Intensity-based axial localization at the quantum limit

We derive fundamental precision bounds for single-point axial localization. For Gaussian beams, this ultimate limit can be achieved with a single intensity scan, provided the camera is placed at one of two optimal transverse detection planes. Hence, for axial localization there is no need of more complicated detection schemes. The theory is verified with an experimental demonstration of axial resolution 3 orders of magnitude below the classical depth of focus

Means and method of detection in chemical separation procedures

A means and method for indirect detection of constituent components of a mixture separated in a chemical separation process. Fluorescing ions are distributed across the area in which separation of the mixture will occur to provide a generally uniform background fluorescence intensity. For example, the mixture is comprised of one or more charged analytes which displace fluorescing ions where its constituent components separate to. Fluorescing ions of the same charge as the charged analyte components cause a displacement. The displacement results in the location of the separated components having a reduced fluorescence intensity to the remainder of the background. Detection of the lower fluorescence intensity areas can be visually, by photographic means and methods, or by automated laser scanning

Enhancing axial localization with wavefront control

Enhancing the ability to resolve axial details is crucial in three-dimensional optical imaging. We provide experimental evidence showcasing the ultimate precision achievable in axial localization using vortex beams. For Laguerre-Gauss (LG) beams, this remarkable limit can be attained with just a single intensity scan. This proof-of-principle demonstrates that microscopy techniques based on LG vortex beams can potentially benefit from the introduced quantum-inspired superresolution protocol.Comment: 10 pages, 6 figures. Comments welcom

Qualitative modelling and analysis of regulations in multi-cellular systems using Petri nets and topological collections

In this paper, we aim at modelling and analyzing the regulation processes in multi-cellular biological systems, in particular tissues. The modelling framework is based on interconnected logical regulatory networks a la Rene Thomas equipped with information about their spatial relationships. The semantics of such models is expressed through colored Petri nets to implement regulation rules, combined with topological collections to implement the spatial information. Some constraints are put on the the representation of spatial information in order to preserve the possibility of an enumerative and exhaustive state space exploration. This paper presents the modelling framework, its semantics, as well as a prototype implementation that allowed preliminary experimentation on some applications.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Lumpability Abstractions of Rule-based Systems

The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Compositional Development in the Event of Interface Difference

We present here an implementation relation which allows compositional development of a network of communicating processes, in the event that corresponding specification and implementation components have different interfaces. This relation enjoys two basic properties which are fundamental to its success. It is compositional, in the sense that a target composed of several connected systems may be implemented by connecting their respective implementations. In addition, an implementation, when plugged into an appropriate environment, is to all intents and purposes a conventional implementation of the target. We illustrate our approach by outlining the development of a fault-tolerant system based on co-ordinated atomic actions (CA actions). As a formal framework of concurrent computation, we use the model of Communicating Sequential Processes (CSP)