A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Characterization of two patched receptors for the vertebrate hedgehog protein family

The multitransmembrane protein Patched (PTCH) is the receptor for Sonic Hedgehog (Shh), a secreted molecule implicated in the formation of embryonic structures and in tumorigenesis. Current models suggest that binding of Shh to PTCH prevents the normal inhibition of the seven-transmembrane-protein Smoothened (SMO) by PTCH. According to this model, the inhibition of SMO signaling is relieved after mutational inactivation of PTCH in the basal cell nevus syndrome. Recently, PTCH2, a molecule with sequence homology to PTCH, has been identified. To characterize both PTCH molecules with respect to the various Hedgehog proteins, we have isolated the human PTCH2 gene. Biochemical analysis of PTCH and PTCH2 shows that they both bind to all hedgehog family members with similar affinity and that they can form a complex with SMO. However, the expression patterns of PTCH and PTCH2 do not fully overlap. While PTCH is expressed throughout the mouse embryo, PTCH2 is found at high levels in the skin and in spermatocytes. Because Desert Hedgehog (Dhh) is expressed specifically in the testis and is required for germ cell development, it is likely that PTCH2 mediates its activity in vivo. Chromosomal localization of PTCH2 places it on chromosome 1p33–34, a region deleted in some germ cell tumors, raising the possibility that PTCH2 may be a tumor suppressor in Dhh target cells.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

Sonic hedgehog protein signals not as a hydrolytic enzyme but as an apparent ligand for Patched

The amino-terminal signaling domain of the Sonic hedgehog secreted protein (Shh-N), which derives from the Shh precursor through an autoprocessing reaction mediated by the carboxyl-terminal domain, executes multiple functions in embryonic tissue patterning, including induction of ventral and suppression of dorsal cell types in the developing neural tube. An apparent catalytic site within Shh-N is suggested by structural homology to a bacterial carboxypeptidase. We demonstrate here that alteration of residues presumed to be critical for a hydrolytic activity does not cause a loss of inductive activity, thus ruling out catalysis by Shh-N as a requirement for signaling. We favor the alternative, that Shh-N functions primarily as a ligand for the putative receptor Patched (Ptc). This possibility is supported by new evidence for direct binding of Shh-N to Ptc and by a strong correlation between the affinity of Ptc-binding and the signaling potency of Shh-N protein variants carrying alterations of conserved residues in a particular region of the protein surface. These results together suggest that direct Shh-N binding to Ptc is a critical event in transduction of the Shh-N signal.

Regulation of patched by sonic hedgehog in the developing neural tube.

Ventral cell fates in the central nervous system are induced by Sonic hedgehog, a homolog of hedgehog, a secreted Drosophila protein. In the central nervous system, Sonic hedgehog has been identified as the signal inducing floor plate, motor neurons, and dopaminergic neurons. Sonic hedgehog is also involved in the induction of ventral cell type in the developing somites. ptc is a key gene in the Drosophila hedgehog signaling pathway where it is involved in transducing the hedgehog signal and is also a transcriptional target of the signal. PTC, a vertebrate homolog of this Drosophila gene, is genetically downstream of Sonic hedgehog (Shh) in the limb bud. We analyze PTC expression during chicken neural and somite development and find it expressed in all regions of these tissues known to be responsive to Sonic hedgehog signal. As in the limb bud, ectopic expression of Sonic hedgehog leads to ectopic induction of PTC in the neural tube and paraxial mesoderm. This conservation of regulation allows us to use PTC as a marker for Sonic hedgehog response. The pattern of PTC expression suggests that Sonic hedgehog may play an inductive role in more dorsal regions of the neural tube than have been previously demonstrated. Examination of the pattern of PTC expression also suggests that PTC may act in a negative feedback loop to attenuate hedgehog signaling.

Motor learning by field approximation.

We investigated how human subjects adapt to forces perturbing the motion of their ams. We found that this kind of learning is based on the capacity of the central nervous system (CNS) to predict and therefore to cancel externally applied perturbing forces. Our experimental results indicate: (i) that the ability of the CNS to compensate for the perturbing forces is restricted to those spatial locations where the perturbations have been experienced by the moving arm. The subjects also are able to compensate for forces experienced at neighboring workspace locations. However, adaptation decays smoothly and quickly with distance from the locations where disturbances had been sensed by the moving limb. (ii) Our experiments also how that the CNS builds an internal model of the external perturbing forces in intrinsic (muscles and / or joints) coordinates.