Solomonoff Induction Violates Nicod's Criterion

Nicod's criterion states that observing a black raven is evidence for the hypothesis H that all ravens are black. We show that Solomonoff induction does not satisfy Nicod's criterion: there are time steps in which observing black ravens decreases the belief in H. Moreover, while observing any computable infinite string compatible with H, the belief in H decreases infinitely often when using the unnormalized Solomonoff prior, but only finitely often when using the normalized Solomonoff prior. We argue that the fault is not with Solomonoff induction; instead we should reject Nicod's criterion.Comment: ALT 201

A hierarchy of avalanche models on arbitrary topography

We use the non-Cartesian, topography-based equations of mass and momentum balance for gravity driven frictional flows of Luca etal. (Math. Mod. Meth. Appl. Sci. 19, 127-171 (2009)) to motivate a study on various approximations of avalanche models for single-phase granular materials. By introducing scaling approximations we develop a hierarchy of model equations which differ by degrees in shallowness, basal curvature, peculiarity of constitutive formulation (non-Newtonian viscous fluids, Savage-Hutter model) and velocity profile parametrization. An interesting result is that differences due to the constitutive behaviour are largely eliminated by scaling approximations. Emphasis is on avalanche flows; however, most equations presented here can be used in the dynamics of other thin films on arbitrary surface

Waveguide containing a backward-wave slab

We have considered theoretically the waveguide properties of a plane two-layered waveguide, whose one layer is a usual magnetodielectric (forward-wave medium), but another one is a slab of so-called backward-wave material (BW-material), whose both permittivity and permeability are negative. We have analyzed the properties of eigenwaves in this waveguide. In particular, it was found that there exist waves of both TE and TM polarizations, whose fields decay exponentially from the interface of the two slabs inside both layers, and their slow-wave factor tends to infinity at small frequencies. Thus, this waveguiding system supports super-slow waves with extremely short wavelengthes, as compared to the free-space wavelength and the cross section size. Other peculiarities of the spectrum are also discussed

Generation of second mode solitary waves by the interaction of a first mode soliton with a sill

International audienceResults of an experimental and theoretical study of the interaction of a first mode internal solitary wave with a localised bottom topography (sill) are presented. Laboratory experiments have been performed in a 10m long and 0.33m wide channel filled with a stratified fluid. The interface between the two layers (fresh and salt water) is diffuse and has a finite thickness. Soliton-type disturbances of the interface having characteristics of the first baroclinic mode are generated at one channel end. They move along the channel and encounter an underwater obstacle (sill) in the middle of the channel, where they break into reflected and transmitted waves. Two types of internal waves are produced by the interaction: a fast first mode internal soliton and a slower (by a factor of approximately 3) second mode soliton-like wave. A numerical model, based on the two-dimensional Navier-Stokes equations in the Boussinesq approximation, is used tore produce the laboratory experiment. The detailed analysis of the horizontal and vertical structures of transmitted and reflected waves showed that the fast reflected and transmitted waves observed in the experiment can be interpreted as a first mode internal solitary wave whose characteristics are very close to those of the K-dV solitons. It is also demonstrated that the slow speed waves, generated during the interaction behind the first fast wave have vertical and horizontal structures very close to the second mode internal K-dV solitons

Multi-Instanton Effects in QCD Sum Rules for the Pion

Multi-instanton contributions to QCD sum rules for the pion are investigated within a framework which models the QCD vacuum as an instanton liquid. It is shown that in singular gauge the sum of planar diagrams in leading order of the $1/N_{c}$ expansion provides similar results as the effective single-instanton contribution. These effects are also analysed in regular gauge. Our findings confirm that at large distances the correlator functions are more adequately described in the singular gauge rather than in the regular one.Comment: 11 pages RevTeX is use

Polymer-based microfluidic device for measuring membrane protein activities

Functional assays of membrane proteins are becoming increasingly important, both in research and drug discovery applications. The majority of current assays use the patch-clamp technology to measure the activity of ion channels which are over-expressed in cells. In future, in vitro assay systems will be available, which use reconstituted membrane proteins in free-standing lipid bilayers suspended in nano- or micrometer-sized pores. Such functional assays require (1) expression, purification and reconstitution of the membrane protein of interest, (2) a reliable method for lipid bilayer formation and membrane protein integration, and (3) a sensitive detection system. For practical applications, especially for automation, the reliable and controllable transport of fluids is essential. In order to achieve a stable free-standing lipid bilayer, a pore diameter in the micro- to nanometer range is essential. Novel microfluidic devices were developed by bonding a thick (300μm) polyether ether ketone foil, bearing a channel structure, to a thin (12μm) foil with a micropore of about 10μm diameter and then utilized for the formation of stable, free-standing lipid bilayers within the pore. A bacterial voltage-gated potassium channel is integrated therein by fusion and the ion channel activity detected by voltage clam

Modeling Shallow Over-Saturated Mixtures on Arbitrary Rigid Topography

In this paper a system of depth-integrated equations for over-saturated debris flows on three-dimensional topography is derived. The lower layer is a saturated mixture of density preserving solid and fluid constituents, where the pore fluid is in excess, so that an upper fluid layer develops above the mixture layer. At the layer interface fluid mass exchange may exist and for this a parameterization is needed. The emphasis is on the description of the influence on the flow by the curvature of the basal surface, and not on proposing rheological models of the avalanching mass. To this end, a coordinate system fitted to the topography has been used to properly account for the geometry of the basal surface. Thus, the modeling equations have been written in terms of these coordinates, and then simplified by using (1) the depth-averaging technique and (2) ordering approximations in terms of an aspect ratio ϵ which accounts for the scale of the flowing mass. The ensuing equations have been complemented by closure relations, but any other such relations can be postulated. For a shallow two-layer debris with clean water in the upper layer, flowing on a slightly curved surface, the equilibrium free surface is shown to be horizonta

Steps towards the development of an experimentally verified simulation of pool nucleate boiling on a silicon wafer with artificial sites

Nucleate boiling is a very effective heat transfer cooling process, used in numerous industrial applications. Despite intensive research over decades, a reliable model of nucleate pool boiling is still not available. This paper presents a numerical and experimental investigation of nucleate boiling from artificial nucleation sites. The numerical investigation described in the first section of the paper is carried out by a hybrid mechanistic numerical code first developed at the University of Ljubljana to simulate the temperature field in a heated stainless steel plate with a large number of nucleation sites during pool boiling of water at atmospheric pressure. It is now being redeveloped to interpret experiments on pool boiling at artificial sites on a silicon plate and as a design tool to investigate different arrangements of sites to achieve high heat fluxes. The code combines full simulation of the temperature field in the solid wall with simplified models or correlations for processes in the liquid-vapour region. The current capabilities and limitations of the code are reviewed and improvements are discussed. Examples are given of the removal of computational constraints on the activation of sites in close proximity and improvements to the bubble growth model. Preliminary simulations are presented to compare the wall conditions to be used in the experiments on silicon at Edinburgh University with the conditions in current experiments on thin metal foils at Ljubljana. An experimental rig for boiling experiments with artificial cavities on a 0.38 mm thick silicon wafer immersed in FC-72, developed at Edinburgh University, is described in the second part of the paper

On the Computability of Solomonoff Induction and Knowledge-Seeking

Solomonoff induction is held as a gold standard for learning, but it is known to be incomputable. We quantify its incomputability by placing various flavors of Solomonoff's prior M in the arithmetical hierarchy. We also derive computability bounds for knowledge-seeking agents, and give a limit-computable weakly asymptotically optimal reinforcement learning agent.Comment: ALT 201