Biomedical subjects
Publications and source records attributed to C Van Den Broeck.
Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present as a first application full analytic results for hypersensitive transport.
We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic "piston" that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze the stationary velocity autocorrelation function C(t). Explicit expressions are obtained for certain typical velocity distributions, serving to elucidate in particular the asymptotic behavior of C(t). It is shown that the occurrence of a nonvanishing probability mass at zero velocity is necessary for the occurrence of a long-time tail in C(t). The conditions under which this is a t(-3) tail are determined. Turning to the inhomogeneous system with different macroscopic states on either side of the piston, we determine its effective diffusion coefficient from the asymptotic behavior of the variance of its position, as well as the leading behavior of the other moments about the mean. Finally, we present an interpretation of the effective noise arising from the dynamics of the two gases, and thence that of the stochastic process to which the position of any particle in the system reduces in the thermodynamic limit.
We study a model of unsupervised learning where the real-valued data vectors are isotropically distributed, except for a single symmetry-breaking binary direction Bin¿-1,+1¿(N), onto which the projections have a Gaussian distribution. We show that a candidate vector J undergoing Gibbs learning in this discrete space, approaches the perfect match J=B exponentially. In addition to the second-order "retarded learning" phase transition for unbiased distributions, we show that first-order transitions can also occur. Extending the known result that the center of mass of the Gibbs ensemble has Bayes-optimal performance, we show that taking the sign of the components of this vector (clipping) leads to the vector with optimal performance in the binary space. These upper bounds are shown generally not to be saturated with the technique of transforming the components of a special continuous vector, except in asymptotic limits and in a special linear case. Simulations are presented which are in excellent agreement with the theoretical results.
Collateral arteries can clearly be visualized in corrosion cast material after ligation of the femoral artery in rats. To characterize the influence of serotonin on the blood circulation under the experimental condition of unilateral ligation, we performed intermuscular thermoflow measurements. The data showed that intraperitoneal serotonin (8.7 and 20 mg.kg-1) injection markedly reduced the muscle temperature in both hindlegs. However, the effect was significantly more pronounced on the ligated side, where the blood was supplied through a collateral circulation, than on the non-ligated side with its normal arterial vasculature. Almost identical changes were obtained in rats with an early as well as in animals with a more advanced stage of collateral development (challenge with 8.7 mg.kg-1 serotonin). Evans blue dye experiments and angiographic data further revealed that, after challenge with 20 mg.kg-1 serotonin, the severe temperature decrease at the ligated side probably reflected a nearly complete blockage of blood supply. Pretreatment with the S2 receptor antagonist ketanserin (2.5 mg.kg-1) resulted in a significant reduction in the extent and duration of the serotonin-induced temperature decrease as revealed by the temperature measurements; such a treatment inhibited also the blockage in blood flow as seen with the other techniques. This study shows that serotonin, through its vasoconstrictive properties, can restrict the blood flow to the lower extremities of the rat, particularly when the blood is supplied through collateral circulation. This probably results in moderate to severe skeletal muscle ischaemia. It also suggests that the vasoconstriction is not only important in the inhibition of collateral blood flow in recently established collaterals but also in collateral vessels in a more advanced stage of development. The in vivo vasoconstriction and subsequent reduction of the blood supply caused by serotonin can be effectively counteracted by pretreatment with ketanserin.