Harold Jeffreys's Theory of Probability Revisited

Published exactly seventy years ago, Jeffreys's Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the derivation of noninformative priors as well as on the scaling of Bayes factors have had a lasting impact on the field. However, the book reflects the characteristics of the time, especially in terms of mathematical rigor. In this paper we point out the fundamental aspects of this reference work, especially the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based on functional divergences. Our major aim here is to help modern readers in navigating in this difficult text and in concentrating on passages that are still relevant today.Comment: This paper commented in: [arXiv:1001.2967], [arXiv:1001.2968], [arXiv:1001.2970], [arXiv:1001.2975], [arXiv:1001.2985], [arXiv:1001.3073]. Rejoinder in [arXiv:0909.1008]. Published in at http://dx.doi.org/10.1214/09-STS284 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical multi-moment bifurcations in random delay coupled swarms

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments

Reactor physics modelling of accident tolerant fuel for LWRs using ANSWERS codes

The majority of nuclear reactors operating in the world today and similarly the majority of near-term new build reactors will be LWRs. These currently accommodate traditional Zr clad UO2/ PuO2 fuel designs which have an excellent performance record for normal operation and most transients. However, the events at Fukushima culminated in significant hydrogen production and hydrogen explosions, resulting from high temperature Zr/steam interaction following core uncovering for an extended period. These events have resulted in increased emphasis towards developing more accident tolerant fuels (ATFs)-clad systems, particularly for current and near-term build LWRs. R&D programmes are underway in the US and elsewhere to develop ATFs and the UK is engaging in these international programmes. Candidate advanced fuel materials include uranium nitride (UN) and uranium silicide (U3Si2). Candidate cladding materials include advanced stainless steel (FeCrAl) and silicon carbide. The UK has a long history in industrial fuel manufacture and fabrication for a wide range of reactor systems including LWRs. This is supported by a national infrastructure to perform experimental and theoretical R&D in fuel performance, fuel transient behaviour and reactor physics. In this paper, an analysis of the Integral Inherently Safe LW R design (I2S-LWR), a reactor concept developed by an international collaboration led by the Georgia Institute of Technology, within a U.S. DOE Nuclear Energy University Program (NEUP) Integrated Research Project (IRP) is considered. The analysis is performed using the ANSWERS reactor physics code WIMS and the EDF Energy core simulator PANTHER by researchers at the University of Cambridge. The I2S-LWR is an advanced 2850 MWt integral PWR with inherent safety features. In order to enhance the safety features, the baseline fuel and cladding materials that were chosen for the I2S- LWR design are U3Si2 and advanced stainless steel respectively. In addition, the I S-LWR design adopts an integral configuration and a fully passive emergency decay heat removal system to provide indefinite cooling capability for a class of accidents. This paper presents the equilibrium cycle core design and reactor physics behaviour of the I2S-LWR with U3Si2 and the advanced steel cladding. The results were obtained using the traditional two-stage approach, in which homogenized macroscopic cross-section sets were generated by WIMS and applied in a full 3D core solution with PANTHER. The results obtained with WIMS/PANTHER were compared against the Monte Carlo Serpent code developed by VTT and previously reported results for the I2S-LWR. The results were found to be in a good agreement (e.g. < 200 pcm in reactivity) among the compared codes, giving confidence that the WIMS/PANTHER reactor physics package can be reliably used in modelling LWRs with ATFs.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1051/epjn/201601

Advances on Matroid Secretary Problems: Free Order Model and Laminar Case

The most well-known conjecture in the context of matroid secretary problems claims the existence of a constant-factor approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true, when assuming that the assignment of weights to the secretaries is not adversarial but uniformly random (Soto [SODA 2011], Oveis Gharan and Vondr\'ak [ESA 2011]). However, so far, there was no variant of the matroid secretary problem with adversarial weight assignment for which a constant-factor approximation was found. We address this point by presenting a 9-approximation for the \emph{free order model}, a model suggested shortly after the introduction of the matroid secretary problem, and for which no constant-factor approximation was known so far. The free order model is a relaxed version of the original matroid secretary problem, with the only difference that one can choose the order in which secretaries are interviewed. Furthermore, we consider the classical matroid secretary problem for the special case of laminar matroids. Only recently, a constant-factor approximation has been found for this case, using a clever but rather involved method and analysis (Im and Wang, [SODA 2011]) that leads to a 16000/3-approximation. This is arguably the most involved special case of the matroid secretary problem for which a constant-factor approximation is known. We present a considerably simpler and stronger $3\sqrt{3}e\approx 14.12$-approximation, based on reducing the problem to a matroid secretary problem on a partition matroid

A New Linear Logic for Deadlock-Free Session-Typed Processes

The π -calculus, viewed as a core concurrent programming language, has been used as the target of much research on type systems for concurrency. In this paper we propose a new type system for deadlock-free session-typed π -calculus processes, by integrating two separate lines of work. The first is the propositions-as-types approach by Caires and Pfenning, which provides a linear logic foundation for session types and guarantees deadlock-freedom by forbidding cyclic process connections. The second is Kobayashi’s approach in which types are annotated with priorities so that the type system can check whether or not processes contain genuine cyclic dependencies between communication operations. We combine these two techniques for the first time, and define a new and more expressive variant of classical linear logic with a proof assignment that gives a session type system with Kobayashi-style priorities. This can be seen in three ways: (i) as a new linear logic in which cyclic structures can be derived and a CYCLE -elimination theorem generalises CUT -elimination; (ii) as a logically-based session type system, which is more expressive than Caires and Pfenning’s; (iii) as a logical foundation for Kobayashi’s system, bringing it into the sphere of the propositions-as-types paradigm

The interaction between policy and education using stroke as an example

This paper discusses the interaction between healthcare policy at the European, UK and Scottish levels and the funding of education that underpins specific health policy priorities. Stroke is used throughout to illustrate the relationship between a designated European and UK health priority and the translation of that priority into clinical delivery. The necessity to build a responsive and sustainable culture to address the healthcare education that underpins changing healthcare policies is emphasized

Black hole production in tachyonic preheating

We present fully non-linear simulations of a self-interacting scalar field in the early universe undergoing tachyonic preheating. We find that density perturbations on sub-horizon scales which are amplified by tachyonic instability maintain long range correlations even during the succeeding parametric resonance, in contrast to the standard models of preheating dominated by parametric resonance. As a result the final spectrum exhibits memory and is not universal in shape. We find that throughout the subsequent era of parametric resonance the equation of state of the universe is almost dust-like, hence the Jeans wavelength is much smaller than the horizon scale. If our 2D simulations are accurate reflections of the situation in 3D, then there are wide regions of parameter space ruled out by over-production of black holes. It is likely however that realistic parameter values, consistent with COBE/WMAP normalisation, are safetly outside this black hole over-production region.Comment: 6pages, 7figures, figures correcte

Spontaneous CP Violation at the Electroweak Scale

Utilizing results on the cosmology of anomalous discrete symmetries we show that models of spontaneous CP violation can in principle avoid the domain wall problem first pointed out by Zel'dovich, Kobzarev and Okun. A small but nonzero $\theta_{QCD}$ explicitly breaks CP and can lift the degeneracy of the two CP conjugate vacua through nonperturbative effects so that the domain walls become unstable, but survive to cosmologically interesting epochs. We explore the viability of spontaneous CP violation in the context of two Higgs models, and find that the invisible axion solution of the strong CP problem cannot be implemented without further extensions of the Higgs sector.Comment: 10 page