Updating beliefs about variables given new information on how those variables relate

Bayesian techniques specify how to update beliefs about a variable given information on that variable or related variables. In many cases, statistical analyses also provide information about the relationship between variables, but the Borel Paradox prohibits many natural ways of updating beliefs conditioned on information about a relationship. This paper presents a method by which beliefs can be updated without violating the Borel Paradox under certain circumstances. We apply our approach to relationships specified by a statistical model (i.e., regression), and relationships described by statistical simulation.     

Apportionment methods

Most democratic countries use apportionment methods to transform election results into whole numbers, which usually give the number of seats in a legislative body that the parties obtained. Which apportionment method does this best can be specified by measuring the error between the allocated result and the ideal proportion. We show how to find an apportionment method which is best suited to a given error function. We also discuss several properties of apportionment methods that have been labelled paradoxa. In particular we explain the highly publicised “Alabama” Paradox for the Hare/Hamilton method and show that other popular apportionment methods come with their very own paradoxa.     

Procyanidins are potent inhibitors of LOX-1: a new player in the French Paradox

Lectin-like oxidized LDL receptor-1 (LOX-1) is an endothelial receptor for oxidized LDL (oxLDL) and plays multiple roles in the development of cardiovascular diseases. We screened more than 400 foodstuff extracts for identifying materials that inhibit oxLDL binding to LOX-1. Results showed that 52 extracts inhibited LOX-1 by more than 70% in cell-free assays. Subsequent cell-based assays revealed that a variety of foodstuffs known to be rich in procyanidins such as grape seed extracts and apple polyphenols, potently inhibited oxLDL uptake in Chinese hamster ovary (CHO) cells expressing LOX-1. Indeed, purified procyanidins significantly inhibited oxLDL binding to LOX-1 while other ingredients of apple polyphenols did not. Moreover, chronic administration of oligomeric procyanidins suppressed lipid accumulation in vascular wall in hypertensive rats fed with high fat diet. These results suggest that procyanidins are LOX-1 inhibitors and LOX-1 inhibition might be a possible underlying mechanism of the well-known vascular protective effects of red wine, the French Paradox.     

Extragalactic background light: inventory of light throughout the cosmic history

The Extragalactic Background Light (EBL) stands for the mean surface brightness of the sky as we would see it from a representative vantage point in the intergalactic space outside of our Milky Way Galaxy. Averaged over the whole 4π solid angle it represents the collective light from all luminous matter radiated throughout the cosmic history. Part of the EBL is resolved into galaxies that, with the increasing detecting power of giant telescopes and sensitive detectors, are seen to deeper and deeper limiting magnitudes. This resolved part is now known to contribute a substantial or even the major part of the EBL. There still remains, however, the challenge of finding out to what extent galaxies too faint or too diffuse to be discerned individually, individual stars or emission by gas outside the galaxies, or – more speculatively – some hitherto unknown light sources such as decaying elementary particles are accounting for the remaining EBL. We review the recent progress that has been made in the measurement of EBL. The current photometric results suggest that there is, beyond the resolved galaxies, an EBL component that cannot be explained by diffuse galaxy halos or intergalactic stars.     

对伯川德博弈的正式数学证明与扩展运用

十九世纪法国经济学家伯川德提出了伯川德寡头模型,尽管中外学者对之给出了各种证明方法,但到目前为止还没有一个正式的数学证明.本文引入广义函数中的冲击函数和阶跃函数,很好地刻画两个寡头基于同质产品的间断需求函数,以代替不是很严密的用直观图形推演或分情况讨论式的证明,从而对伯川德博弈进行了严密的数学证明.本文证明:原始伯川德博弈的结论是近似的,严格上的纳什均衡点是双方都定价于比边际成本高的一个相同位置上,这是由于基于完全信息的理性行为,只有市场需求曲线为水平线时,均衡结果才收敛于伯川德博弈.因此,从完全信息出发,可以证明所谓的"伯川德博弈"只在有限条件下存在.另外,作为一个扩展应用,本文还运用冲击函数和阶跃函数的性质对斯威齐模型进行了数学证明,并演示了如何运用该方法对此类问题进行动态分析.     

Verification of the inverted temperature gradient condition via molecular dynamics simulation

We perform molecular dynamics simulations to verify the critical condition for the existence of an inverted temperature profile in the vapor between two liquid slabs at slightly different temperatures. Reasonable agreement is found between the kinetic theory based condition and simulations. The deviation from theory can be explained by deviation from ideal gas behavior on which the kinetic condition is based and by deviation in the MD from diffuse boundary conditions, which are used in deriving the kinetic condition.     

Generalizing the Disappearing Act: A Reply to István Aranyosi

In “The Reappearing Act” István Aranyosi postulates a new way of seeing to solve a puzzle posed in “The Disappearing Act;” an object that is exactly shaded can be seen simply by virtue of its contrast with its environment – just like a shadow. This object need not reflect, refract, absorb or block light. To undermine the motive for this heretical innovation, I generalize the puzzle to situations involving inexact shading. Aranyosi cannot extend his solution to these variations because he needs to conserve principles of camouflage. On the bright side, the solution to the puzzle that I propose in my book Seeing Dark Things does extend to these variations.     

Einstein—Podolsky—Rosen experiments: The structure of the probability space. II

In part I, we have described the Einstein-Podolsky-Rosen experiments in the framework of an axiomatic probability theory. In part II, we present the proofs of the results stated in part I.     

A Semantic Resolution of the Paradox of Analysis

The paradox of analysis has been a problem for analytic philosophers at least since Moore’s time, and it is especially significant for those who seek an account of analysis along classical lines. The present paper offers a new solution to the paradox, where a theory of analysis is given where (1) analysandum and analysans are distinct concepts, due to their failing to share the same conceptual form, yet (2) they are related in virtue of satisfying various semantic constraints on the analysis relation. Rather than distinguish between analysandum and analysans by appeal to epistemic considerations, the paper appeals to semantic considerations in giving a candidate account of the identity conditions for concepts. The distinctness of analysandum and analysans then serves to block the paradox in a straightforward way.