Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems

A family of polynomial differential systems describing the behavior of a chemical reaction network with generalized mass action kinetics is investigated. The coefficients and monomials are given by graphs. The aim of this investigation is to clarify the algebraic-discrete aspects of a Hopf bifurcation in these special differential equations. We apply concepts from toric geometry and convex geometry. As usual in stoichiometric network analysis we consider the solution set as a convex polyhedral cone and we intersect it with the deformed toric variety of the monomials. Using Gröbner bases the polynomial entries of the Jacobian are expressed in different coordinate systems. Then the Hurwitz criterion is applied in order to determine parameter regions where a Hopf bifurcation occurs. Examples from chemistry illustrate the theoretical results.     

Neural dynamics, bifurcations, and firing rates in a quadratic integrate-and-fire model with a recovery variable. I: Deterministic behavior

We study the dynamics of a quadratic integrate-and-fire model of a single-compartment neuron with a slow recovery variable, as input current and parameters describing timescales, recovery variable, and postspike reset change. Analysis of a codimension 2 bifurcation reveals that the domain of attraction of a stable hyperpolarized rest state interacts subtly with reset parameters, which reposition the system state after spiking. We obtain explicit approximations of instantaneous firing rates for fixed values of the recovery variable, and use the averaging theorem to obtain asymptotic firing rates as a function of current and reset parameters. Along with the different phase-plane geometries, these computations provide explicit tools for the interpretation of different spiking patterns and guide parameter selection in modeling different cortical cell types.     

Divergence,Hopf and double-zero bifurcations of a nonlinear planar beam

The multiple scale method is directly applied to a one-dimensional continuous model to derive the equations governing the system asymptotic dynamic around a bifurcation point. The theory is illustrated with reference to a specific example, namely an internally constrained planar beam, equipped with a lumped visco-elastic device and loaded by a follower force. Nonlinear, integro-differential equations of motion are derived and expanded upto cubic terms in the transversal displacements and velocities of the beam. The linear stability of the trivial equilibrium is first studied. It reveals the existence of divergence and Hopf and double-zero bifurcations. The spectral properties of the linear operator are studied at the bifurcation points by obtaining closed-form expressions. Notably, the system posses an incomplete system of eigenvectors at the double-zero point (i.e. it is defective or nilpotent), thus entailing the need to find a generalized eigenvector. A multiple-scale analysis is then performed for the three bifurcations and the relevant bifurcation equations are derived directly in their normal forms. Finally, they are numerically studied to furnish a comprehensive scenario of the postcritical behaviour around the bifurcations.     

Local bifurcations and feasibility regions indifferential-algebraic systems

The dynamics of a large class of physical systems such as the general power system can be represented by parameter-dependent differential-algebraic models of the form x˙=f and 0=g. Typically, such constrained models have singularities. This paper analyzes the generic local bifurcations including those which are directly related to the singularity. The notion of a feasibility region is introduced and analyzed. It consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability. It is shown that generically loss of stability at the feasibility boundary is caused by one of three different local bifurcations, namely the saddle-node and Hopf bifurcations and a new bifurcation called the singularity induced bifurcation which is analyzed precisely here for the first time. The latter results when an equilibrium point is at the singular surface. Under certain transversality conditions, the change in the eigenstructure of the system Jacobian at the equilibrium is established and the local dynamical structure of the trajectories near this bifurcation point is analyzed     

Multiple states, topology and bifurcations of natural convection in a cubical cavity

A numerical investigation has been conducted to explore the steady nonlinear low Prandtl number flow/thermal transition in a differentially heated cubic cavity. For small values of Rayleigh number (Ra), it is observed that initially there was only one symmetric steady-state solution. When the Ra was amplified, the system bifurcates from one fixed-point solution to the two stationary solutions, namely, Mode I and Mode II pitchfork bifurcations. This is due to the symmetric nature existing along the vertical and diagonal planes. The flow structure in the present nonlinear system consists of a pair of asymmetric counter-rotating helical cells in a double helix structure, foliated with invariant helically symmetric surfaces containing the fibre-like fluid particle orbits. Also the evolution of different symmetry-breaking orientations on the transverse and diagonal planes of the cavity was noticed. In the Mode I orientation a symmetric vortex coreline was observed. However, in the Mode II orientation a pair of anti-symmetric vortex corelines was observed. Detailed topological study was made based on the rule of Hunt and the structural stability criteria. Also the simulated results were corroborated with numerical evidence. The existence of the critical Ra values was ascertained with the aid of the predicted L₂-error norms, thermal/flow iso-contours and streamlines. The route of Mode I orientation was made of the alternate symmetric and asymmetric flows as Ra was augmented.     

