Second-order Relation Research Articles

Structural testing of multi-input linear—nonlinear cascade models for cells in macaque striate cortex

Structural testing methods based on experimental white noise stimulus-response data were used to evaluate multi-input linear—nonlinear (LN) cascade models for simple and complex cells in macaque striate cortex. An LN structural test index, based on white noise stimulation, was developed and found to be suitable for classifying cells as simple vs complex. In particular, classification results based on the LN structural test index were similar to classification results based on a traditional modulation index derived from cell responses to drifting sinewave gratings. Judging from their structural test indices, complex cells deviated more strongly from LN behavior than did simple cells. Yet, even with simple cells, on average, only about 60% of the first- and second-order white noise stimulus-response relation was consistent with LN behavior. Just two of thirteen simple cells studied had an LN consistency level that exceeded 80%. Similar results were found in tests for consistency with an LNL model which includes an additional linear post-filter. We conclude that a conventional multi-input LN network model may be a useful approximation to the response behavior of some simple cells. However, even during steady state stimulus conditions, subcortical and/or cortical nonlinearities other than a static output nonlinearity play a very significant role in shaping the responses of most simple cells in the macaque striate cortex.

Second-order electron mass dispersion relation at finite temperature. II.

Using the real-time finite-temperature methods the result of a detailed and explicit calculation of the renormalized electron mass to second order in {alpha} in QED is presented. The calculation is in the low-temperature approximation {ital T}{much lt}{ital m}{sub {ital e}} (electron mass) and demonstrates the consistency of the finite-temperature renormalization scheme.

Fourth-order Lagrangian of short waves riding on long waves

Applying the variational principle, a fourth-order wave-action conservation and second-order dispersion relation of a short-wave train riding on a long wave are derived from its fourth-order Lagrangian. The modulated nonlinear Schrödinger equation describing the evolution of short waves on long waves is obtained through the combination of the wave-action conservation and dispersion relation, and is identical to the previous derivation through a WKB perturbation method. The relationship between a Schrödinger equation and a Lagrangian is explored, revealing that their solutions for a steady short-wave train are generally different in accuracy except for the leading order.

Second-order electron mass dispersion relation at finite temperature

Using the real-time finite-temperature methods the result of a detailed and explicit calculation of the renormalized electron mass to second order in $\ensuremath{\alpha}$ in QED is presented. The calculation is in the low-temperature approximation $T\ensuremath{\ll}{m}_{e}$ (electron mass) and demonstrates the consistency of the finite-temperature renormalization scheme.

Errors of Five-Day Mean Surface Wind and Temperature Conditions due to Inadequate Sampling

Surface meteorological reports of wind components, wind speed, air temperature, and sea-surface temperature from buoys located in equatorial and midlatitude regions are used in a simulation of random sampling to determine errors of the calculated means due to inadequate sampling. Subsampling the data with several different sample sizes leads to estimates of the accuracy of the subsampled means. The number N of random observations needed to compute mean winds with chosen accuracies of 0.5 (N sub 0.5) and 1.0 (N sub 1,0) m/s and mean air and sea surface temperatures with chosen accuracies of 0.1 (N sub 0.1) and 0.2 (N sub 0.2) C were calculated for each 5-day and 30-day period in the buoy datasets. Mean values of N for the various accuracies and datasets are given. A second-order polynomial relation is established between N and the variability of the data record. This relationship demonstrates that for the same accuracy, N increases as the variability of the data record increases. The relationship is also independent of the data source. Volunteer-observing ship data do not satisfy the recommended minimum number of observations for obtaining 0.5 m/s and 0.2 C accuracy for most locations. The effect of having remotely sensed data is discussed.

