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  • 1
    ISSN: 1520-6025
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 64 (1991), S. 231-241 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We study the influence of a variable neuronal threshold on fixed points and convergence rates of an associative neural network in the presence of noise. We allow a random distribution in the activity levels of the patterns stored, and a modification to the standard Hebbian learning rule is proposed for this purpose. There is a threshold at which the retrieval ability, including the average final overlap and the convergence rate, is optimized for patterns with a particular activity level at a given noise level. This type of selective attention to one class of patterns with a certain activity level may be obtained at the cost of reducing the retrieval ability of the network for patterns with different activity levels. The effects of a constant threshold independent of noise, time, and pattern are discussed. For high-(low-) activity patterns, the average final overlap is shown to be increased at high noise levels and decreased at low noise levels by a negative (positive) constant threshold, whereas a positive (negative) threshold always reduces the final average overlap. When the magnitude of the constant threshold exceeds a critical value, there is no retrieval. Rates of convergence towards the stored pattern with negative (positive) thresholds are greater than those with positive (negative) thresholds. These results are related to (de)sensitization and anesthesia. For certain threshold values and patterns with certain activity levels, hysteresis appears in the plot of the average final overlap versus the noise level, even for first order interactions. We make the analogy between the pattern-dependent neuronal threshold proposed in the present paper and the “task-related” modulation in neuronal excitability determined by cognitive factors, such as the attentional state of a higher animal. A constant threshold is associated with overall changes in neuronal excitability caused, e.g., by various drugs and physical injuries. Neurophysiological evidence of a dynamically variable neuronal threshold, such as accommodation and potentiation, is presented.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 3644-3648 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The deterministic kinetics of chemical reactions is compared with a stochastic description for the cubic Schlögl model with a single stable steady state, which has a nonlinear reaction mechanism. We solve numerically the birth-death master equation for this system for various numbers of particles (N=20–160). For small systems with tens of particles the deviation of the first moment of the stochastic distribution from the deterministic temporal variation of concentration can be substantial in the initial relaxation towards a stationary state. The relaxation of the master equation is faster than that of the deterministic equation. The maximum deviation in trajectories decreases as the parameters in the kinetic model are altered towards a linear mechanism. The maximum deviation differs from N1/2 as N decreases, but approaches N1/2 as N increases. Deviations from deterministic temporal evolution due to fluctuations depend on the extent of nonlinearity of the reaction. The variance of a stationary distribution of the master equation is shown to be significantly larger than the average for a nonlinear system.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 3569-3578 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In a series of articles M. Garfinkle has presented an empirical thermodynamic approach to chemical reactions from an initial nonequilibrium state to equilibrium in a closed isothermal system. He claims that (1) (essential points made by M. Garfinkle are numbered for reference later in the text) "a stoichiometric chemical reaction in a closed system traverses a unique natural path from reaction initiation to equilibrium. Along such a natural reaction path the time rate of change of the thermodynamic functions can be analytically described independently of phenomenological or mechanistic consideration'' [M. Garfinkle, J. Phys. Chem. 93, 2158 (1989)]. We show these and other claims not to be correct; this approach has validity limited to: reaction mechanisms with essentially only one velocity (mechanisms with one rate-determining step or mechanisms in a quasi-stationary state); reactions occurring at times close to the initial time; and no products present at the initial time. Garfinkle's method of plotting kinetic data, as a function of t−1, suppress information at later times, which shows the inadequacy of his proposed form of the affinity decay, and leads to the erroneous conclusion that a parameter in this form, tk equal to the most probable time to reach equilibrium, is finite, when in fact it is infinite. The affinity decay rate in general depends on the reaction mechanism, or on the order of the empirical rate equation if determined experimentally.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 1936-1946 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report the first measurement of the relative stability of two stable stationary states in a bistable system, that of an optically bistable ZnSe interference filter. A thin ZnSe rectangle is illuminated and bounded by nonilluminated regions at room temperature. This geometry allows the observation of a boundary between the upper and lower stationary state. We describe the inhomogeneous experiments, discuss relative stability in such systems, and compare them with the relative stability of the related homogeneous system. The right marginal stability point of the hysteresis loop is marked by the appearance of the upper stationary state. The homogeneous left marginal stability point is determined by a measurement of the transient relaxation in our inhomogeneous experiment. At the constraint of illumination corresponding to equistability of the two stable stationary states, the upper state becomes unstable for inhomogeneous conditions. We find close agreement between our experiments and the predictions of deterministic physical kinetics. In an accompanying article we discuss the issue of the relative stability of bistable states with thermodynamic fluctuations for inhomogeneous conditions and homogeneous conditions with noise that is independent of the state variable.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 3559-3568 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Periodic perturbations are applied to the input fluxes of reactants in a system which exhibits autonomous oscillations, the combustion of acetaldehyde (ACH) and oxygen, and a system which exhibits damped oscillations, the combustion of methane and oxygen. The ACH system is studied by experiments and numerical analysis and the methane system is studied by numerical analysis. The periodic perturbations are in the form of a two-term Fourier series. Such perturbations may generate multiple attractors, which are either periodic or chaotic. We discuss two types of bistable responses: a new phase bistability, in which a subharmonic frequency is added to a sinusoidal perturbation at different phases relative to the periodic response; and jump phenomena, in which the resonant frequency of a nonlinear oscillator depends on the amplitude of the periodic perturbation. Both the ACH and the methane systems confirm the phase bistability. The additional complex behavior of bistability due to jump phenomena is seen only in calculations in the methane system. In both types of bistability a hysteresis loop is formed as we vary the form of the periodic perturbation. In the methane system, we find period doubling to chaos occuring on one branch of the hysteresis loop while the other branch remains periodic. The methane system has been studied in the context of the efficiency of power production. We calculate the efficiency corresponding to each bistable attractor and find one branch of each pair to be the more efficient mode of operation. In the case of the coexisting periodic and chaotic attractors the chaotic attractor is the more efficient mode of operation.