Classifying Invariant Structures of Step Traces

In the study of behaviours of concurrent systems, traces are sets of behaviourally equivalent action sequences. Traces can be represented by causal partial orders. Step traces, on the other hand, are sets of behaviourally equivalent step sequences, each step being a set of simultaneous actions. Step traces can be represented by relational structures comprising non-simultaneity and weak causality. In this paper, we propose a classification of step alphabets as well as the corresponding step traces and relational structures representing them. We also explain how the original trace model fits into the overall framework.Algorithms and the Foundations of Software technolog

Relational structures for concurrent behaviours

\ua9 2020 The Author(s). Relational structures based on acyclic relations can successfully model fundamental aspects of concurrent systems behaviour. Examples include Elementary Net systems and Mazurkiewicz traces. There are however cases where more general relational structures are needed. In this paper, we present a general model of relational structures which can be used for a broad class of concurrent behaviours. We demonstrate how this general set-up works for combined order structures which are based on two relations, viz. an acyclic ‘before’ relation and a possibly cyclic ‘not later than’ relation

Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functions

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain assumptions. It is shown that the limit superior of the risk for p asymptotically small has a minimum over all (possibly randomized) estimators. This minimum is achieved by certain non-randomized estimators. The model includes commonly used quality criteria as particular cases. Applications to the non-asymptotic regime are discussed considering specific loss functions, for which minimax estimators are derived.Comment: Journal of Statistical Planning and Inference. Published online 201

A Precise Characterisation of Step Traces and Their Concurrent Histories

Step traces are an extension of Mazurkiewicz traces where each equivalence class (trace) consists of sequences of steps instead of sequences of atomic actions. Relations between the actions of the system are defined statically, as parameters of a concurrent step alphabet. By allowing only some of the possible relationships between actions, subclasses of step alphabets can be derived in a natural way. Properties of these classes can then be investigated in terms of invariant structures, i.e., the relational structures that represent the causal invariants that underlie the corresponding step traces. In this paper, we refine an earlier classification of subclasses of step alphabets and add eight new subclasses to this hierarchy. We divide these eight classes into three families on basis of the absence of a specific behavioural relation and then characterise the corresponding invariant structures

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hat pp$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p$ tends to $0$, and which guarantee that, for any $p$ in $(0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $r$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $r$ tends to infinity when $a=b$.Comment: 4 figure

Paradoxical regulation of Bcl-2 family proteins by 17β-oestradiol in human breast cancer cells MCF-7

Tumorigenesis is related to the dysregulation of cell growth or cell death pathways. Hence, elucidation of the mechanisms involved in the modulation of pro- or anti-apoptotic proteins is important in furthering understanding of breast cancer aetiology and may aid in designing prevention and treatment strategies. In the present study, we examined the role of 17β-oestradiol on the regulation of apoptosis in the breast cancer cell line MCF-7. Using multi-probe RNAase protection assays, we found changes in the mRNA levels of several Bcl-2 family proteins upon treatment of MCF-7 cells with 17β-oestradiol. Unexpectedly, we found a paradoxical effects of 17β-oestradiol on two anti-apoptotic proteins Bcl-2 and Bcl-x. Treatment with 17β-oestradiol resulted in up-regulation of Bcl-2 mRNA and protein, but down-regulated Bcl-x(L) mRNA and protein. The effect of 17β-oestradiol on Bcl-x(L) occurred at concentration-dependent fashion. The effect was specific to 17β-oestradiol since other steroid hormones exert no effect on Bcl-x(L). Tamoxifen, an anti-oestrogen, blocked the down-regulation of Bcl-x(L) by 17β-oestradiol demonstrating this effect is oestrogen receptor-dependent. We speculate that different members of the Bcl-2 family proteins may be regulated through different pathway and these pathways may be modulated by 17β-oestradiol. © 1999 Cancer Research Campaig