Glimpses of the Octonions and Quaternions History and Today’s Applications in Quantum Physics

Before we dive in this essay into the accessibility stream of nowadays indicatory applications of octonions and quaternions to computer and other sciences and to quantum physics (see for example [50-53], [41], [33]) and to Clifford algebras (see for example [17,16], 18) let us focus for a while on the crucially relevant events for today’s revival on interest to nonassociativities while the role of associative quaternions in eight periodicity constructive classification of associative Clifford algebras is now a text-book knowledge.     

Explanation in Metaphysics?

Arguments from explanation, i.e. arguments in which the explanatory value of a hypothesis or premise is appealed to, are common in science, and explanatory considerations are becoming more popular in metaphysics. The paper begins by arguing that explanatory arguments in science—even when these are metaphysical explanations—may fail to be explanatory in metaphysics; there is a distinction to be drawn between metaphysical explanation and explanation in metaphysics. This makes it potentially problematic to deploy arguments from explanation in, for instance, metaphysics of science. Part of this problem has its source in that the explanatory concept differs between contexts. The paper discusses a few explanatory concepts and their corresponding arguments from explanation. Towards the end of the paper, I identify two allegedly explanatory arguments in metaphysical discourse by the concluding decisions they give rise to: the rejection of X as a metaphysical fact if X does not explain anything (the argument from explanatory inability) and the rejection of X as a metaphysical fact if X can be non-metaphysically explained (the argument from the non-metaphysically explained). I ask: What kind of concept of explanation do these arguments rely upon, and is that concept suited to the metaphysical task? Two recent examples of these arguments are used as illustration. The preliminary conclusion is that several of the strengths of arguments from explanation in science seem not to be present in metaphysical contexts.     

WatchMan project—A Python CASE framework for High Energy Physics data analysis in the LHC era

The world's largest particle collider LHC is taking data at CERN, in Geneva, providing a huge amount of data to be looked at, of the order of several Petabytes per year. Nowadays, Data Analysis in High Energy Physics (HEP) means handling billions of experimental data in custom software frameworks. Physicists have to access and select data interacting with the experiment using dedicated tools; they also have to apply filter functions and analysis algorithms to test hypotheses about the physics underlain. Modern HEP experiments rely on complex software frameworks, hence writing the analysis code is not always an easy task, and the learning curve is usually quite steep. Moreover each hypothesis requires a dedicated analysis, in order to have a better control on it and to be able to validate the results among different groups of researchers. And the writing of so many analyses can be error prone and time consuming.In order to ease the writing of such data analysis code, we built a software-generator: the idea is that the user inserts the settings of the physics analyses, and the final analysis code is automatically and dynamically generated, ready to be run on data. Python helped us to build such a package. Its high-level and dynamic nature, together with its flexibility and prototyping speed are the key features which made our choice.So we conceived and developed WatchMan, a Python CASE (Computer-Aided Software Engineering) framework to automatically generate reliable, easy to maintain and easy to validate HEP data analysis code.     

Voter model in a random environment in ? d

We consider the voter model with flip rates determined by {?? _e , e ?? E _d }, where E _d is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice ? ^d . Suppose that {?? _e , e ?? E _d } are independent and identically distributed (i.i.d.) random variables satisfying ?? _e ? 1. We prove that when d = 2, almost surely for all random environments, the voter model has only two extremal invariant measures: ?? ₀ and ?? ₁.     

A Bernstein type theorem in ? × ? n

In this paper, as suitable application of the so-called Omori-Yau generalized maximum principle, we obtain a Bernstein type theorem concerning to complete hypersurfaces immersed with constant mean curvature in the product space ℝ × ℍ ⁿ . Furthermore, we treat the case that such hypersurfaces are vertical graphs.     

Finite axiomatizability in ?ukasiewicz logic

We classify every finitely axiomatizable theory in infinite-valued propositional ?ukasiewicz logic by an abstract simplicial complex (V,Σ) equipped with a weight function ω:V→{1,2,…}. Using the W?odarczyk–Morelli solution of the weak Oda conjecture for toric varieties, we then construct a Turing computable one–one correspondence between (Alexander) equivalence classes of weighted abstract simplicial complexes, and equivalence classes of finitely axiomatizable theories, two theories being equivalent if their Lindenbaum algebras are isomorphic. We discuss the relationship between our classification and Markov’s undecidability theorem for PL-homeomorphism of rational polyhedra.     

Is simulation in health different?

It is often stated that health simulation is quite different and even that it is more difficult than in other sectors. But is simulation in health really different to simulation elsewhere? In this paper we explore this question through a survey of simulation modellers and academics. We elicit their opinions across a range of factors concerning the difficulties of health modelling against modelling in other domains. The analysis considers the responses of the whole group of respondents and the sub-group of respondents who have experience both in and outside of health modelling. The results show that overall, there is a perception that health modelling is different and that it is more difficult across a range of factors. The implications for simulation research and practice in health are discussed.     

