Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the \emph{exact} posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this paper: when the likelihood has some \emph{local} regularity, the number of model evaluations per MCMC step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ODE and PDE inference problems, with both synthetic and real data.Comment: A major update of the theory and example

Aerodynamical Investigations on Reaction Turbine Blades

So far no theory of the Reaction Turbine has as yet been investigated which is capable of clarifying fully the effect of such factors as the number of blades, the blade angle, the blade pitch and the breadth of the blade upon the action of these machines. It Is known that the "lift" of biplanes and triplanes per unit of wing surface is Inferior to that of a monoplane, and that the degree of departure depends upon the gap-chord ratio. Published data indicate that the lift increases with increasing gap, apparently towards some limiting value. Regarding steam turbine wheels as rings of multiplanes, it may be asked "Is there any direct evidence that the torque on each blade Is influenced by the presence of the other blades?" Many experiments have been made to determine the optimum circumferential pitch for a given blade shape, but most of these have aimed simply at arriving empirically at the best efficiency, without inquiry into the factors involved. The present investigations were carried out on Model Reaction Blades reproduced several times the actual full size so that the Reynold's number is maintained at a value of interest in turbine design, but with comparatively low air speeds usual in WIND TUNNEL work, to examine the effects of the number of blades, the blade pitch and the blade angle

Magnetization reversal and spin dynamics exchange in biased F/AF bilayers probed with complex permeability spectra

The spin dynamics of the ferromagnetic pinned layer of ferro-antiferromagnetic coupled NiFe/MnNi bilayers is investigated in a broad frequency range (30 MHz-6 GHz). A phenomenological model based on the Landau-Lifshitz equation for the complex permeability of the F/AF bilayer is proposed. The experimental results are compared to theoretical predictions. We show that the resonance frequencies, measured during the magnetization, are likewise hysteretic.Comment: 4 pages, 4 figure

Evolution Of Special Ruled Surfaces Via The Evolution Of Their Directrices In Euclidean 3-Space E3

In this paper, evolutions of ruled surfaces that are generated by the normal and binormal vector fields of space curve (normal and binormal surfaces) are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrices. Geometric visualization of these ruled surfaces are presented. In addition, the conditions which make these surfaces of types inextensible, developable and minimal are obtained

Which one is better: presentation-based or content-based math search?

Mathematical content is a valuable information source and retrieving this content has become an important issue. This paper compares two searching strategies for math expressions: presentation-based and content-based approaches. Presentation-based search uses state-of-the-art math search system while content-based search uses semantic enrichment of math expressions to convert math expressions into their content forms and searching is done using these content-based expressions. By considering the meaning of math expressions, the quality of search system is improved over presentation-based systems

The Path to Entrepreneurship: The Role of Social Networks in Driving Entrepreneurial Learning and Education

This research aims to examine the extent to which the way entrepreneurs learn is reflected in entrepreneurship education, highlighting the existing gap between the literature on entrepreneurial learning and the practice of entrepreneurship education. To explore entrepreneurial learning in-depth, we adopted an interpretivist-constructivist approach that involves participant observation at coworking spaces and semi-structured interviews with entrepreneurs. Data were subsequently analyzed using thematic analysis. Major findings indicate that social networks play a vital role in facilitating entrepreneurial learning, with context and network serving as essential learning mechanisms. However, these elements are often disregarded in traditional entrepreneurship education approaches. This study highlights a gap in the literature where the focus of entrepreneurial learning is primarily on entrepreneurs, while entrepreneurship education primarily focuses on students and educators. The study’s contribution is its emphasis on the importance of social networks in entrepreneurial learning and its potential for redesigning entrepreneurship education. By bridging the gap between entrepreneurial learning and entrepreneurship education, it is possible to create educational approaches that more closely mimic how entrepreneurs learn in real life, potentially leading to more impactful entrepreneurial activity

Long Term Culture of Hepatocytes of Some Fish Species of the Chesapeake Bay

The liver is an important site of metabolism and effects of toxic chemicals. This makes it an important organ for tumorigenesis studies. This study was aimed at investigating the optimal culture characteristics of liver cells derived from some indigenous Chesapeake Bay fish species. Hepatocytes from Atlantic -menhaden (Brevootia tyraMus), toadfish (Opsanus tau), croaker (Micropogonius undulatus), and hogchocker (Trinectes maculatus) were isolated using an enzymatic dispersion technique. The highest yield was obtained from toadfish livers (14.9±5. lx 1 o5 cells/g oflive weight) and the lowest was from the croaker (5.9±3. lx 1 o5 cells/g of live body weight). The percentage of hepatocytes in cell preparations exceeded 90% except for the toadfish liver cells preparation (82.3%). Freshly isolated hepatocytes were globular with irregular contour and occurred as individual cells or small clusters of 2-30 cells. A confluent monolayer of attached cells was obtained after two weeks of incubation. An osmolality of 325 m Osm/kg best supported the multiplication of hepatocytes of the four fish species. While the optimum temperature for hogchocker and toadfish hepatocytes appeared to be 33oC; it ranged from 21-27oC for menhaden and croaker. The medium that best supported the growth of culture The potential of long term hepatocyte culture using fish of Chesapeake Bay will enable further studies on the activation and detoxification processes of xenobiotics and, therefore, help in understanding pollution related neoplasia and diseaseshttps://scholarworks.wm.edu/vimsbooks/1181/thumbnail.jp

Bayesian Probabilities and the Histories Algebra

We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes.Comment: 10 pages, accepted by Int. J. Theo. Phys. Feb 200