Multistability,bifurcations, and biological neural networks: A synaptic drive firing model for cerebral cortex transition in the induction of general anesthesia

This paper focuses on multistability theory for discontinuous dynamical systems having a set of multiple isolated equilibria and/or a continuum of equilibria. Multistability is the property whereby the solutions of a dynamical system can alternate between two or more mutually exclusive Lyapunov stable and convergent equilibrium states under asymptotically slowly changing inputs or system parameters. In this paper, we extend the definition and theory of multistability to discontinuous autonomous dynamical systems. In particular, nontangency Lyapunov-based tests for multistability of discontinuous systems with Filippov and Carathéodory solutions are established. The results are then applied to excitatory and inhibitory biological neuronal networks to explain the underlying mechanism of action for anesthesia and consciousness from a multistable dynamical system perspective, thereby providing a theoretical foundation for general anesthesia using the network properties of the brain.     

Global stability of a two-species piecewise linear volterra ecosystem

This paper extends the results of Goh [1], and Takeuchi and Adachi [2,3] concerning the generalized linear Volterra model. We introduce a piecewise linear Volterra model for a two- species system. The solution of the steady-state problem is then shown to be equivalent to finding the solution to the Generalized Linear Complementarity Problem. We show when this nonnegative equilibrium is unique and globally asymptotically stable in the sense of Goh [1].     

Disjunctive cuts for continuous linear bilevel programming

This work shows how disjunctive cuts can be generated for a bilevel linear programming problem (BLP) with continuous variables. First, a brief summary on disjunctive programming and bilevel programming is presented. Then duality theory is used to reformulate BLP as a disjunctive program and, from there, disjunctive programming results are applied to derive valid cuts. These cuts tighten the domain of the linear relaxation of BLP. An example is given to illustrate this idea, and a discussion follows on how these cuts may be incorporated in an algorithm for solving BLP.     

Impulse capture basins of sets under impulse control systems

Given a target contained in a constrained set and an impulse control system governing the evolutions of runs or executions, that are hybrids of continuous and discrete evolutions, this paper studies and provides several characterizations of the capture basin of the target viable in the constrained set. It is the subset of initial runs from which start at least one run viable in the constrained set until it reaches the target in finite time. It also provides algorithms and regulation rules governing the runs that reach the targets while obeying state constraints.     

A Nitrite Electrochemical Sensor Based on Boron‐Doped Diamond Planar Electrochemical Microcells Modified with a Monolacunary Silicotungstate Polyoxoanion

A new boron doped diamond microcells (BDD) was modified, for rapid, selective and highly sensitive determination of nitrite, using a coating film of polyoxometalates (POMs), formed by cyclic voltammetry on the molecular p‐phenylenediamine (PPD) functionalized BDD. The scanning electron microscopy (SEM) technique was used to examine the morphology of (PPD/SiW₁₁) modified (BDD) electrode. It was found that (SiW₁₁) layer was uniformly formed on the electrode surface. It was observed that (BDD/PPD/SiW₁₁) showed excellent electrocatalytic activities towards nitrite ion. Under the selected conditions, the anodic peak maximum at ?0.6 V was linear versus nitrite concentration in the 40 µM–4 mM range, and the detection limit obtained was 20 µM. The newly developed electrode has been successfully applied to the determination of nitrite content in real river water samples.     

Crystal supramolecularity in 2,2′-iminodipyridinium tetrahalometallate(II) salts: Supramolecular motifs that control tetrahedral halometallate solid state structures

N⁺–H$?$Br–M and (π)C–H$?$Br–M hydrogen bond synthons have been exploited in the crystallization of a series of 2,2′-iminodipyridinium(2+) dication (hereafter 2,2′-imdipyH₂), (C₁₀H₁₁N₃)[MX₄] salts (M = Co and Hg; X = Cl and Br) and 2,2′-iminodipyridinium(1+) cation (hereafter 2,2′-imdipyH), (C₁₀H₁₀N₃)₂[MX₄] salts (M = Co, Hg; X = Cl and Br). Intermolecular interactions and crystal supramolecularity adopted in these structures were analyzed and compared with reported similar structures, (C₁₀H₁₁N₃)[CuCl₄] and (C₁₀H₁₀N₃)₂[CoCl₄]. In these salts only one structural form for the halometallate species is observed namely mononuclear tetrahedral. The crystal supramolecularity in the (2,2′-imdipyH₂)[MX₄] series corresponds to three distinct structural motifs: Parallel ribbons of infinitely connected cyclic dimers of two dications and two anions found in the isomorphous salts of [CoCl₄]^2? and [CuCl₄]^2?; and cyclic dimer hearing-bone packing motif found in the isomorphous dication salts of [CoBr₄]^2? and [HgBr₄]^2?. Infinitely helical layers based on alternating $?$anion$?$two stacked cations $?$anion$?$ two stacked cations$?$ are found in the isomorphous salts of (2,2′-imdipyH)₂[CoCl₄] and (2,2′-imdipyH)₂[HgBr₄].     

Zwitterionic-type hydrophilic interaction nano-liquid chromatography of complex and high mannose glycans coupled with electrospray ionisation high resolution time of flight mass spectrometry

In this study we describe a new method for rapid and sensitive analysis of reduced high mannose and complex glycans using zwitterionic-type hydrophilic interaction nano-liquid chromatography (nano ZIC-HILIC, 75 μm I.D.×150 mm) coupled with high resolution nanoelectrospray ionisation time of flight mass spectrometry (nano ESI-TOF-MS). The retention of neutral glycans increases with increasing molecular weight and is higher for high mannose glycans than for complex-type glycans. The selectivity of ZIC-HILIC for sialylated glycans differs from that for the neutral glycans and is believed to involve electrostatic repulsion; therefore, charged glycans are eluted earlier than neutral glycans with comparable molecular weight. Due to the improved sensitivity achieved by employing a ZIC-HILIC nano-column, a range of less common complex glycans has been studied and the high resolution mass spectrometry enabled confirmation of glycan composition for the proposed structures. Good sensitivity for glycans was achieved without prior fluorescent labelling, and the time of the analysis was significantly reduced compared to the separation of glycans on a conventional-size column. The proposed method offers a fast and sensitive approach for glycan profiling applied to analysis of biopharmaceuticals.