A model is given of the development of a radialised larval head pattern inLimnaea stagnalis, as it occurs under certain experimental conditions. It is assumed that the differentiation of the pattern is entirely based on cell-internal factors, and that the internal state of each cell is dependent on that of its progenitor and on the direction of the division by which it is produced. This internal state determines the direction of the subsequent division or the nature of the cell's differentiation. (...) Cell interactions, which are during this period of minor importance, are left out of consideration. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:HUME, THE CAUSAL PRINCIPLE, AN'D KEMP SMITH When we say of a proposition that it is possible, we sometimes mean no more than that it is logically possible, that is, consistent with itself. A proposition can be possible in stronger senses than this, but not in any weaker one. For a sense of "p is possible" that did not entail "p is self-consistent, "would have to be a sense (...) of "p is possible" which was consistent with "p is self-inconsistent" And it is obvious that there can be no such sense as that. One of the stronger senses in which a proposition can be possible is this: consistent (with itself and in addition) with every observation-statement. (I mean by an observationstatement, a proposition which, if it were true, could in principle be discovered by experience to be true.) If a proposition? is contingent, (that is, neither necessarily true??t necessarily false), then its negation (its contradictory) not-p is contingent too; and since contingent, not necessarily false; and since not necessarily false, consistent with itself. So, given any contingent propositions, its falsity is among those propositions which are possible in the first and weak sense mentioned above. If a proposition? is not only contingent but unverifiable,(that is, not deducible from any observation- statement), then not-p is consistent both with itself and with every observation -statement. So, given any unverifiable contingent proposition, its falsity is among those propositions which are possible in the second and stronger sense mentioned above. Some stock examples. "Whatever is a raven is black" is contingent, and its falsity therefore possible in the first sense; so too is its contradictory "There are such things as non-black ravens" contingent, and its falsity possible in the first sense. But the latter proposition is not unverifiable, since there are observation-statements from which it is deducible. ("There are such things as green ravens", for example; or "A green raven was in captivity at Taronga Park Zoo in January 31st 1975".) The former proposition, on the other hand, is not only contingent but unverifiable; since there are no observation -statements from which it is deducible. Hence, "whatever is a raven is black" is a proposition the falsity of which is possible both in the first and in the second sense noticed above. A third and still stronger sense in which a proposition can be possible is the following:? is possible if and only if (p is consistent with itself,every observation-statement is consistent with p, and in addition)? is neither more nor less probable in relation to the conjunction of e and n, where e is any observation-statement and? any necessary truth, than it is in relation to? alone. The last condition may be expressed, symbolically, as "P(p/n.e) » P(p/n) for all necessarily true? and all observation-statements e"; or in Carnap' s phrase as, "every observation- statement is initially irrelevant to p." Some examples will quickly make the idea of initial irrelevance, and its opposite, more familiar; and hence will make the third sense of "p is possible" more familiar. Let? be any necessary truth and e any observation-statement. Now let? be, for- example,some necessarily false proposition; then, since P(p/n) « o = P(p/n.e), e is initially irrelevant to p. Or let? be necessarily true; then, since P(p/n) ¦ 1 = P(p/n.e), e is again initially irrelevant to p. Again, let? be "Whatever is a raven is black": then some observation- statements e are initially relevant to p. For if e is "This raven is black," for example, P(p/n.e)>P(p/n) ; or at any rate, that is what we think if we are not inductive sceptic?. Again, if? is "The Holy Ghost proceeds from the Father and the Son", it is at least very plausible to say that every observational e is initially irrelevant to p; since there appears to be no observational e such that P(p/n.e)>P(p/n), or P(p/n.e). (shrink)

The notion that our society, its education system and its intellectual life, is characterised by a split between two cultures – the arts or humanities on one hand and the sciences on the other – has a long history. But it was C. P. Snow's Rede lecture of 1959 that brought it to prominence and began a public debate that is still raging in the media today. This fiftieth anniversary printing of The Two Cultures and its successor piece, A Second (...) Look features an introduction by Stefan Collini, charting the history and context of the debate, its implications and its afterlife. The importance of science and technology in policy run largely by non-scientists, the future for education and research, and the problem of fragmentation threatening hopes for a common culture are just some of the subjects discussed. (shrink)

A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated (...) reproduction numbers are greater than unity. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase in antiretroviral use. (shrink)

We formalise the notion of those infinite binary sequences z that admit a single program P which expresses the entire algorithmical structure of z. Such a program P minimizes the information which must be used in a relative computation for z. We propose two concepts with different strength for this notion, the learnable and the super-learnable sequences. We establish three different equivalent characterizations of learnable (super-learnable, resp.) sequences. In particular, we prove that a sequences z is learnable (super-learnable, resp.) if (...) and only if there is a computable probability measure p such that p is Schnorr (Martin-Lof, resp.) p-random. There is a recursively enumerable sequence which is not learnable. The learnable sequences are invariant with respect to all total and effective transformations of infinite binary sequences. (shrink)

Between 1069, the year of his arrival at St. Martin in Mainz, where he spent the rest of his life in voluntary enclosure in a cell, and his death in 1082, the Irish monk Marianus Scottus dedicated countless hours to assembling the most sophisticated and comprehensive work on historical chronology that had ever been produced by a Latin writer up to that time. The fruits of his labors became a massive world chronicle, completed in 1076, whose most famous innovation consisted (...) in a far-reaching correction to the Christian, or “common,” era, which had been introduced by Dionysius Exiguus in the sixth century. Having compared the data of the Easter computus with the chronological parameters traditionally associated with the passion of Christ—the fifteenth day of the moon on Friday, 25 March—Marianus found that the only year in which the numbers could be made to fit was AD 12 rather than the traditionally accepted AD 34. As a result, he decided to predate the life of Jesus by twenty-two years, assigning his birth to the year corresponding to 22 BC. This gave rise to a new “corrected” era , which he used alongside its Dionysiac equivalent. (shrink)