Medical Expertise, Bodies, and the Law in Early Modern Courts

Commissioned 3000-word essay for the section Focus of ISIS, the leading journal in the history of science internationally. This section aims to present innovative historiographical approaches, in this case in relation to the theme 'Science and Law'. While discussing recent studies in the history of early modern legal medicine, the article outlines the future research agenda in the area, with a special focus on epistemological issues, including the specific nature of medico-legal evidence, and the role of medical semiotics in its makin

A numerical method to calculate the muon relaxation function in the presence of diffusion

We present an accurate and efficient method to calculate the effect of random fluctuations of the local field at the muon, for instance in the case muon diffusion, within the framework of the strong collision approximation. The method is based on a reformulation of the Markovian process over a discretized time base, leading to a summation equation for the muon polarization function which is solved by discrete Fourier transform. The latter is formally analogous, though not identical, to the integral equation of the original continuous-time model, solved by Laplace transform. With real-case parameter values, the solution of the discrete-time strong collision model is found to approximate the continuous-time solution with excellent accuracy even with a coarse-grained time sampling. Its calculation by the fast Fourier transform algorithm is very efficient and suitable for real time fitting of experimental data even on a slow computer.Comment: 7 pages, 3 figures. Submitted to Journal of Physics: Condensed Matte

Renormalized Hennings Invariants and 2+1-TQFTs

We construct non-semisimple $2+1$-TQFTs yielding mapping class group representations in Lyubashenko's spaces. In order to do this, we first generalize Beliakova, Blanchet and Geer's logarithmic Hennings invariants based on quantum $\mathfrak{sl}_2$ to the setting of finite-dimensional non-degenerate unimodular ribbon Hopf algebras. The tools used for this construction are a Hennings-augmented Reshetikhin-Turaev functor and modified traces. When the Hopf algebra is factorizable, we further show that the universal construction of Blanchet, Habegger, Masbaum and Vogel produces a $2+1$-TQFT on a not completely rigid monoidal subcategory of cobordisms

A view from inside iron-based superconductors

Muon spin spectroscopy is one of the most powerful tools to investigate the microscopic properties of superconductors. In this manuscript, an overview on some of the main achievements obtained by this technique in the iron-based superconductors (IBS) are presented. It is shown how the muons allow to probe the whole phase diagram of IBS, from the magnetic to the superconducting phase, and their sensitivity to unravel the modifications of the magnetic and the superconducting order parameters, as the phase diagram is spanned either by charge doping, by an external pressure or by introducing magnetic and non-magnetic impurities. Moreover, it is highlighted that the muons are unique probes for the study of the nanoscopic coexistence between magnetism and superconductivity taking place at the crossover between the two ground-states.Comment: 28 pages, 18 figure

Enterprise Risk Management, Corporate Governance And Systemic Risk: Some Research Perspectives

The general goal of Enterprise Risk Management (ERM) processes is to generate economic value through the coverage of firm business risk, on the one hand, and by exploiting the positive side of uncertainty conditions, on the other hand. The increasing attention attributed to ERM in the creation of economic value has led to even greater interactions between risk management mechanisms and the corporate governance system. In other words, in the last two decades, the relationships between corporate governance and ERM increased since the ERM processes have been considered more and more as critical drivers to combine strategic objectives with relative low volatility of company performance. The basic idea is that a good corporate governance system must deal about specific risks along with their interactions and, at the same time, the firm’s business risk as a whole. Moreover, an efficient and effective ERM system provides clear information about linkages between strategic opportunities and risk exposure and offers tools able to manage in an optimal way the negative side of business risk (or downside risk) as wellas its positive side (or upside risk). Accordingly, extant studies concerning the relationships between ERM and corporate governance have been focusing on a micro-level of analyses (i.e., the individual organization) and, specifically, on a firm’s benefits that stem from the adoption of proper ERM processes that are consistent with corporate governance goals and are able to sustain the increase of economic value while maintaining a bearable business risk over time. From our initial analyses, a gap in literature arises. We argue that the interdependence between ERM and corporate governance may be analyzed from a broader point of view as well (i.e., the firm and its task environment composed by its suppliers, customers, and partners). In particular, our research idea is to enlarge traditional studies about interrelations between corporate governance and ERM taking into account whether such interrelations could be a driver of risk transfer from the focal organization to other organizations that belong to its task environment. Moreover, this study aims to deepen the mechanisms by which the transfer of risk from a focal organization to its task environment may foster the emergence of systemic risk, i.e., a macro risk coming from domino and/or network effects. Therefore, our paper aims to find new research areas by combining micro and macro issues tied to corporate governance, ERM and systemic risk. The starting point of our work is the three following assumptions: 1) The compliance of a firm to ERM processes as well as to corporate governance rules implies the reduction as much as possible of firm business risk; 2) The reduction of the firm business risk leads to externalizing the firm business risk through risk-sharing mechanisms; 3) The risk-sharing may arise like a driver of systemic risk especially in those industries featured by strong network interrelations. Starting from the above assumptions, the paper goal is to open a new research area which combines four academic fields (ERM, corporate governance, corporate finance, and macro-finance). So far, our initial findings tell us that the following research questions arise: RQ1: What are the conditions under which the transfer of business risk towards organizations that belong to a firm task environment is likely to become a source of systemic risk in a specific industry? RQ2: How does the capital structure of a focal firm affect its propensity to transfer business risk not only to commercial but also to financial stakeholders included in firm task environment? RQ3: How does the transfer of business risk influence the capital cost of the focal firm as well as of the organizations that absorbed such risk

