Model Checking Tap Withdrawal in C. Elegans

We present what we believe to be the first formal verification of a biologically realistic (nonlinear ODE) model of a neural circuit in a multicellular organism: Tap Withdrawal (TW) in \emph{C. Elegans}, the common roundworm. TW is a reflexive behavior exhibited by \emph{C. Elegans} in response to vibrating the surface on which it is moving; the neural circuit underlying this response is the subject of this investigation. Specifically, we perform reachability analysis on the TW circuit model of Wicks et al. (1996), which enables us to estimate key circuit parameters. Underlying our approach is the use of Fan and Mitra's recently developed technique for automatically computing local discrepancy (convergence and divergence rates) of general nonlinear systems. We show that the results we obtain are in agreement with the experimental results of Wicks et al. (1995). As opposed to the fixed parameters found in most biological models, which can only produce the predominant behavior, our techniques characterize ranges of parameters that produce (and do not produce) all three observed behaviors: reversal of movement, acceleration, and lack of response

Approximate probabilistic verification of hybrid systems

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability $1$. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximately- that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings

Multi-membership gene regulation in pathway based microarray analysis

This article is available through the Brunel Open Access Publishing Fund. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Gene expression analysis has been intensively researched for more than a decade. Recently, there has been elevated interest in the integration of microarray data analysis with other types of biological knowledge in a holistic analytical approach. We propose a methodology that can be facilitated for pathway based microarray data analysis, based on the observation that a substantial proportion of genes present in biochemical pathway databases are members of a number of distinct pathways. Our methodology aims towards establishing the state of individual pathways, by identifying those truly affected by the experimental conditions based on the behaviour of such genes. For that purpose it considers all the pathways in which a gene participates and the general census of gene expression per pathway. Results: We utilise hill climbing, simulated annealing and a genetic algorithm to analyse the consistency of the produced results, through the application of fuzzy adjusted rand indexes and hamming distance. All algorithms produce highly consistent genes to pathways allocations, revealing the contribution of genes to pathway functionality, in agreement with current pathway state visualisation techniques, with the simulated annealing search proving slightly superior in terms of efficiency. Conclusions: We show that the expression values of genes, which are members of a number of biochemical pathways or modules, are the net effect of the contribution of each gene to these biochemical processes. We show that by manipulating the pathway and module contribution of such genes to follow underlying trends we can interpret microarray results centred on the behaviour of these genes.The work was sponsored by the studentship scheme of the School of Information Systems, Computing and Mathematics, Brunel Universit

Amino-acid PET versus MRI guided re-irradiation in patients with recurrent glioblastoma multiforme (GLIAA) – protocol of a randomized phase II trial (NOA 10/ARO 2013-1)

Background: The higher specificity of amino-acid positron emission tomography (AA-PET) in the diagnosis of gliomas, as well as in the differentiation between recurrence and treatment-related alterations, in comparison to contrast enhancement in T1-weighted MRI was demonstrated in many studies and is the rationale for their implementation into radiation oncology treatment planning. Several clinical trials have demonstrated the significant differences between AA-PET and standard MRI concerning the definition of the gross tumor volume (GTV). A small single-center non-randomized prospective study in patients with recurrent high grade gliomas treated with stereotactic fractionated radiotherapy (SFRT) showed a significant improvement in survival when AA-PET was integrated in target volume delineation, in comparison to patients treated based on CT/MRI alone. Methods: This protocol describes a prospective, open label, randomized, multi-center phase II trial designed to test if radiotherapy target volume delineation based on FET-PET leads to improvement in progression free survival (PFS) in patients with recurrent glioblastoma (GBM) treated with re-irradiation, compared to target volume delineation based on T1Gd-MRI. The target sample size is 200 randomized patients with a 1:1 allocation ratio to both arms. The primary endpoint (PFS) is determined by serial MRI scans, supplemented by AA-PET-scans and/or biopsy/surgery if suspicious of progression. Secondary endpoints include overall survival (OS), locally controlled survival (time to local progression or death), volumetric assessment of GTV delineated by either method, topography of progression in relation to MRIor PET-derived target volumes, rate of long term survivors (> 1 year), localization of necrosis after re-irradiation, quality of life (QoL) assessed by the EORTC QLQ-C15 PAL questionnaire, evaluation of safety of FET-application in AA-PET imaging and toxicity of re-irradiation. Discussion: This is a protocol of a randomized phase II trial designed to test a new strategy of radiotherapy target volume delineation for improving the outcome of patients with recurrent GBM. Moreover, the trial will help to develop a standardized methodology for the integration of AA-PET and other imaging biomarkers in radiation treatment planning. Trial registration: The GLIAA trial is registered with ClinicalTrials.gov (NCT01252459, registration date 02.12.2010), German Clinical Trials Registry (DRKS00000634, registration date 10.10.2014), and European Clinical Trials Database (EudraCT-No. 2012-001121-27, registration date 27.02.2012)

Electron-fluctuation interaction in a non-Fermi superconductor

We studied the influence of the amplitude fluctuations of a non-Fermi superconductor on the energy spectrum of the 2D Anderson non-Fermi system. The classical fluctuations give a temperature dependence in the pseudogap induced in the fermionic excitations.Comment: revtex fil

Dynamics of immigrant entrepreneurship in Romania

Immigrant entrepreneurship may represent a means for diminishing the negative effects specific to the migration phenomenon and for emphasising the positive ones, contributing to the development of strong regions. The present paper outlines a series of information gathered through an ongoing complex and comprehensive research on immigrant entrepreneurship in Romania, approached from economic, social, institutional, and cultural perspectives. The major aim of the research is to provide a wide image on the investigated phenomenon in order to raise awareness among policymakers of its importance and complexity. The paper puts forward a series of empirical results obtained through the development of an econometrical analysis of statistical data and interview-based research. Results highlight a strong positive correlation between the number of enterprises (total and newly registered) and the number of immigrants in Romania. In this context, the hypothesis of the existence of another variable - especially related to the socio-economic and legislative environments - with an impact on both the number of enterprises and the one of immigrants may arise. Furthermore, in-depth explanations are provided by the carried out interviews. Debated issues refer to motivations, incentives, and obstacles in business development, cultural and social norms, commercial infrastructure, regulatory aspects, etc

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe