Chains of infinite order, chains with memory of variable length, and maps of the interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we caracterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval

Post-Partum Pituitary Insufficiency and Livedo Reticularis Presenting a Diagnostic Challenge in a Resource Limited Setting in Tanzania: A Case Report, Clinical Discussion and Brief Review of Existing Literature.

Pituitary disorders following pregnancy are an important yet under reported clinical entity in the developing world. Conversely, post partum panhypopituitarism has a more devastating impact on women in such settings due to high fertility rates, poor obstetric care and scarcity of diagnostic and therapeutic resources available. A 37 year old African female presented ten years post partum with features of multiple endocrine deficiencies including hypothyroidism, hypoadrenalism, lactation failure and secondary amenorrhea. In addition she had clinical features of an underlying autoimmune condition. These included a history of post-partum thyroiditis, alopecia areata, livedo reticularis and deranged coagulation indices. A remarkable clinical response followed appropriate hormone replacement therapy including steroids. This constellation has never been reported before; we therefore present an interesting clinical discussion including a brief review of existing literature. Post partum pituitary insufficiency is an under-reported condition of immense clinical importance especially in the developing world. A high clinical index of suspicion is vital to ensure an early and correct diagnosis which will have a direct bearing on management and patient outcome

Variable Length Markov Chains, Persistent Random Walks: a close encounter

Book chapterThis is the story of the encounter between two worlds: the world of random walks and the world of Variable Length Markov Chains (VLMC). The meeting point turns around the semi-Markov property of underlying processes

Some multivariate risk indicators ; minimization by using a Kiefer-Wolfowitz approach to the mirror stochastic algorithm. submitted

Abstract. We consider some risk indicators of vectorial risk processes. These indicators take into account the dependencies between business lines as well as some temporal dependencies. By using stochastic algorithms, we may estimate the minimum of these risk indicators, under a fixed total capital constraint. This minimization may apply to optimal reserve allocation

RISK INDICATORS WITH SEVERAL LINES OF BUSINESS: COMPARISON, ASYMPTOTIC BEHAVIOR AND APPLICATIONS TO OPTIMAL RESERVE ALLOCATION

Abstract. In a multi-dimensional risk model with dependent lines of business, we propose to allocate capital with respect to the minimization of some risk indicators. These indicators are sums of expected penalties due to the insolvency of a branch while the global reserve is either positive or negative. Explicit formulas in the case of two branches are obtained for several models (independent exponential, correlated Pareto). The asymptotic behavior (as the initial capital goes to infinity) is studied. For higher dimension and several periods, no explicit expression is available. Using a stochastic algorithm, we get estimations of the allocation, compare the different allocations and study the impact of dependence

Unravelling redox processes of Li 7 MnN 4 upon electrochemical Li extraction–insertion using operando XAS

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