Non-Semisimple Extended Topological Quantum Field Theories

We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative modular categories, a class of ribbon categories which are modeled on representations of unrolled quantum groups, and which can be thought of as a non-semisimple analogue to modular categories. Our approach exploits a 2-categorical version of the universal construction introduced by Blanchet, Habegger, Masbaum, and Vogel. The 1+1+1-EQFTs thus obtained are realized by symmetric monoidal 2-functors which are defined over non-rigid 2-categories of admissible cobordisms decorated with colored ribbon graphs and cohomology classes, and which take values in 2-categories of complete graded linear categories. In particular, our construction extends the family of graded 2+1-TQFTs defined for the unrolled version of quantum $\mathfrak{sl}_2$ by Blanchet, Costantino, Geer, and Patureau to a new family of graded ETQFTs. The non-semisimplicity of the theory is witnessed by the presence of non-semisimple graded linear categories associated with critical 1-manifolds.Comment: 172 pages, 46 figures, entirely rewritten, several appendices adde

Milnor-Wood type inequalities

The Gauss-Bonnet Theorem, which was generalized by Shiing-Shen Chern in 1944 to all oriented closed even-dimensional smooth manifolds, correlates the curvature of the Levi-Civita connection of a Riemannian manifold with its Euler characteristic. This result provides a strong restriction on the kind of geometry such a manifold can support. For instance, let us consider Euclidean manifolds, i.e. manifolds which admit an atlas whose coordinate change functions are isometries of $\mathbb R^n$. Since the curvature of the Levi-Civita connection they inherit from $\mathbb R^n$ vanishes, the Euler characteristic represents an obstruction to the existence of Euclidean structures: indeed if $\chi(M) \neq 0$ then $M$ cannot support a flat metric. On the other hand, let us consider affine manifolds, i.e. manifolds which admit an atlas whose coordinate change functions are affine isomorphisms of $\mathbb R^n$. These can be characterized as those manifolds whose tangent bundle supports flat and symmetric connections. Although they may seem to be a mild generalization of Euclidean manifolds, the attempt to generalize the above result to affine manifolds resulted in the formulation of a long standing open conjecture: \textbf{Conjecture 1:} The Euler characteristic of a closed oriented affine manifold vanishes. The key point is that the Euler characteristic of a manifold cannot be computed from the curvature of an arbitrary linear connection $\nabla$, because it is essential for $\nabla$ to be compatible with a Riemannian metric. Now, although Conjecture 1 was shown to hold true for complete affine manifolds by Bertram Kostant and Dennis Sullivan, the non-complete case is much more difficult. There are known examples, due to John Smillie, of manifods with non-zero Euler characteristic and flat tangent bundle in every even dimension greater than 2. However, as William Goldman points out, since the torsion of these connections seems hard to control they do not disprove Conjecture 1. None of Smillie’s manifolds is aspherical, and indeed another open conjecture is: \textbf{Conjecture 1:} The Euler characteristic of a closed oriented aspherical manifold whose tangent bundle is flat vanishes. The first important breakthrough was made by John Milnor in 1958, when he proved both conjectures for closed oriented surfaces. He exploited the fact that the existence of a flat connection on a rank-$m$ vector bundle $\pi : E \rightarrow M$ is equivalent to the existence of a holonomy representation $\rho : \pi_1(M,x_0) \rightarrow \mathrm{GL}^+(m,\mathbb R)$ which induces the bundle. The study of all possible holonomy representations for closed oriented surfaces enabled him to establish a much more detailed result: he managed to characterize all flat oriented plane bundles over closed oriented surfaces by means of their Euler class, that is a cohomology class in the cohomology ring of the base space which generalizes the Euler characteristic. What happens is that the Euler class of flat bundles over a fixed surface $\Sigma$ is bounded, that is, just a finite number (up to isomorphism) of oriented plane bundles over $\Sigma$ can support flat connections. In particular, none of these is the tangent bundle if $\Sigma$ is not the torus. This remarkable result is now known as Milnor-Wood inequality (the name celebrates John Wood's generalization to $S^1$-bundles). While it has been proven that the boundedness of the Euler class of flat bundles generalizes to all dimensions, Conjectures 1 and 2 remain elusive. Indeed one needs explicit inequalities in order to determine whether the tangent bundle can be ruled out from the flat ones or not. Since Milnor's work very little progress has been made until very recently. In 2011 Michelle Bucher and Tsachik Gelander published a generalization of Milnor-Wood inequality to closed oriented manifolds whose universal cover is isometric to $(\mathbb H^2)^n$, thus confirming both conjectures for all manifolds which are locally isometric to a product of surfaces of constant curvature. Their work, which takes up the largest part of our exposition, uses the theory of bounded cohomology developed by Mikha\"{i}l Gromov in 1982 and some deep results about the super-rigidity of lattices in semisimple Lie groups due to Gregori Margulis

Teoria dels mapes

Teoria dels mape

El problema del límite entre Secundario y Terciario en las proximidades de Serraduy, en el valle del Isábena (Provincia de Huesca)

El problema del límite entre Secundario y Terciario es uno de los problemas esenciales de la estratigrafía de las series sedimentarias del Prepirineo. La formación garumniense, cuya base es evidentemente cretácica, tiene un techo cuya edad es problemática, cosa destacada ya por diversos autores que han estudiado la cuestión. Nosotros hemos estudiado el problema en las proximidades del pueblo de Serraduy (Huesca) y hemos podido hallar una serie de intercalaciones marinas entre las margas rojas de la facies garumniense; la más inferior de estas capas marinas contenía Alveolina (Glomalveolina) primaeva REICHEL, cuya presencia indica una edad Montiense-Tanaeciense (Paleoceno) y, por tanto, ya claramente terciaria