Causation and universals

The world contains objective causal relations and universals, both of which are intimately connected. If these claims are true, they must have far-reaching consequences, breathing new life into the theory of empirical knowledge and reinforcing epistemological realism. Without causes and universals, Professor Fales argues, realism is defeated, and idealism or scepticism wins. Fales begins with a detailed analysis of David Hume's argument that we have no direct experience of necessary connections between events, concluding that Hume was mistaken on this fundamental point. Then, adopting the view of Armstrong and others that causation is grounded in a second-order relation between universals, he explores a range of topics for which the resulting analysis of causation has systematic implications. In particular, causal identity conditions for physical universals are proposed, which generate a new argument for Platonism. The nature of space and time is discussed, with arguments against backward causation and for the view that space and time can exist independently of matter or causal process. Many of Professor Fales's conclusions seem to run counter to received opinion among contemporary empiricists. Yet his method is classically empiricist in spirit, and a chief motive for these metaphysical explorations is epistemological. The final chapters investigate the perennial question of whether an empiricist, internalist and foundational epistemology can support scientific realism.

On the associated orthogonal polynomials

By using the second-order recurrence relation this paper gives some new results on associated orthogonal polynomials without referring to the continued fractions' tool. Some results are very useful for obtaining the second-order differential equation satisfied by the semi-classical orthogonal polynomials (Hendriksen and van Rossum (1985), Maroni (1987)) (cf. Section 3). Also, the main formula derives from Proposition 2.6, by which the fourth-order differential equation, satisfied by some Laguerre–Hahn polynomials (Magnus (1984)), is obtained (cf. Belmehdi and Ronveaux (1989), Dini (1989), Ronveaux (1990)).

Polymorphic Phase Transformation of Lead Monoxide and Its Influence on Lead Zirconate Titanate Formation

The polymorphic phase transformation of PbO from massicot to litharge phase is easily produced by mechanical force. The transformation is relatively quick by wet ball‐milling. The additions of TiO2 and ZrO2 tend to retard it. A second‐order exponential relation is observed between the fractional conversion and the milling time for pure PbO, PbO‐TiO2, and PbO‐ZrO2‐TiO2 systems with a rutile constituent. This exponential relation is changed into a first‐order logarithmic relation when anatase instead of rutile is used. Although the PbOss phase is observed irrespective of the phase of the PbO in the raw materials, this PbOss peak is more obvious when massicot PbO or anatase TiO2 is used. The formation of PbOss phase is also dependent on the reactivity of the ZrO2, and its presence can affect the formation and piezoelectric properties of PZT ceramics.

Pollination with irradiated pollen in rice—Oryza sativa L. I. First (M1) generation

Pollen from a paternal rice cultivar was pre-irradiated with gamma rays before using them to pollinate the emasculated florets of a maternal cultivar. A second-order polynomial regression relation was established between radiation dosage and seed set. LD50 for seed set was 10 krad. In the first generation derived from such irradiated pollination, the M1 progeny were either identical to the F1 plants in both polygenic and major gene traits, or were hemizygous plants showing recessive maternal major gene markers. Many hemizygous M1 plants were mutated and sterile. Irradiated pollination did not induce parthenogenic maternal plants in rice. None of the M1 progeny was maternal and at the same time, having also some paternal characteristics. The net effect of pollination with irradiated pollen in rice is the inheritance and expression of damaged paternal alleles by the M1 progeny, rather than the limited transfer of genetic fragments from the irradiated pollen genome to the M1 generation, as originally proposed by Pandey (1975).

Derivation of the third-order evolution equations for weakly nonlinear water waves propagating over uneven bottoms

Using the multi-scale perturbation methods, the evolution equations for the modulated wave groups over an uneven bottom are derived. The bottom topography consists of two components: the slowly varying component whose horizontal lenght scale is longer than the carrier wave lenght, and the fast varying component with the carrier wave lenght as the horizontal lenght scale. The size of the fast varying depth component is, however, much smaller than the carrier wave amplitude. Assuming that the nonlinearity parameter ε is in the same order of magnitude as the modulation parameter δ, a detailed perturbation expansion analysis based on the carrier wave frequency and carrier wave number is presented. The third-order evolution equation is coupled with a long wave equation which describes the generation and the propagation of a second-order long wave associated with the modulated wave train. It is also shown that the real part of the evolution equation represents a modified wave action equation, while the imaginary part of the evolution equation gives the second-order dispersion relation. For quasi-steady state problems simplifications are made to derive a nonlinear parabolic wave equation.

