Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs

We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with Sequential Monte Carlo, this automatically yields improvements such as locally-optimal proposals and Rao-Blackwellization. The mechanism maintains a directed graph alongside the running program that evolves dynamically as operations are triggered upon it. Nodes of the graph represent random variables, edges the analytically-tractable relationships between them. Random variables remain in the graph for as long as possible, to be sampled only when they are used by the program in a way that cannot be resolved analytically. In the meantime, they are conditioned on as many observations as possible. We demonstrate the mechanism with a few pedagogical examples, as well as a linear-nonlinear state-space model with simulated data, and an epidemiological model with real data of a dengue outbreak in Micronesia. In all cases one or more variables are automatically marginalized out to significantly reduce variance in estimates of the marginal likelihood, in the final case facilitating a random-weight or pseudo-marginal-type importance sampler for parameter estimation. We have implemented the approach in Anglican and a new probabilistic programming language called Birch.Comment: 13 pages, 4 figure

Optimum design of unbraced multi-story frames by plastic theory

The purpose of this paper is to describe a computer procedure developed for optimum weight design of unbraced three-bay, regular rectangular plane building frames using plastic theory

Estimation of Restraint Forces for Z-purlin Roofs under Gravity Loads

The current specification provisions for the prediction of lateral restraint forces in Z-purlin supported roof systems under gravity loads are in Section D3.1 of the 1996 AlSI Specification for the Design of Cold-Formed Steel Structural Members (1996). The provisions need refinement, because they are empirical, have an incorrect treatment of roof slope and system effects, and ignore the effect of panel stiffness on restraint forces. Therefore, a new restraint force design procedure, having a stronger reliance on engineering principles, is proposed. Elastic stiffness models, with varying roof slope, panel stiffness, and cross-sectional properties, were used to develop the procedure. A new treatment of Z-purlin statics has led to a more accurate method of addressing roof slope. A system effect factor accounts for the observed nonlinear increase in restraint force with the number of restrained purlins. An adjustment factor varies the predicted restraint force depending on the shear stiffness of the roof panel. The proposed procedure applies to five bracing configurations: support, third-point, midspan, quarter point, and third-point plus support restraints

Shear Plus Bending in Lapped Z-purlins

Six two purlin line, three span continuous Z-purlin tests were conducted to show that combined shear plus bending is a possible failure mode immediately outside the lapped portion of the purlin lines. AISI Specification provisions predicted that combined shear plus bending was the controlling limit state. Strain gage data showed that local buckling occurred immediately outside of the lapped portion of the purlins lines prior to failure which caused moment to redistribute to the positive moment region. It is concluded that shear plus bending is a possible controlling limit state for continuous lapped purlins

VIBRATION OF STEEL BEAM CONCRETE SLAB FLOOR SYSTEMS

This report deals with the research to date (April, 1968) conducted on the vibration of steel beam-concrete slab floor systems

A non-apoptotic role for caspase-9 in muscle differentiation

Caspases, a family of cysteine proteases most often investigated for their roles in apoptosis, have also been demonstrated to have functions that are vital for the efficient execution of cell differentiation. One such role that has been described is the requirement of caspase-3 for the differentiation of skeletal myoblasts into myotubes but, as yet, the mechanism leading to caspase-3 activation in this case remains elusive. Here, we demonstrate that caspase-9, an initiator caspase in the mitochondrial death pathway, is responsible for the activation of caspase-3 in differentiating C2C12 cells. Reduction of caspase-9 levels, using an shRNA construct, prevented caspase-3 activation and inhibited myoblast fusion. Myosin-heavy-chain expression, which accompanies myoblastic differentiation, was not caspase-dependent. Overexpression of Bcl-xL, a protein that inhibits caspase-9 activation, had the same effect on muscle differentiation as knockdown of caspase-9. These data suggest that the mitochondrial pathway is required for differentiation; however, the release of cytochrome c or Smac (Diablo) could not be detected, raising the possibility of a novel mechanism of caspase-9 activation during muscle differentiation.</jats:p