An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’

Predictive Coding Theories of Cortical Function

Predictive coding is a unifying framework for understanding perception, action and neocortical organization. In predictive coding, different areas of the neocortex implement a hierarchical generative model of the world that is learned from sensory inputs. Cortical circuits are hypothesized to perform Bayesian inference based on this generative model. Specifically, the Rao-Ballard hierarchical predictive coding model assumes that the top-down feedback connections from higher to lower order cortical areas convey predictions of lower-level activities. The bottom-up, feedforward connections in turn convey the errors between top-down predictions and actual activities. These errors are used to correct current estimates of the state of the world and generate new predictions. Through the objective of minimizing prediction errors, predictive coding provides a functional explanation for a wide range of neural responses and many aspects of brain organization

Analysis of Dislocation Mechanism for Melting of Elements: Pressure Dependence

In the framework of melting as a dislocation-mediated phase transition we derive an equation for the pressure dependence of the melting temperatures of the elements valid up to pressures of order their ambient bulk moduli. Melting curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar, Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated melting curves are in good agreement with existing data. We also discuss the apparent equivalence of our melting relation and the Lindemann criterion, and the lack of the rigorous proof of their equivalence. We show that the would-be mathematical equivalence of both formulas must manifest itself in a new relation between the Gr\"{u}neisen constant, bulk and shear moduli, and the pressure derivative of the shear modulus.Comment: 19 pages, LaTeX, 9 eps figure

Vlasov scaling for the Glauber dynamics in continuum

We consider Vlasov-type scaling for the Glauber dynamics in continuum with a positive integrable potential, and construct rescaled and limiting evolutions of correlation functions. Convergence to the limiting evolution for the positive density system in infinite volume is shown. Chaos preservation property of this evolution gives a possibility to derive a non-linear Vlasov-type equation for the particle density of the limiting system.Comment: 32 page

Effects of barley based diets with three different rumen degradable protein balances on performance and carcass characteristics of feedlot steers

Non-Peer ReviewedThe objective of this study was to determine the effect of dietary optimal or suboptimal rumen available protein to energy ratios generated by substituting barley grain by wheat –based dried distillers’ grains with soluble (wDDGS) on finishing feedlot cattle performance. Three hundred crossbred steers were randomly assigned to twelve pens (25 heads in each pen) and fed one of three grain based finishing diets with: (i) negative rumen degradable protein balance (DPB; -12 g/kg DM); (ii) neutral DPB (0 g/kg DM); and (iii) positive DPB (14 g/kg DM). Ration with negative DPB (conventional feed) contained 88.3% rolled barley grain, 7.0% supplement and 4.7% barley silage. For the rations with neutral - and positive DPB, the barley grain was replaced by wDDGS at 11 or 22% of the diet, respectively. Over the 131-d finishing period, animal performance and carcass traits were similar among steers fed either of 3 finishing diets. In conclusion, barley grain in common feedlot diets can be substituted by wDDGS up to 22%, without altering steer performance and carcass characteristics

Expressive probabilistic sampling in recurrent neural networks

In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for $\textit{recurrent}$ neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples (sampler-only network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits reservoir-sampler networks (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based brain models

An analysis of Australia's carbon pollution reduction scheme

The authors review the decision-making since the Labour Government came into office (November 2007). The Australian Government’s ‘Carbon Pollution Reduction Scheme’ White Paper (15 December 2008) proposes that an Australian Emissions Trading Scheme (AETS) be implemented in mid-2010. Acknowledging that the scheme is comprehensive, the paper finds that in many cases, Australia will take a softer approach to climate change through the AETS than the European Union ETS(EUETS). The paper assesses key issues in the White Paper such as emissions reduction targets, GHG coverage, sectoral coverage, inclusion of unlimited quantities of offsets from Kyoto international markets and exclusion of deforestation activities