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 3579-3589 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The first experiments are presented which show that an external periodic perturbation imposed on a nonlinear isothermal biochemical reaction far from equilibrium may change the dissipation and hence the efficiency of that reaction; the results confirm earlier theoretical and numerical predictions. The reaction is driven and maintained far from equilibrium, a process thermodynamically equivalent to the establishment and maintenance of a concentration gradient across a membrane, i.e., a biochemical pump. We study the highly nonlinear oxidation of NADH catalyzed by the enzyme horseradish peroxidase (HRP) under conditions of continuous oxygen influx. NAD+ is recycled to NADH by a second enzymatic reaction. Experimental conditions are set so that the (HRP) reaction is in a stable limit cycle (autonomous oscillations). We then apply a periodic perturbation to the oxygen influx such that the average influx during the perturbation equals the previous steady influx. We present data obtained for a variety of frequencies and amplitudes of sinusoidal variations in the oxygen influx. Upon imposition of the periodic perturbation, we find changes in the average steady-state concentration of NADH, the average ΔG of the (HRP) reaction, the average rate of the (HRP) reaction, the phase difference between ΔG and the rate, the response of the system to the perturbation, and the dissipation of the reaction. Changes in dissipation which occur upon the imposition of an external periodic perturbation are a result of a combination of changes which occur in the thermodynamic quantities listed. These results confirm the possibility of variable efficiency of biological pumps since the establishment and maintenance of a chemical potential difference across a membrane is thermodynamically equivalent to the establishment and maintenance of a nonequilibrium stationary state in a single phase, open, homogeneous system. Moreover, the results confirm the possibility of an alternating current chemistry of control and optimization of thermodynamic efficiency, dissipation, and yield by means of an external variation of constraints in nonlinear (bio)chemical reactions and biological pumps.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 1613-1625 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider chemical reactions which at equilibrium have multiple stationary states due to nonidealities of chemical species. When such reactions are included in a simple reaction mechanism open to mass flow, without autocatalysis or feedback steps, there may occur complex dynamics such as relaxation oscillations, as reported earlier for regular solutions. Here we consider both regular solution and ionic species (Debye–Hückel nonideality), show that chemical oscillations may occur arbitrarily close to chemical equilibrium, and trace the topological structure of the complex dynamics of relaxation oscillations, sustained oscillations, stable focus, and stable nodes to the multiplicity of equilibrium states, for stated constraints. Relaxation oscillations occur around an unstable stationary state which, on approach to equilibrium, connects to an unstable equilibrium state. Thus, there is no bifurcation to oscillations on removing the systems from equilibrium. Neither is there a region where linear irreversible thermodynamics is valid close to equilibrium. Earlier work on ionic systems is found to be in error.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 2572-2581 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider chemical reactions occurring in a compartment separated by semipermeable membranes from reservoirs of reactant and product, both held at constant pressure. In earlier work, we have developed a nonequilibrium thermodynamic theory applicable to systems with a single reactive intermediate, and we have established a link between the thermodynamic and stochastic analyses of such systems. Here we show that our results generalize directly to cases with two or more reactive intermediates, if the reaction mechanism is nonautocatalytic, or if the system is evolving toward an equilibrium steady state in the reaction compartment without first exhausting the reactant or product reservoir. Starting with nonautocatalytic mechanisms, we identify effective driving forces for each intermediate; we then obtain the driving force for an arbitrary system by mapping to an instantaneously equivalent nonautocatalytic system. The driving force can be cast thermodynamically in terms of the difference between the actual chemical potential of the intermediate and its chemical potential at a reference state (the steady state of the instantaneously equivalent nonautocatalytic system); it can also be cast kinetically in terms of reactive fluxes in the instantaneously equivalent system. Taking the product of the driving force and the net flux of each intermediate and then summing over the species gives a term in the dissipation that is specific to the intermediates. This term is minimized at nonequilibrium steady states, unlike the total dissipation (or entropy production). For the nonautocatalytic or equilibrating systems, an integral of the driving forces yields a Liapunov function for the evolution of the reaction chamber toward the steady state. The same integral also determines the stationary solution of the birth–death master equation for the species numbers of intermediates in the reaction compartment; this generalizes the Einstein relation for the probability of equilibrium fluctuations to far-from-equilibrium conditions.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 1947-1955 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We compare theory and experiments on relative stability of the two stable stationary states in optically bistable ZnSe interference filters. We examine the equistability predictions of the master equation, the Fokker–Planck equation, and a deterministic analysis. For this effectively one-variable system there exists a potential for each of these descriptions. We derive a master and Fokker–Planck equation for the fluctuations in temperature expected in our system and find that the three theoretical potentials differ significantly for homogeneous geometries of the system, but the stochastic predictions agree with the deterministic equistability point for inhomogeneous systems. We also examine the effect of external noise, which is independent of the state variable, and find that a very small amount of noise reduces the equistability prediction of the homogeneous master and Fokker–Planck equations to that of the deterministic potential. Noise in the constraints (such as light intensity) results in a new effective potential.
    Type of Medium: Electronic Resource
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