A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise.

Synthesis, stability, antiviral activity, and protease-bound structures of substrate-mimicking constrained macrocyclic inhibitors of HIV-1 protease

Three new peptidomimetics (1-3) have been developed with highly stable and conformationally constrained macrocyclic components that replace tripeptide segments of protease substrates. Each compound inhibits both HIV-1 protease and viral replication (HIV-I, HIV-2) at nanomolar concentrations without cytotoxicity to uninfected cells below 10 mu M. Their activities against HIV-1 protease (K-i 1.7 nM (1), 0.6 nM (2), 0.3 nM (3)) are 1-2 orders of magnitude greater than their antiviral potencies against HIV-1-infected primary peripheral blood mononuclear cells (IC50 45 nM (1), 56 nM (2), 95 nM (3)) or HIV-1-infected MT2 cells (IC50 90 nM (1), 60 nM (2)), suggesting suboptimal cellular uptake. However their antiviral potencies are similar to those of indinavir and amprenavir under identical conditions. There were significant differences in their capacities to inhibit the replication of HIV-1 and HIV-2 in infected MT2 cells, 1 being ineffective against HIV-2 while 2 was equally effective against both virus types. Evidence is presented that 1 and 2 inhibit cleavage of the HIV-1 structural protein precursor Pr55(gag) to p24 in virions derived from chronically infected cells, consistent with inhibition of the viral protease in cells. Crystal structures refined to 1.75 Angstrom (1) and 1.85 Angstrom (2) for two of the macrocyclic inhibitors bound to HIV-1 protease establish structural mimicry of the tripeptides that the cycles were designed to imitate. Structural comparisons between protease-bound macrocyclic inhibitors, VX478 (amprenavir), and L-735,524 (indinavir) show that their common acyclic components share the same space in the active site of the enzyme and make identical interactions with enzyme residues. This substrate-mimicking minimalist approach to drug design could have benefits in the context of viral resistance, since mutations which induce inhibitor resistance may also be those which prevent substrate processing.