Independence of ? in Lafforgue's theorem

Let X be a smooth curve over a finite field of characteristic p, let ?≠p be a prime number, and let be an irreducible lisse -sheaf on X whose determinant is of finite order. By a theorem of L. Lafforgue, for each prime number ?′≠p, there exists an irreducible lisse -sheaf on X which is compatible with , in the sense that at every closed point x of X, the characteristic polynomials of Frobenius at x for and are equal. We prove an “independence of ?” assertion on the fields of definition of these irreducible ?′-adic sheaves : namely, that there exists a number field F such that for any prime number ?′≠p, the -sheaf above is defined over the completion of F at one of its ?′-adic places.     

What is reasoning in geometry?

The word "reasoning"is used in a very broad range of meanings. Any move, any trial and error , any procedure to solve a difficulty is often considered as a form of reasoning. More specifically any process which enables us to draw new information from given information is considered as "reasoning". In this way, induction, abduction and inference are various kinds of reasoning. From a cognitive point of view, there are different kinds of processes that depend on the form in which information is presented and also on the way information can be organized.     

Grossmann and Millán-Puelles on the Argument from Physics

The paper focuses on Reinhardt Grossmann’s analysis of the Argument from Physics, as well as the analysis by the Spanish philosopher Antonio Millán-Puelles, in an attempt to assess the validity of the Argument on the basis of their respective critical views. Both authors agree in perceptual realism and in the need to distinguish between the scope and objects of Physics and the ordinary objects of natural perception. Their criticisms mainly concern the inappropriate use of the principle of reduction in the Argument and the distinction between secondary and primary qualities, which is, according to Grossmann, one of the sources of idealism and phenomenalism.     

Fuzzy rough sets in ?ostak sense

In this paper, we defined the fuzzy operator Φ_λin a fuzzy ideal approximation space (X, R, I) associated with a fuzzy rough set λ in ?ostak sense. Associated with Φ_λ, there are fuzzy ideal interior and closure operators int_Φ^λand cl_Φ^λ, respectively. r-fuzzy separation axioms, r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation ...     

Denting points in K?the-Bochner spaces

A characterization of denting points in the unit ball of Köthe-Bochner spaceE(X) is given. This characterization is a generalization of some analogous theorems for Bochner and Musielak Orlicz spaces and it is compared to similar known results concerning strongly extreme points inE(X).Scholar of Ministere de la Recherche et de la Technologie of France, while on leave from Technical University at Pozna, Poland.     

Innovative research in OR/MS?

This paper is a contribution to the continuing debate about research priorities and publications in OR/MS. It categorises research publications in several different ways. First it uses approaches suggested in the information systems and operations management literature. It then takes previous examinations of leading OR/MS journals to gain a different perspective on the same issues. Finally, it uses a multi-faceted view of OR/MS to try to capture its full richness. These analyses confirm the view that much published research in OR is unengaged and focuses on decision mathematics or optimisation, apparently for its own sake. That is, most papers published in the leading OR/MS journals take little or no account of how their findings might be used in practice, nor do they express much concern about this issue. The reasons for this state of affairs are discussed, so as to consider whether a change might be overdue.     

Tautness and Fatou Components in ?2

Hyperbolicity played an important role in the classification of Fatou components for rational functions in the Riemann sphere. In higher dimensions Fatou components are not nearly as well understood. We investigate the Kobayashi completeness and tautness of invariant Fatou components for holomorphic endomorphisms of ?² and for Hénon mappings. We show that basins of attraction and domains with an attracting Riemann surface, previously known to be taut, are also complete, which is strictly stronger. We also prove tautness for a class of Siegel domains.     

A Kuhnian Crisis in Management Science?

A survey of the Journal of the O.R. Society in 1978 shows that Ackoff's papers were part of a quite widespread and often pessimistic debate about the practical success of O.R. A similar survey for 1968 shows, on the other hand, a widespread mood of optimism. It is suggested that O.R. is now in a period of crisis analogous to that described by Kuhn in the Natural Sciences, when the dominant framework of assumptions appears to fail in relation to important problems. When such failures persist, alternative frameworks are proposed challenging the hitherto accepted view, and an increasingly wide-ranging debate develops. Many of the features of such debates, as outlined by Kuhn, seem to be present in the current controversy within O.R. More specifically, it seems possible in O.R. and related fields to identify three rival sets of proposals, which may be labelled official, reformist (e.g. Ackoffian) and revolutionary. However, the debate in O.R. differs from that in the Natural Sciences because it is not just about the best means of understanding the empirical world. It is also about the type of social world to be constructed through the framework of assumptions adopted. Our view is that in the current debate, proponents of the reformist stance will probably win. However, this may be very much an interim solution.