Learning (ICML 2019), 13 page

Dimensions and Determinants of Peoples’ Participation in Watershed Development Programmes in Rajasthan

Peoples’ participation has been at the centre-stage of the resource conservation and rural development efforts in the developing countries. The study on peoples’ participation in watershed development programmes in Rajasthan has revealed that a very low proportion of beneficiaries is contributing at different stages of the programme in terms of either labour or finances or both. The determinants of participation have been identified using Tobit regression. The institutional effectiveness has been found as the key factor towards guaranteeing involvement of people in the watershed programmes. The other factors positively related with peoples’ participation are training of farmers, age, and frequency of the visit of extension workers. A negative relationship has been found between participation and off-farm income. Therefore, efforts should be made for developing effective local institutions, capacity building through training of farmers and providing off-farm employment opportunities in the countryside itself for safeguarding the livelihoods of people in the rainfed areas.Agricultural and Food Policy,

La Fusta. Patrimoni cultural i biològic

Wood: biological and cultural heritage. Anthracology is a branch of archaeobotany that came into being at the beginning of the 20th Century for the botanical identification of prehistoric wood and carbon. The goals are paleoecological, ethnological and methodological. The protocol followed for this analysis involves the observation of plant tissues under reflected-light microscopy and scanning electron microscopy to identify the material botanically. In recent years, this kind of analysis is being applied to heritage objects and those in restoration; here we will give some examples: an historic object, the restoration of a monument and the reconstruction of a prehistoric landscape