Probabilistic event structures and domains

AbstractThis paper studies how to adjoin probability to event structures, leading to the model of probabilistic event structures. In their simplest form, probabilistic choice is localised to cells, where conflict arises; in which case probabilistic independence coincides with causal independence. An event structure is associated with a domain—that of its configurations ordered by inclusion. In domain theory, probabilistic processes are denoted by continuous valuations on a domain. A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion-free event structure correspond to the probabilistic event structures it supports. We explore how to extend probability to event structures which are not confusion-free via two notions of probabilistic runs of a general event structure. Finally, we show how probabilistic correlation and probabilistic event structures with confusion can arise from event structures which are originally confusion-free by using morphisms to rename and hide events

Semantic Domains for Combining Probability and Non-Determinism

AbstractWe present domain-theoretic models that support both probabilistic and nondeterministic choice. In [A. McIver and C. Morgan. Partial correctness for probablistic demonic programs. Theoretical Computer Science, 266:513–541, 2001], Morgan and McIver developed an ad hoc semantics for a simple imperative language with both probabilistic and nondeterministic choice operators over a discrete state space, using domain-theoretic tools. We present a model also using domain theory in the sense of D.S. Scott (see e.g. [G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove, and D. S. Scott. Continuous Lattices and Domains, volume 93 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 2003]), but built over quite general continuous domains instead of discrete state spaces.Our construction combines the well-known domains modelling nondeterminism – the lower, upper and convex powerdomains, with the probabilistic powerdomain of Jones and Plotkin [C. Jones and G. Plotkin. A probabilistic powerdomain of evaluations. In Proceedings of the Fourth Annual Symposium on Logic in Computer Science, pages 186–195. IEEE Computer Society Press, 1989] modelling probabilistic choice. The results are variants of the upper, lower and convex powerdomains over the probabilistic powerdomain (see Chapter 4). In order to prove the desired universal equational properties of these combined powerdomains, we develop sandwich and separation theorems of Hahn-Banach type for Scott-continuous linear, sub- and superlinear functionals on continuous directed complete partially ordered cones, endowed with their Scott topologies, in analogy to the corresponding theorems for topological vector spaces in functional analysis (see Chapter 3). In the end, we show that our semantic domains work well for the language used by Morgan and McIver

Measure, Randomness and Sublocales

This paper investigates aspects of measure and randomness in the context of locale theory (point-free topology). We prove that every measure (σ-continuous valuation) µ, on the σ-frame of opens of a fitted σ-locale X, extends to a measure on the lattice of all σ-sublocales of X (Theorem 1). Furthermore, when µ is a finite measure with µ(X) = M, the σ-locale X has a smallest σ-sublocale of measure M (Theorem 2). In particular, when µ is a probability measure, X has a smallest σ-sublocale of measure 1. All σ prefixes can be dropped from these statements whenever X is a strongly Lindelöf locale, as is the case in the following applications. When µ is Lebesgue measure on Euclidean space R n, Theorem 1 produces a isometry-invariant measure that, via the inclusion of the powerset P(R n) in the lattice of sublocales, assigns a weight to every subset of R n. (Contradiction is avoided because disjoint subsets need not be disjoint as sublocales.) When µ is the uniform probability measure on Cantor space {0, 1} ω, the smallest measure-1 sublocale, given by Theorem 2, provides a canonical locale of random sequences, where randomness means that all probabilistic laws (measure-1 properties) are satisfied. 1

Secretion of Novel SEL1L Endogenous Variants Is Promoted by ER Stress/UPR via Endosomes and Shed Vesicles in Human Cancer Cells

We describe here two novel endogenous variants of the human endoplasmic reticulum (ER) cargo receptor SEL1LA, designated p38 and p28. Biochemical and RNA interference studies in tumorigenic and non-tumorigenic cells indicate that p38 and p28 are N-terminal, ER-anchorless and more stable relative to the canonical transmembrane SEL1LA. P38 is expressed and constitutively secreted, with increase after ER stress, in the KMS11 myeloma line and in the breast cancer lines MCF7 and SKBr3, but not in the non-tumorigenic breast epithelial MCF10A line. P28 is detected only in the poorly differentiated SKBr3 cell line, where it is secreted after ER stress. Consistently with the presence of p38 and p28 in culture media, morphological studies of SKBr3 and KMS11 cells detect N-terminal SEL1L immunolabeling in secretory/degradative compartments and extracellularly-released membrane vesicles. Our findings suggest that the two new SEL1L variants are engaged in endosomal trafficking and secretion via vesicles, which could contribute to relieve ER stress in tumorigenic cells. P38 and p28 could therefore be relevant as diagnostic markers and/or therapeutic targets in cancer

Glycan labeling strategies and their use in identification and quantification

Most methods for the analysis of oligosaccharides from biological sources require a glycan derivatization step: glycans may be derivatized to introduce a chromophore or fluorophore, facilitating detection after chromatographic or electrophoretic separation. Derivatization can also be applied to link charged or hydrophobic groups at the reducing end to enhance glycan separation and mass-spectrometric detection. Moreover, derivatization steps such as permethylation aim at stabilizing sialic acid residues, enhancing mass-spectrometric sensitivity, and supporting detailed structural characterization by (tandem) mass spectrometry. Finally, many glycan labels serve as a linker for oligosaccharide attachment to surfaces or carrier proteins, thereby allowing interaction studies with carbohydrate-binding proteins. In this review, various aspects of glycan labeling, separation, and detection strategies are discussed

Measure theoretic results for continuous valuations on partially ordered spaces

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