Analysis of parametric biological models with non-linear dynamics

In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to two case studies of biological systems: one is a cardiac cell model for studying the conditions for cardiac abnormalities, and the second is a model of insect nest-site choice.Comment: In Proceedings HSB 2012, arXiv:1208.315

EPICOG-SCH: A brief battery to screen cognitive impact of schizophrenia in stable outpatients

Brief batteries in schizophrenia, are needed to screen for the cognitive impact of schizophrenia. We aimed to validate and co-norm the Epidemiological Study of Cognitive Impairment in Schizophrenia (EPICOG-SCH) derived brief cognitive battery. A cross-sectional outpatient evaluation was conducted of six-hundred-seventy-two patients recruited from 234 centers. The brief battery included well-known subtests available worldwide that cover cognitive domains related to functional outcomes: WAIS-III-Letter-Number-Sequencing-LNS, Category Fluency Test-CFT, Logical-Memory Immediate Recall-LM, and Digit-Symbol-Coding-DSC. CGI-SCH Severity and WHO-DAS-S were used to assess clinical severity and functional impairment, respectively. Unit Composite Score (UCS) and functional regression-weighted Composite Scores (FWCS) were obtained; discriminant properties of FWCS to identify patients with different levels of functional disability were analyzed using receiver-operating characteristic (ROC) technique. The battery showed good internal consistency, Cronbach's alpha = 0.78. The differences between cognitive performance across CGI-SCH severity level subscales ranged from 0.5 to 1 SD. Discriminant capacity of the battery in identifying patients with up to moderate disability levels showed fair discriminant accuracy with areas under the curve (AUC) > 0.70, p < 0.0001. An FWCS mean cut-off score ≥ 100 showed likelihood ratios (LR) up to 4.7, with an LR+ of 2.3 and a LR− of 0.5. An FWCS cut-off ≥ 96 provided the best balance between sensitivity (0.74) and specificity (0.62). The EPICOG-SCH proved to be a useful brief tool to screen for the cognitive impact of schizophrenia, and its regression-weighted Composite Score was an efficient complement to clinical interviews for confirming patients' potential functional outcomes and can be useful for monitoring cognition during routine outpatient follow-up visits

Thin-film flow in helically wound rectangular channels with small torsion

Laminar gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section with small torsion in which the fluid depth is small is considered. Neglecting the entrance and exit regions we obtain the steady-state solution that is independent of position along the axis of the channel, so that the flow, which comprises a primary flow in the direction of the axis of the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity and pressure in terms of the free-surface shape, the latter satisfying a non-linear ordinary differential equation that has a simple exact solution in the special case of a channel of rectangular cross-section. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier–Stokes equations. The present work has particular relevance to spiral particle separators used in the mineral-processing industry. The validity of an assumption commonly used in modelling flow in spiral separators, namely that the flow in the outer region of the separator cross-section is described by a free vortex, is shown to depend on the problem parameters

Partnership, ownership and control: the impact of corporate governance on employment relations

Prevailing patterns of dispersed share ownership and rules of corporate governance for UK listed companies appear to constrain the ability of managers to make credible, long-term commitments to employees of the kind needed to foster effective labour-management partnerships. We present case study evidence which suggests that such partnerships can nevertheless emerge where product market conditions and the regulatory environment favour a stakeholder orientation. Proactive and mature partnerships may also be sustained where the board takes a strategic approach to mediating between the claims of different stakeholder groups, institutional investors are prepared to take a long-term view of their holdings, and strong and independent trade unions are in a position to facilitate organisational change

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

Ecology under lake ice

Winter conditions are rapidly changing in temperate ecosystems, particularly for those that experience periods of snow and ice cover. Relatively little is known of winter ecology in these systems, due to a historical research focus on summer ‘growing seasons’. We executed the first global quantitative synthesis on under‐ice lake ecology, including 36 abiotic and biotic variables from 42 research groups and 101 lakes, examining seasonal differences and connections as well as how seasonal differences vary with geophysical factors. Plankton were more abundant under ice than expected; mean winter values were 43.2% of summer values for chlorophyll a, 15.8% of summer phytoplankton biovolume and 25.3% of summer zooplankton density. Dissolved nitrogen concentrations were typically higher during winter, and these differences were exaggerated in smaller lakes. Lake size also influenced winter‐summer patterns for dissolved organic carbon (DOC), with higher winter DOC in smaller lakes. At coarse levels of taxonomic aggregation, phytoplankton and zooplankton community composition showed few systematic differences between seasons, although literature suggests that seasonal differences are frequently lake‐specific, species‐specific, or occur at the level of functional group. Within the subset of lakes that had longer time series, winter influenced the subsequent summer for some nutrient variables and zooplankton biomass

Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity

The strong existence and the pathwise uniqueness of solutions with (Formula presented.) -vorticity of the 2D stochastic Euler equations are proved. The noise is multiplicative and it involves the first derivatives. A Lagrangian approach is implemented, where a stochastic flow solving a nonlinear flow equation is constructed. The stability under regularizations is also proved

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)