A second-order heavy traffic approximation for the queue GI/G/1

1981 ◽  
Vol 13 (1) ◽  
pp. 167-185
Author(s):  
Julian Köllerström
Keyword(s):  
Waiting Time ◽  
Order Term ◽  
Heavy Traffic ◽  
Convolution Equation ◽  
Second Order ◽  
First Order ◽  
Functional Convergence ◽  
Ladder Height ◽  
Stationary Waiting Time ◽  
Heavy Traffic Approximation

A second-order heavy traffic approximation for the stationary waiting-time d.f. G for GI/G/1 queues is derived, the first-order term of which is Kingman's (1961), (1962a), (1965) exponential approximation. On the way to this result there are others of independent interest, such as a convolution equation relating this waiting time d.f. G with the d.f. of a related ladder height, an integral equation for G and some stochastic bounds for G. The main result requires a particular type of functional convergence that may also be of interest.

A second-order heavy traffic approximation for the queue GI/G/1

1981 ◽  
Vol 13 (01) ◽  
pp. 167-185
Author(s):  
Julian Köllerström
Keyword(s):  
Waiting Time ◽  
Order Term ◽  
Heavy Traffic ◽  
Convolution Equation ◽  
Second Order ◽  
First Order ◽  
Functional Convergence ◽  
Ladder Height ◽  
Stationary Waiting Time ◽  
Heavy Traffic Approximation

A second-order heavy traffic approximation for the stationary waiting-time d.f. G for GI/G/1 queues is derived, the first-order term of which is Kingman's (1961), (1962a), (1965) exponential approximation. On the way to this result there are others of independent interest, such as a convolution equation relating this waiting time d.f. G with the d.f. of a related ladder height, an integral equation for G and some stochastic bounds for G. The main result requires a particular type of functional convergence that may also be of interest.

Neural computation of motion in the fly visual system: quadratic nonlinearity of responses induced by picrotoxin in the HS and CH cells

1995 ◽  
Vol 74 (6) ◽  
pp. 2665-2684 ◽  
Author(s):  
Y. Kondoh ◽  
Y. Hasegawa ◽  
J. Okuma ◽  
F. Takahashi
Keyword(s):  
Mean Square Error ◽  
Order Term ◽  
Mirror Image ◽  
Second Order ◽  
The Other ◽  
Linear Component ◽  
Mean Square ◽  
Nonlinear Component ◽  
First Order ◽  
Order Kernel

1. A computational model accounting for motion detection in the fly was examined by comparing responses in motion-sensitive horizontal system (HS) and centrifugal horizontal (CH) cells in the fly's lobula plate with a computer simulation implemented on a motion detector of the correlation type, the Reichardt detector. First-order (linear) and second-order (quadratic nonlinear) Wiener kernels from intracellularly recorded responses to moving patterns were computed by cross correlating with the time-dependent position of the stimulus, and were used to characterize response to motion in those cells. 2. When the fly was stimulated with moving vertical stripes with a spatial wavelength of 5-40 degrees, the HS and CH cells showed basically a biphasic first-order kernel, having an initial depolarization that was followed by hyperpolarization. The linear model matched well with the actual response, with a mean square error of 27% at best, indicating that the linear component comprises a major part of responses in these cells. The second-order nonlinearity was insignificant. When stimulated at a spatial wavelength of 2.5 degrees, the first-order kernel showed a significant decrease in amplitude, and was initially hyperpolarized; the second-order kernel was, on the other hand, well defined, having two hyperpolarizing valleys on the diagonal with two off-diagonal peaks. 3. The blockage of inhibitory interactions in the visual system by application of 10-4 M picrotoxin, however, evoked a nonlinear response that could be decomposed into the sum of the first-order (linear) and second-order (quadratic nonlinear) terms with a mean square error of 30-50%. The first-order term, comprising 10-20% of the picrotoxin-evoked response, is characterized by a differentiating first-order kernel. It thus codes the velocity of motion. The second-order term, comprising 30-40% of the response, is defined by a second-order kernel with two depolarizing peaks on the diagonal and two off-diagonal hyperpolarizing valleys, suggesting that the nonlinear component represents the power of motion. 4. Responses in the Reichardt detector, consisting of two mirror-image subunits with spatiotemporal low-pass filters followed by a multiplication stage, were computer simulated and then analyzed by the Wiener kernel method. The simulated responses were linearly related to the pattern velocity (with a mean square error of 13% for the linear model) and matched well with the observed responses in the HS and CH cells. After the multiplication stage, the linear component comprised 15-25% and the quadratic nonlinear component comprised 60-70% of the simulated response, which was similar to the picrotoxin-induced response in the HS cells. The quadratic nonlinear components were balanced between the right and left sides, and could be eliminated completely by their contralateral counterpart via a subtraction process. On the other hand, the linear component on one side was the mirror image of that on the other side, as expected from the kernel configurations. 5. These results suggest that responses to motion in the HS and CH cells depend on the multiplication process in which both the velocity and power components of motion are computed, and that a putative subtraction process selectively eliminates the nonlinear components but amplifies the linear component. The nonlinear component is directionally insensitive because of its quadratic non-linearity. Therefore the subtraction process allows the subsequent cells integrating motion (such as the HS cells) to tune the direction of motion more sharply.

Perturbation Theory and the Triangular Well Potential

1975 ◽  
Vol 53 (1) ◽  
pp. 5-12 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Order Term ◽  
Second Order ◽  
First Order ◽  
Triangular Well Potential

Accurate calculations of the second order term in the free energy and the first order term in the radial distribution function in the Barker–Henderson (BH) perturbation theory are presented for the triangular well potential. The BH theory is found to be fully satisfactory for this system. Thus, the conclusions of Card and Walkley regarding the accuracy of the BH theory are erroneous.

