Configuration Flatness of Lagrangian Systems Underactuated by One Control

Lagrangian control systems that are differentially flat with flat outputs that only depend on configuration variables are said to be configuration flat. We provide a complete characterisation of configuration flatness for systems with n degrees of freedom and n - 1 controls whose range of control forces only depends on configuration and whose Lagrangian has the form of kinetic energy minus potential. The method presented allows us to determine if such a system is configuration flat and, if so provides a constructive method for finding all possible configuration flat outputs. Our characterisation relates configuration flatness to Riemannian geometry. We illustrate the method by two examples

A Test for Differential Flatness by Reduction to Single Input Systems

For nonlinear control systems (p inputs), we present a test for flatness. The method consists of making an initial guess for p-1 of the flat outputs, which may involve parameters still to be determined. A choice of functions of time for the p-1 outputs reduce the system to one with a single input. For single input systems the problem of flatness has been solved and thus leads to the identification of the last flat output, or to obstructions to flatness under the hypotheses. We demonstrate the method for a coupled rigid body in ℝ2 and for a single rigid body in ℝ3

Differential Flatness and Absolute Equivalence

In this paper we give a formulation of differential flatness---a concept originally introduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differentiable algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we shown that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are *not* equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions will be discussed. Revised 14 Aug 9

Tuna drift gillnet fishery at Chennai, Tamil Nadu- an update

The present study describes the status of multiday drift gillnet fishery for tuna from Chennai fishing harbour based on data for the years 2016 – 2017. The data is also compared with that during 1999- 2006. Both the craft and gear increased in size with consequent extension of fishing grounds and increase in the number of days/ fishing trip. The size of the boats increased to 20-23 m OAL from 11-12 m OAL and weight of the gear from 1 to more than 6 t. Annual average catch increased to 8523 t during 2016-2017 from 595 t during 1999-2006. Average catch per unit effort was 8310 kg as against 730 kg during 1999-2006. Yellowfin tuna, Thunnus albacares and Skipjack tuna, Katsuwonus pelamis were the dominant species. The stock position of skipjack tuna and yellowfin tuna vis-àvis the three indicators indicated that the percentage of mature yellowfin tuna in the catch in 2017 was 68%, fish in optimum length 35% and mega-spawners 33% whereas in skipjack tuna the respective percentages were 99.5, 21.1 and 79.1. Problems and prospects of multiday tuna drift gillnet fishery are also discussed

The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady state approximation based on the semi-classical approximation of the partial differential equation for the generating function associated with the Chemical Master Equation. Such approximation proceeds by optimising an action functional whose associated set of Euler-Lagrange (Hamilton) equations provide the most likely fluctuation path. We show that, under appropriate conditions granting time scale separation, the Hamiltonian can be re-scaled so that the set of Hamilton equations splits up into slow and fast variables, whereby the quasi-steady state approximation can be applied. We analyse two particular examples of systems whose mean-field limit has been shown to exhibit bi-stability: an enzyme-catalysed system of two mutually-inhibitory proteins and a gene regulatory circuit with self-activation. Our theory establishes that the number of molecules of the conserved species are order parameters whose variation regulates bistable behaviour in the associated systems beyond the predictions of the mean-field theory. This prediction is fully confirmed by direct numerical simulations using the stochastic simulation algorithm. This result allows us to propose strategies whereby, by varying the number of molecules of the three conserved chemical species, cell properties associated to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.Comment: 33 pages, 9 figures, accepted for publication in the Journal of Chemical Physic

Differential flatness and absolute equivalence

In this paper we give a formulation of differential flatness-a concept originally introduced by Fliess, Levine, Martin, and Rouchon (1992)-in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differential algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we show that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are not equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions are also discussed

Pathwise Sensitivity Analysis in Transient Regimes

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example

Bacterial RNA:DNA hybrids are activators of the NLRP3 inflammasome

Enterohemorrhagic Escherichia coli (EHEC) is an extracellular pathogen that causes hemorrhagic colitis and hemolytic uremic syndrome. The proinflammatory cytokine, interleukin-1beta, has been linked to hemolytic uremic syndrome. Here we identify the nucleotide-binding domain and leucine rich repeat containing family, pyrin domain containing 3 (NLRP3) inflammasome as an essential mediator of EHEC-induced IL-1beta. Whereas EHEC-specific virulence factors were dispensable for NLRP3 activation, bacterial nucleic acids such as RNA:DNA hybrids and RNA gained cytosolic access and mediated inflammasome-dependent responses. Consistent with a direct role for RNA:DNA hybrids in inflammasome activation, delivery of synthetic EHEC RNA:DNA hybrids into the cytosol triggered NLRP3-dependent responses, and introduction of RNase H, which degrades such hybrids, into infected cells specifically inhibited inflammasome activation. Notably, an E. coli rnhA mutant, which is incapable of producing RNase H and thus harbors increased levels of RNA:DNA hybrid, induced elevated levels of NLRP3-dependent caspase-1 activation and IL-1beta maturation. Collectively, these findings identify RNA:DNA hybrids of bacterial origin as a unique microbial trigger of the NLRP3 inflammasome

Chitosan but not chitin activates the inflammasome by a mechanism dependent upon phagocytosis

Chitin is an abundant polysaccharide found in fungal cell walls, crustacean shells, and insect exoskeletons. The immunological properties of both chitin and its deacetylated derivative chitosan are of relevance because of frequent natural exposure and their use in medical applications. Depending on the preparation studied and the end point measured, these compounds have been reported to induce allergic responses, inflammatory responses, or no response at all. We prepared highly purified chitosan and chitin and examined the capacity of these glycans to stimulate murine macrophages to release the inflammasome-associated cytokine IL-1beta. We found that although chitosan was a potent NLRP3 inflammasome activator, acetylation of the chitosan to chitin resulted in a near total loss of activity. The size of the chitosan particles played an important role, with small particles eliciting the greatest activity. An inverse relationship between size and stimulatory activity was demonstrated using chitosan passed through size exclusion filters as well as with chitosan-coated beads of defined size. Partial digestion of chitosan with pepsin resulted in a larger fraction of small phagocytosable particles and more potent inflammasome activity. Inhibition of phagocytosis with cytochalasin D abolished the IL-1beta stimulatory activity of chitosan, offering an explanation for why the largest particles were nearly devoid of activity. Thus, the deacetylated polysaccharide chitosan potently activates the NLRP3 inflammasome in a phagocytosis-dependent manner. In contrast, chitin is relatively inert