It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the theorem.

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic (...) types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality. (shrink)

A diagrammatic representation is given of the 24 rays of Peres that makes it easy to pick out all the 512 parity proofs of the Kochen-Specker theorem contained in them. The origin of this representation in the four-dimensional geometry of the rays is pointed out.

It is shown how the 300 rays associated with the antipodal pairs of vertices of a 120-cell (a four-dimensional regular polytope) can be used to give numerous “parity proofs” of the Kochen–Specker theorem ruling out the existence of noncontextual hidden variables theories. The symmetries of the 120-cell are exploited to give a simple construction of its Kochen–Specker diagram, which is exhibited in the form of a “basis table” showing all the orthogonalities between its rays. The basis table consists of 675 (...) bases (a basis being a set of four mutually orthogonal rays), but all the bases can be written down from the few listed in this paper using some simple rules. The basis table is shown to contain a wide variety of parity proofs, ranging from 19 bases (or contexts) at the low end to 41 bases at the high end. Some explicit examples of these proofs are given, and their implications are discussed. (shrink)

A Principle of fundamental importance, if it is valid, for the interpretation of the Pentekontaetia is laid down by the authors of A. T.L. iii in its most rigorous terms: it is that Thucydides has set events ‘in proper order … without any deviation whatever’. The conclusion appears to the present writer to be founded ultimately on a false assumption about Thucydides' purpose in these chapters, namely that he set out to write an outline history of the period of fifty (...) years to which he refers in 118.2 and, in effect, in 97. An examination of these passages reveals that it is not the outline of a period as a period that is offered, but rather the account of a particular theme or process falling within the period: his purpose in presenting the theme there defined is to be seen from the setting of the excursus as a unit in Bk. I rather than from the statement in 97.2: the due significance of this last, and of the demarcation of a period in 118. 2, is to be seen only in this wider context. (shrink)

An epistemic logic is built up on the basis of an analysis of two skeptical arguments. the method used is to first construct an inference relation appropriate to epistemic contexts and introduce "a knows that..." as an operator giving rise to sentences closed with respect to this new concept of inference. soundness and completeness proofs are provided using auxiliary three-valued valuations.

. Book Reviews. International Journal of Philosophical Studies: Vol. 8, No. 1, pp. 125-145.

Structural change in the cellular prion protein, PrPC to a ProteinaseK‐resistant β‐sheet‐rich insoluble form PrPSC and its accumulation have been considered to be central to the pathogenesis of the prion diseases (TSE). In a recent paper, Deleault et al have shown that specific endogenous RNA molecules can induce in vitro structural conversion of endogenous PrPC to PrPSC.1 Small highly structured synthetic RNAs can also induce this conversion process.2 However, recent in vivo results show that PrPSC is not directly involved in (...) the prion pathogenesis.3 It is possible, however, that nucleic‐acid‐induced PrPSC associated with the inducer nucleic acid could be the components of the infectious agent. BioEssays 26:469–473, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

Study on Īśvarakr̥ṣṇa's Sāṅkhyakārikā, basic work of the Sankhya school in Hindu philosophy, and its commentary Sāṅkhyataruvasanta by Mudumba Narasimhacarya, 1842-1928.

The purpose of this article is to comprehensively review studies that have examined the relation between diet and childhood obesity. The review specifically considers the roles of total energy intake and energy density; dietary composition; individual foods, food groups, and dietary patterns; beverage consumption; and eating behaviors. The paper also discusses methodological considerations and future research directions and concludes by summarizing the evidence presented and highlighting the ethical issues surrounding providing dietary advice.

Childhood obesity is a serious problem for increasing numbers of children around the world. According to the International Obesity Task Force, 1 of 10 schoolaged children worldwide is overweight or obese, a number totaling 155 million; of these, 2-3% are obese. Prevalence is highest in the Americas and Europe, followed by the Near/Middle East, with smaller but growing numbers in the Asia-Pacific and Sub-Saharan regions of the world.In the United States, which provides the data for much of this report, prevalence (...) continues to rise. The most recent nationally representative data indicate that 33.6% of individuals aged 2-19 years were overweight and 17.1% were at risk for overweight in 2003-2004, compared to 28.2% and 13.9% in 1999-2000, respectively. In this age group, the prevalence of overweight or at risk for overweight was highest among Mexican Americans, followed by Non-Hispanic blacks and Non-Hispanic whites, and a higher percentage of males were overweight compared to females. (shrink)

Desmosomes are junctions involved in intercellular adhesion of epithelial cells and hemidesmosomes are junctions involved in adhesion of epithelia to basement membranes. Both are characterised at the ultrastructural level by dense cytoplasmic plaques which are linked to the intermediate filament cytoskeleton of the cells. The plaques strongly resemble each other suggesting a relationship between the two kinds of junctions, as implied by their names. Recent characterisation of the molecular components of the junctions shows they are, in fact, quite unrelated implying (...) that structural similarity is fortuitous. The molecular biology raises many fascinating problems relating to their structure and function. (shrink)