Local and global bifurcations in simple Takagi-Sugeno fuzzy systems

The relevance of bifurcation analysis in Takagi-Sugeno (T-S) fuzzy systems is emphasized mainly through examples. It is demonstrated that even the most simple cases can show a great variety of behaviors. To understand the richness of asymptotic dynamics one can find in T-S systems, a methodology is proposed by invoking bifurcation theory. Several local and global bifurcations (some of them, degenerate) are detected and summarized in the corresponding bifurcation diagrams. It is claimed,that this kind of careful analysis could help to cope with some criticism raised regarding the blind use of fuzzy systems     

Compressible flows through micro-channels with sharp edged turns and bifurcations

Bends and bifurcations connecting straight channels are common features in micro-channel networks. We apply our recently extended Hele-Shaw asymptotic scheme to study the viscous compressible gas flow through a shallow bend (whose depth is small relative to all other characteristic dimensions). By the use of analytic-function theory, we obtain closed-form solutions for arbitrary values of the turn angle and the ratio between the upstream- and downstream- channel widths, respectively. The viscous resistance is thereby evaluated in terms of the geometrical parameters characterizing the bend. The linearity of the problem in terms of an appropriately defined quadratic form of the pressure allows us to briefly consider the role of bifurcations in the viscous resistance of tree-like micro-channel networks.     

Neural networks,rational functions,and realization theory

The problem of parametrizing single hidden layer scalar neural networks with continuous activation functions is investigated. A connection is drawn between realization theory for linear dynamical systems, rational functions, and neural networks that appears to be new. A result of this connection is a general parametrization of such neural networks in terms of strictly proper rational functions. Some existence and uniqueness results are derived. Jordan decompositions are developed, which show how the general form can be expressed in terms of a sum of canonical second order sections. The parametrization may be useful for studying learning algorithms.This work was supported by the Australian Research Council, the Australian Telecommunications and Electronics Research Board, and the Boeing Commencai Aircraft Company (thanks to John Moore).     

Traditional posterior load carriage: effects of load mass and size on torso kinematics,kinetics, muscle activity and movement stability

Traditional posterior load carriage (PLC), done without the use of an assistive device (e.g. backpack), has been associated with low back pain (LBP) development. This study evaluated the effects of important task demands, related to load mass and size, on potential mechanisms linking traditional PLC with LBP. Nine healthy participants completed PLC tasks with three load masses (20%, 35% and 50% of individual body mass) and three load sizes (small, medium and large). Torso kinematics, kinetics, muscle activity and slip risk were evaluated during PLC on a walkway, and torso movement stability was quantified during PLC on a treadmill. Increasing load mass caused increased torso flexion, L5/S1 flexion moment, abdominal muscle activity and torso movement stability in the frontal plane. Increasing load size also caused higher torso flexion, peak torso angular velocity and acceleration, and abdominal muscle activity. Complex interactive effects of load mass and size were found on paraspinal muscle activity and slip risk. Specific task demands, related to load mass and size, may thus influence the risk of LBP during PLC.     

A classification of generic families of control-affine systems and their bifurcations

We study control-affine systems with n − 1 inputs evolving on an n-dimensional manifold for which the distribution spanned by the control vector fields is involutive and of constant rank (equivalently, they may be considered as 1-dimensional systems with n − 1 inputs entering nonlinearly). We provide a complete classification of such generic systems and their one-parameter families. We show that a generic family for n > 2 is equivalent (with respect to feedback or orbital feedback transformations) to one of nine canonical forms which differ from those for n = 2 by quadratic terms only. We also describe all generic bifurcations of 1-parameter families of systems of the above form.     

Elderly people activity monitoring with involved binary sensors and Deep Convolution Neural Network

Neural Computing and Applications - Data reveal that by 2025, the number of elderly population will have surpassed 1.4 billion. The percent of the elderly desire a healthy and private environment....     

Neural machine translation: past,present, and future

Neural Computing and Applications - Deep neural networks (DNN) have achieved great success in several research areas like information retrieval, image processing, and speech recognition. In the...     

