Infinitesimals without Logic

We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals without any need of a background in mathematical logic. In particular, on the contrary with respect to SIA, which admits models only in intuitionistic logic, the theory of Fermat reals is consistent with classical logic. We face the problem to decide if the product of powers of nilpotent infinitesimals is zero or not, the identity principle for polynomials, the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order preserving geometrical representation. Using nilpotent infinitesimals, every smooth functions becomes a polynomial because in Taylor's formulas the rest is now zero. Finally, we present several applications to informal classical calculations used in Physics: now all these calculations become rigorous and, at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, that clarifies how to formalize the approximations tied with Hook's law using this language of nilpotent infinitesimals.Comment: The first part of the preprint is taken directly form arXiv:0907.1872 The second part is new and contains a list of example

Tiling groupoids and Bratteli diagrams

Let T be an aperiodic and repetitive tiling of R^d with finite local complexity. Let O be its tiling space with canonical transversal X. The tiling equivalence relation R_X is the set of pairs of tilings in X which are translates of each others, with a certain (etale) topology. In this paper R_X is reconstructed as a generalized "tail equivalence" on a Bratteli diagram, with its standard AF-relation as a subequivalence relation. Using a generalization of the Anderson-Putnam complex, O is identified with the inverse limit of a sequence of finite CW-complexes. A Bratteli diagram B is built from this sequence, and its set of infinite paths dB is homeomorphic to X. The diagram B is endowed with a horizontal structure: additional edges that encode the adjacencies of patches in T. This allows to define an etale equivalence relation R_B on dB which is homeomorphic to R_X, and contains the AF-relation of "tail equivalence".Comment: 34 pages, 4 figure

Isospin Dynamics in Heavy Ion Collisions: from Coulomb Barrier to Quark Gluon Plasma

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We will first discuss the Isospin Equilibration Dynamics. At low energies this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation with the symmetry term acting as a restoring force. At higher beam energies Iso-EoS effects will be seen in Imbalance Ratio Measurements, in particular from the correlations with the total kinetic energy loss. For fragmentation reactions in central events we suggest to look at the coupling between isospin distillation and radial flow. In Neck Fragmentation reactions important $Iso-EoS$ information can be obtained from the correlation between isospin content and alignement. The high density symmetry term can be probed from isospin effects on heavy ion reactions at relativistic energies (few AGeV range). Rather isospin sensitive observables are proposed from nucleon/cluster emissions, collective flows and meson production. The possibility to shed light on the controversial neutron/proton effective mass splitting in asymmetric matter is also suggested. A large symmetry repulsion at high baryon density will also lead to an "earlier" hadron-deconfinement transition in n-rich matter. A suitable treatment of the isovector interaction in the partonic EoS appears very relevant.Comment: 18 pages, 12 figures, lecture at the 2008 Erice School on Nuclear Physics, to appear in Progress in Particle and Nuclear Physic

Morphology, dynamics and plasma parameters of plumes and inter-plume regions in solar coronal holes

Coronal plumes, which extend from solar coronal holes (CH) into the high corona and - possibly - into the solar wind (SW), can now continuously be studied with modern telescopes and spectrometers on spacecraft, in addition to investigations from the ground, in particular, during total eclipses. Despite the large amount of data available on these prominent features and related phenomena, many questions remained unanswered as to their generation and relative contributions to the high-speed streams emanating from CHs. An understanding of the processes of plume formation and evolution requires a better knowledge of the physical conditions at the base of CHs, in plumes and in the surrounding inter-plume regions (IPR). More specifically, information is needed on the magnetic field configuration, the electron densities and temperatures, effective ion temperatures, non-thermal motions, plume cross-sections relative to the size of a CH, the plasma bulk speeds, as well as any plume signatures in the SW. In spring 2007, the authors proposed a study on "Structure and dynamics of coronal plumes and inter-plume regions in solar coronal holes" to the International Space Science Institute (ISSI) in Bern to clarify some of these aspects by considering relevant observations and the extensive literature. This review summarizes the results and conclusions of the study. Stereoscopic observations allowed us to include three-dimensional reconstructions of plumes. Multi-instrument investigations carried out during several campaigns led to progress in some areas, such as plasma densities, temperatures, plume structure and the relation to other solar phenomena, but not all questions could be answered concerning the details of plume generation process(es) and interaction with the SW.Comment: To appear on: The Astronomy and Astrophysics Review. 72 pages, 30 figure

Thioredoxin Inhibitors Attenuate Platelet Function and Thrombus Formation.