Tightness of the stationary waiting time in heavy traffic

1999 ◽  
Vol 31 (3) ◽  
pp. 788-794 ◽  
Author(s):  
Władysław Szczotka
Keyword(s):  
Waiting Time ◽  
Heavy Traffic ◽  
Sufficient Conditions ◽  
Stationary Waiting Time

Sufficient conditions are given ensuring tightness of a suitably normalized stationary waiting time in the FIFO G/G/1 queue under heavy traffic.

A note on the perturbation theory and the triangular well potential

1977 ◽  
Vol 55 (7-8) ◽  
pp. 632-634 ◽  
Author(s):  
P. C. Wankhede ◽  
K. N. Swamy
Keyword(s):  
Monte Carlo ◽  
Perturbation Theory ◽  
Order Term ◽  
Second Order ◽  
First Order ◽  
Monte Carlo Calculations ◽  
Theory Of Liquids ◽  
Compressibility Factors ◽  
Triangular Well Potential

The integrals which appear in the first order term and the macroscopic compressibility (mc) and the local compressibility (lc) approximation for the second order term in the Barker–Henderson (BH) perturbation theory of liquids are evaluated analytically for the triangular-well potential. The compressibility factors so calculated are compared with the Monte Carlo calculations.

Tightness of the stationary waiting time in heavy traffic

1999 ◽  
Vol 31 (03) ◽  
pp. 788-794
Author(s):  
Władysław Szczotka
Keyword(s):  
Waiting Time ◽  
Heavy Traffic ◽  
Sufficient Conditions ◽  
Stationary Waiting Time

Sufficient conditions are given ensuring tightness of a suitably normalized stationary waiting time in the FIFO G/G/1 queue under heavy traffic.

Perturbation theory and the local compressibility approximation in classical statistical mechanics

1968 ◽  
Vol 46 (15) ◽  
pp. 1725-1727 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Perturbation Theory ◽  
Statistical Mechanics ◽  
Order Term ◽  
Second Order ◽  
Three Dimensions ◽  
First Order ◽  
Classical Statistical Mechanics ◽  
Square Well ◽  
Exact Calculations

The integrals which appear in the first-order term and the local compressibility approximation to the second-order term in the Barker–Henderson perturbation theory of fluids are evaluated analytically for the square-well potential in one and three dimensions and are compared with exact calculations.

The nitrous acid catalysed nitration of naphthalene. Evidence for a kinetic term that is second order with respect to the aromatic compound

1989 ◽  
Vol 67 (11) ◽  
pp. 1677-1682 ◽  
Author(s):  
J. Ramón Leis ◽  
M. Elena Pena ◽  
John H. Ridd
Keyword(s):  
Electron Transfer ◽  
Acetic Acid ◽  
Nitrous Acid ◽  
Order Term ◽  
Second Order ◽  
Rate Coefficients ◽  
Kinetic Term ◽  
Aqueous Mixtures ◽  
Electron Transfer Mechanism ◽  
First Order

The kinetic equation for the nitrous acid catalysed nitration of naphthalene in aqueous mixtures of sulphuric acid and acetic acid has at least two kinetic terms: one first order with respect to naphthalene and one second order with respect to naphthalene. The orders with respect to nitrous acid and nitric acid vary with the conditions in the way characteristic of the electron transfer mechanism of this reaction. The second-order term with respect to naphthalene is considered to derive from the formation of the dimeric radical cation (ArH)2+•. The acidity dependence of the rate coefficients and the absence of a normal isotope effect in the reaction of naphthalene-d8 are consistent with this interpretation. Keywords: naphthalene, nitration, nitrous acid.

Application des miroirs électrostatiques à l'élimination de l'effet chromatique dans les spectromètres magnétiques. Première partie: théorie linéaire

1969 ◽  
Vol 47 (3) ◽  
pp. 331-340 ◽  
Author(s):  
Marcel Baril
Keyword(s):  
Matrix Algebra ◽  
Order Term ◽  
Order Theory ◽  
Second Order ◽  
Energy Dispersive ◽  
Powerful Method ◽  
First Order ◽  
First Order Theory ◽  
Electrostatic Mirror ◽  
Premiere Partie

Combining an energy-dispersive element with a magnetic prism results in an achromatic mass dispersive instrument, if parameters are chosen appropriately. A plane electrostatic mirror has been chosen as the energy-dispersive element. Trajectories are described in terms of lateral, angular, and energy variations about the principal trajectory. Achromatism and conjugate plane conditions have been calculated by the powerful method of matrix algebra. The first order theory is given in this article (part one), the second order term will be studied in part two which will be published later.

scholarly journals Signatures of Noncommutativity in Bar Detectors of Gravitational Waves

2019 ◽  
Vol 64 (11) ◽  
pp. 1029 ◽  
Author(s):  
S. Gangopadhyay ◽  
S. Bhattacharyya ◽  
A. Saha
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Excited States ◽  
Ground State ◽  
Order Term ◽  
Second Order ◽  
Length Scale ◽  
Length Variation ◽  
Wave Perturbation ◽  
First Order

The comparison between the noncommutative length scale √θ and the length variation δL = hL, detected in the GW detectors, indicates that there is a strong possibility to detect the noncommutative structure of space in the GW detector setup. Therefore, we explore how the response of a bar detector gets affected due to the presence of a noncommutative structure of space keeping terms up to the second order in a gravitational wave perturbation (h) in the Hamiltonian. Interestingly, the second-order term in h shows a transition between the ground state and one of the perturbed second excited states that was absent, when the calculation was restricted only to the first order in h.

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