Experiments may not reveal their full import at the time that they are performed. The scientists who perform them usually are testing a specific hypothesis and quite often have specific expectations limiting the possible inferences that can be drawn from the experiment. Nonetheless, as Hacking has said, experiments have lives of their own. Those lives do not end with the initial report of the results and consequences of the experiment. Going back and rethinking the consequences of the experiment in a new context, theoretical or empirical, has great merit as a strategy for investigation and for scientific problem analysis. I apply this analysis to the interplay between Fizeau’s classic optical experiments and the building of special relativity. Einstein’s understanding of the problems facing classical electrodynamics and optics, in part, was informed by Fizeau’s 1851 experiments. However, between 1851 and 1905, Fizeau’s experiments were duplicated and reinterpreted by a succession of scientists, including Hertz, Lorentz, and Michelson

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment. But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.

Charles Peirce develops a scheme for classifying different kinds of monadic, dyadic and triadic relations. His account of these different classes of relations figures prominently in the development of his algebraic and diagrammatic systems of mathematical logic. Our aim in this essay is to reconstruct and examine central features of the classificatory system that he develops. Given the complexity of the system, we will focus our attention on the classification and explanation of of degenerate and genuine dyadic relations, and we will take up the discussion of triadic relations elsewhere. One of our reasons for wanting to explore this account of relations is to better understand how it informed the later development of relations as they figure in the history of mathematical logic. The earlier work of Peirce on dyadic relations influenced the development of the account of dyadic logical relations in works of Ernst Schroder, Leopold Lowenheim, Thoralf Skolem and Alfred Tarski. As such, our primary aim in this essay is to trace the early development of these ideas about the formal relation of the dyad for the sake of better understanding how it might have influenced these later developments.

On the odd day, a mathematician might wonder what constructive mathematics is all about. They may have heard arguments in favor of constructivism but are not at all convinced by them, and in any case they may care little about philosophy. A typical introductory text about constructivism spends a great deal of time explaining the principles and contains only trivial mathematics, while advanced constructive texts are impenetrable, like all unfamiliar mathematics. How then can a mathematician find out what constructive mathematics feels like? What new and relevant ideas does constructive mathematics have to offer, if any? I shall attempt to answer these questions.

The Italian civil nuclear projects had a very early origin, with the first ideas originating as far back as 1945. The construction of the first three plants dated back to the period 1956-1964, and at that time Italy ranked third in the world for installed power. However, the very ambitious projects were immediately after thwarted in the early 1960s by the “Ippolito trial”. Actually, a whole range of advanced programmes for the development of the country went to a stop, since they clashed with national and international major powers. Italy was relegated to a second rank power. The fourth nuclear plan was designed in 1970, and its commercial operation began in 1981. In the meantime, a strong anti-nuclear movement grew, and the position of the pro-nuclear Italian Communist Party began to change. After the Chernobyl accident, a national referendum was held, which in 1987 put an end to the Italian nuclear programmes.

The aim of this work is to create systematic trading strategies built upon several financial crisis indicators based on the spectral properties of market dynamics. Within the limitations of our framework and data, we will demonstrate that our systematic trading strategies are able to make money, not as a result of pure luck but, in a reproducible way and while avoiding the pitfall of over fitting, as a result of the skill of the operators and their understanding and knowledge of the financial market. Using singular value decomposition (SVD) techniques in order to compute all spectra in an efficient way, we have built two kinds of financial crisis indicators with a demonstrable power of prediction. Firstly, there are those that compare at every date the distribution of the eigenvalues of a covariance or correlation matrix to a distribution of reference representing either a calm or agitated market reference. Secondly, we have those that merely compute at every date a chosen spectral property (trace, spectral radius or Frobenius norm) of a covariance or correlation matrix. Aggregating the signals provided by all the indicators in order to minimize false positive errors, we then build systematic trading strategies based on a discrete set of rules governing the investment decisions of the investor.

We begin with the extraordinary observation that the length distribution of 80 million proteins in UniProt, the Universal Protein Resource, measured in amino acids, is qualitatively identical to the length distribution of large collections of computer functions measured in programming language tokens, at all scales. That two such disparate discrete systems share important structural properties suggests that yet other apparently unrelated discrete systems might share the same properties, and certainly invites an explanation.

The arrangements of particles and forces in granular materials and particulate matter have a complex organization on multiple spatial scales that range from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate mathematical, statistical, physical, and computational frameworks. Traditionally, granular materials have been investigated using particulate or continuum models, each of which tends to be implicitly agnostic to multiscale organization. Recently, tools from network science have emerged as powerful approaches for probing and characterizing heterogeneous architectures in complex systems, and a diverse set of methods have yielded fascinating insights into granular materials.

No new issues are discussed but we try to improve on the didactics of some well-known elementary features of multiple seats elections that rely on a single vote such as common elections for Parliament or the U.S. Congress. The didactics concentrate on proportionality versus districts. Since some people in the UK want more proportionality and some people in Holland want more districts, the examples of the UK 2010 and Dutch 2006 general elections are developed in some detail. Subordinate issues are (1) majority versus plurality, and (2) threshold methods versus the mechanisms of highest average, greatest remainder and the principle of Sainte-Laguë & Webster. The latter can be optimal for apportionment of states or districts that will get at least one seat. That kind of optimality can be dubious for political parties. Firstly because a party with a majority in the turnout may miss out on majority in Parliament and secondly since voters for some party A may not want that their vote, if wasted, goes to some party B. A proportional representation of the wasted vote w in total n is also possible by leaving seats empty or by filling the seats and taking a qualified majority f = 1/2 * n / (n – w). We thus should distinguish the mirroring of the proportions in the vote and the mirroring of a majority (and it is not quite true that the first takes care of the latter). For a coalition formed after the elections there is the more complex threshold of a “coalition qualified majority” since the coalition may not always be a solid block.

The following measures against unemployment are proposed: In the short term, to promote greater income for the poorest sectors. It is shown that this can be paid with the resulting increased production, without losing income to the other economic agents. In the mid term, the creation of ad-hoc companies for investment in projects profitable but long lasting. And in the long run, the abandonment of the competitive models. As these proposals go against current ideas (liberalisation, labour market flexibility, free market, etc.), the statements are rigorously demonstrated, even at the risk of making the lecture harder. Part 1 explores the problem and uses a simple model and others heuristic arguments to create familiarity with macroeconomic models. Part 2 is a simplified summary of Macroeconomic Theory textbook. It serves as a review to the reader whose knowledge in economy are out of date, or as a first approximation to the topic if he or she does not have them. In the light of the theory, economic policies are evaluated for the Argentine case in the 90’s. The work accepts the Keynesian explanation of unemployment (insufficient demand), but we disagree on its solution (public expenditure). Finally, in Part 3 we elaborate and justify the proposals.