Regional placement of bone mineral mass, fat mass, and lean soft tissue mass in young adult rugby union players

The purpose of the present study was to ascertain whether differences existed in the regional placement of bone mineral mass (BMM), fat mass (FM) and lean soft tissue mass (LSTM) between playing units in Rugby Union Football and between players and control subjects. Thirty young adult rugby players and 21 controls participated in the study. Players were assigned to groups as either forwards (n = 15) or backs (n = 15). Control subjects were matched (n = 15) to rugby players using the mean BMI of forwards and backs. BMM, FM and LSTM were measured using dual-energy X-ray absorptiometry. The digital image of each subject was partitioned into regional anatomical segments comprising the head, right and left arms, trunk, and right and left legs. Measurements were summed for the arms and legs respectively. One-way ANOVA was used to differentiate between- and within-groups; Tukey's post-hoc test was applied to identify pairwise differences. The alpha level was set throughout at p = 0.01. Principal components analysis was utilized to contrast the regional segments of each tissue in each of the groups. Forwards exhibited larger absolute (kg) amounts of BMM, FM and LSTM than backs or controls. In relative terms (%) there were no significant differences in BMM(%) between forwards, backs and controls in the arms and legs, but differences did occur between backs and controls at the trunk (2.9 vs. 2.5%). Backs had a significantly larger LSTM(%) than forwards at the arms (84.4 vs. 76.5%), legs (80.0 vs. 71.9%) and trunk (89.2 vs. 79.0%), whereas forwards had a greater FM(%) than backs at the arms (18.7 vs. 10.6%), legs (23.1 vs. 14.7%), and trunk (18.4 vs. 8.0%). The distribution of BMM showed a lower body-upper body contrast in forwards, a trunk-extremity contrast in backs and an arm-lower body contrast in controls. FM exhibited a trunk-extremity contrast in all three groups, while LSTM displayed an arm-lower body contrast in all three groups. It is concluded that there are significant regional tissue differences between forwards and backs, which may be related to playing function, and also differences between rugby players and controls.     

Gold Price, Neural Networks and Genetic Algorithm

Economic theory has failed to provide sufficient explanation of the dynamicpath of price movement over time. Therefore, the use of any linear ornon-linear functional form to model the gold price movement is bound to bearbitrary in nature. Neural Networks equipped with genetic algorithm have theadvantage of simulating the non-linear models when little a priori knowledgeof the structure of problem domains exist. Studies suggest that such a systemprovides better predictions when compared with traditional econometric models.The NeuroGenetic Optimizer software is applied to the NYMEX database of dailygold cash price covering 12/31/1974–12/31/1998 period. Among differentmethods, back-propagation neural networks with genetic algorithms is used topredict gold price movement. The results indicate that prices in the past, upto 36 days, strongly affect the gold prices of the future. This confirms thefact that there is short-term time dependence in gold price movements.     

Neural networks in art,sound and design

Neural Computing and Applications -     

Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation

The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol s...     

Resonant terms and bifurcations of nonlinear control systems with one uncontrollable mode

In this paper we provide a simple algorithm of feedback design for systems with uncontrollable linearization with only quadratic degeneracy, such as transcritical and saddle-node bifurcations. This approach avoids the computation of nonlinear normal forms. It is based only on quadratic invariants which can be determined directly from the quadratic terms in the uncontrollable dynamics.     

Metabolic rate of carrying added mass: A function of walking speed,carried mass and mass location

The effort of carrying additional mass at different body locations is important in ergonomics and in designing wearable robotics. We investigate the metabolic rate of carrying a load as a function of its mass, its location on the body and the subject’s walking speed. Novel metabolic rate prediction equations for walking while carrying loads at the ankle, knees and back were developed based on experiments where subjects walked on a treadmill at 4, 5 or 6 km/h bearing different amounts of added mass (up to 2 kg per leg and 22 kg for back). Compared to previously reported equations, ours are 7–69% more accurate. Results also show that relative cost for carrying a mass at a distal versus a proximal location changes with speed and mass. Contrary to mass carried on the back, mass attached to the leg cannot be modeled as an increase in body mass.     

Static, Dynamic, and Hybrid Neural Networks in Forecasting Inflation

The back-propagation neural network (BPN) model has been the most popular form of artificial neural network model used for forecasting, particularly in economics and finance. It is a static (feed-forward) model which has a learning process in both hidden and output layers. In this paper we compare the performance of the BPN model with that of two other neural network models, viz., the radial basis function network (RBFN) model and the recurrent neural network (RNN) model, in the context of forecasting inflation. The RBFN model is a hybrid model with a learning process that is much faster than the BPN model and that is able to generate almost the same results as the BPN model. The RNN model is a dynamic model which allows feedback from other layers to the input layer, enabling it to capture the dynamic behavior of the series. The results of the ANN models are also compared with those of the econometric time series models.