Automatic Derivation of Statistical Algorithms: The EM Family and Beyond

Machine learning has reached a point where many probabilistic methods can be understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms customized for different models. Here, we describe the AUTOBAYES system which takes a high-level statistical model specification, uses powerful symbolic techniques based on schema-based program synthesis and computer algebra to derive an efficient specialized algorithm for learning that model, and generates executable code implementing that algorithm. This capability is far beyond that of code collections such as Matlab toolboxes or even tools for model-independent optimization such as BUGS for Gibbs sampling: complex new algorithms can be generated without new programming, algorithms can be highly specialized and tightly crafted for the exact structure of the model and data, and efficient and commented code can be generated for different languages or systems. We present automatically-derived algorithms ranging from closed-form solutions of Bayesian textbook problems to recently-proposed EM algorithms for clustering, regression, and a multinomial form of PCA

Urban and regional land use analysis: CARETS and Census Cities experiment package

There are no author-identified significant results in this report

Urban and regional land use analysis: CARETS and Census Cities experiment package

The author has identified the following significant results. A number of likely applications and follow-on analyses are suggested by the census cities evaluation of ERTS-1 and Skylab data. Some of these applications are: (1) estimate water use requirements; (2) define urban expansion; (3) document the pattern of residential development and assess quality of residential environment: (4) project future population densities, and estimate changes in population distribution between censuses; (5) assess environmental impact resulting from gradual as well as catastrophic changes

High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems

The classical problem of determining the density and capacity of arrays of potential sources is studied. This corresponds to a wide variety of physical problems such as electrostatic capacitance, stress in elastostatics and the evaporation of fluid droplets. An asymptotic solution is derived that is shown to give excellent accuracy for arbitrary arrays of sources with non-circular footprints, including polygonal footprints. The solution is extensively validated against both experimental and numerical results. We illustrate the power of the solution by showcasing a variety of newly accessible classical problems that may be solved in a rapid, accurate manner

Reduced-order modelling of thick inertial flows around rotating cylinders

A new model for the behaviour of a thick, two-dimensional layer of fluid on the surface of a rotating cylinder is presented, incorporating the effects of inertia, rotation, viscosity, gravity and capillarity. Comparisons against direct numerical simulations (DNS) show good accuracy for fluid layers of thickness of the same order as the cylinder radius, even for Reynolds numbers up to Re∼10. A rich and complex parameter space is revealed, and is elucidated via a variety of analytical and numerical techniques. At moderate rotation rates and fluid masses, the system exhibits either periodic behaviour or converges to a steady state, with the latter generally being favoured by greater masses and lower rotation rates. These behaviours, and the bifurcation structure of the transitions between them, are examined using a combination of both the low-order model and DNS. Specific attention is dedicated to newly accessible regions of parameter space, including the multiple steady state solutions observed for the same parameter values by Lopes et al.(2018), where the corresponding triple limit point bifurcation structure is recovered by the new low-order model. We also inspect states in which the interface becomes multivalued - and thus outside the reach of the reduced-order model - via DNS.This leads to highly nonlinear multivalued periodic structures appearing at moderate thicknesses and relatively large rotation rates. Even much thicker films may eventually reach steady states (following complex early evolution), provided these are maintained by a combination of forces sufficiently large to counteract gravity

Polar relaxation by dynein-mediated removal of cortical myosin II

Nearly 6 decades ago, Lewis Wolpert proposed the relaxation of the polar cell cortex by the radial arrays of astral microtubules as a mechanism for cleavage furrow induction (White and Borisy, 1983; Wolpert, 1960). While this mechanism has remained controversial (Rappaport, 1996), recent work has provided evidence for polar relaxation by astral microtubules (Chen et al., 2008; Dechant and Glotzer, 2003; Foe and Dassow, 2008; Murthy and Wadsworth, 2008; Werner et al., 2007), although its molecular mechanisms remain elusive. Here, using C. elegans embryos, we show that polar relaxation is achieved through dynein-mediated removal of myosin II from the polar cortexes. Mutants that position centrosomes closer to the polar cortex accelerated furrow induction whereas suppression of dynein activity delayed furrowing. We provide evidence that dynein-mediated removal of myosin II from the polar cortexes triggers cortical flow towards the cell equator, which induces the assembly of the actomyosin contractile ring. These studies for the first time provide a molecular basis for the aster-dependent polar relaxation, which works in parallel with equatorial stimulation to promote robust cytokinesis