The electrocatalytic activities of the Pd-doped MnO 2 for the chlorine evolution reaction

The anodic evolution of chlorine on the massive β-MnO 2 doped with various amounts of Pd was investigated in acidic chloride solution. A second-order relation was found between the rate of the chlorine evolution reaction and the number of active Pd sites at the electrode surface. And it was confirmed that, in the relatively low doped electrodes, the active sites are more effectively dispersed on the surface with microscopic homogeneity. From the activation energies, it was also suggested that the reaction mechanism on the MnO 2 doped with relatively small amounts of Pd is somewhat different from that on the pure PdO electrode.

An Analytical Model for Nitric Oxide Formation in a Gas Turbine Combustor

Comparing Eq. (B7) to the unforced second-order filtering relation given in Eq. (31), one can see that the prior state error co variance matrix Mk contains the forcing matrix Qk-i while in Eq. (31) the forcing matrix is missing. One may observe that if the same state estimate value of xk_1 is used for both methods, when the unknown thrusting is applied in the interval [/c— 1,/c], the rapid estimation scheme provides the correct state error covariance matrix while the second order filtering relation given in Eq. (31) provides an inaccurate estimate due to the presence of the unknown thrusting.

Transient response of a case-bonded nonlinear viscoelastic cylinder.

The problem of a rapidly pressurized, infinitely long, thick-walled viscoelastic cylinder bonded to a thin elastic shell is considered. The plane strain solution is obtained when the strain e and deformation rate d in the viscoelastic cylinder are such that terms of order three and higher in e and d can be neglected in comparison with e and d. The strains in the shell, however, are restricted to magnitudes for which infinitesimal elasticity theory applies. The effect of inertia of the viscoelastic cylinder is included in the analysis. The cylinder is internally pressurized by two types of pressure programs: a step pressure and a ramp pressure with four different rise-times. For these loadings the Eulerian strain and circumferential stress response at the inner and outer radii of the viscoelastic cylinder are obtained using a second-order constitutive relation in which the stress depends only on the displacement and velocity gradients.

Second-order forces and pressure distributions on three-dimensional bodies by reverse-flow integral method

The general second-order reverse-flow relation derived by Glarke has been applied to fusiform bodies and to combinations of fusiform bodies and quasi-cylindrical wings. It is first shown that the second-order drag of an isolated fusiform body can be expressed in terms of the firstorder forward and reverse flow over the body provided the angle of incidence is not too large. The innovation of a reverse flow which is not simply antiparallel to the forward-flow at infinity is introduced and then used to derive separate integral statements on the three rectangular components of the second-order velocity perturbation on the surface of an isolated fusiform body. Two of these integral statements are inverted to yield information on the second-order surface pressure distribution. The inversions effected are valid for unrestricted incidence. The uninclined body is covered as a special case. By considering the perturbation field of a wing-body combination as a sum of isolated body and wing fields and an interference field, the leading contribution of the interference field to the second-order drag is obtained from the reverse-flow relation. The result presumes that the second-order fields of the isolated body and wing are known in advance. The reverse flow due to a two-dimensional flat-plate wing is then used to achieve an integral for the leading second-order contribution to the lift on a wing-body combination. This integral is used to calculate the lift contribution on the conical wing-body configuration for cone half-angles dc of 5° and 10°. The numerical results are compared to those obtained by direct application of Van Dyke's second-order cone potential. The difference ranges from 4%, for [(M2 — 1)1/2 tanSc] = 0.2, to 16%, for [(M2 - 1) 1/2 tanSc] = 0.8.