Thioredoxin (Trx) is an oxidoreductase with important physiological function. Imbalances in the NADPH/thioredoxin reductase/thioredoxin system are associated with a number of pathologies, particularly cancer, and a number of clinical trials for thioredoxin and thioredoxin reductase inhibitors have been carried out or are underway. Due to the emerging role and importance of oxidoreductases for haemostasis and the current interest in developing inhibitors for clinical use, we thought it pertinent to assess whether inhibition of the NADPH/thioredoxin reductase/thioredoxin system affects platelet function and thrombosis. We used small molecule inhibitors of Trx (PMX 464 and PX-12) to determine whether Trx activity influences platelet function, as well as an unbiased proteomics approach to identify potential Trx substrates on the surface of platelets that might contribute to platelet reactivity and function. Using LC-MS/MS we found that PMX 464 and PX-12 affected the oxidation state of thiols in a number of cell surface proteins. Key surface receptors for platelet adhesion and activation were affected, including the collagen receptor GPVI and the von Willebrand factor receptor, GPIb. To experimentally validate these findings we assessed platelet function in the presence of PMX 464, PX-12, and rutin (a selective inhibitor of the related protein disulphide isomerase). In agreement with the proteomics data, small molecule inhibitors of thioredoxin selectively inhibited GPVI-mediated platelet activation, and attenuated ristocetin-induced GPIb-vWF-mediated platelet agglutination, thus validating the findings of the proteomics study. These data reveal a novel role for thioredoxin in regulating platelet reactivity via proteins required for early platelet responses at sites of vessel injury (GPVI and GPIb). This work also highlights a potential opportunity for repurposing of PMX 464 and PX-12 as antiplatelet agents.CM is funded by Medical Research Council Grant No G9826026. AR was funded by a British Heart Foundation Centre of Research Excellence-funded Vacation Studentship. CHC is funded by British Heart Foundation Fellowship FS/11/49/28751.This is the final version of the article. It first appeared from PLOS via https://doi.org/10.1371/journal.pone.016300

Kinetically driven glassy transition in an exactly solvable toy model with reversible mode coupling mechanism and trivial statics

We propose a toy model with reversible mode coupling mechanism and with trivial Hamiltonian (and hence trivial statics). The model can be analyzed exactly without relying upon uncontrolled approximation such as the factorization approximation employed in the current MCT. We show that the model exhibits a kinetically driven transition from an ergodic phase to nonergodic phase. The nonergodic state is the nonequilibrium stationary solution of the Fokker-Planck equation for the distribution function of the modelComment: 10 pages, 1 figure, contribution to the Proceedings of the Barcelona Workshop 'Glassy Behavior of Kinetically Constrained Models'. To appear in J. Phys. Condens. Matte

Comparison of the sidereal angular velocity of subphotospheric layers and small bright coronal structures during the declining phase of solar cycle 23

Context. We compare solar differential rotation of subphotospheric layers derived from local helioseismology analysis of GONG++ dopplergrams and the one derived from tracing small bright coronal structures (SBCS) using EIT/SOHO images for the period August 2001 - December 2006, which correspond to the declining phase of solar cycle 23. Aims. The study aims to find a relationship between the rotation of the SBCS and the subphotospheric angular velocity. The northsouth asymmetries of both rotation velocity measurements are also investigated. Methods. Subphotospheric differential rotation was derived using ring-diagram analysis of GONG++ full-disk dopplergrams of 1 min cadence. The coronal rotation was derived by using an automatic method to identify and track the small bright coronal structures in EIT full-disk images of 6 hours cadence. Results. We find that the SBCS rotate faster than the considered upper subphotospheric layer (3Mm) by about 0.5 deg/day at the equator. This result joins the results of several other magnetic features (sunspots, plages, faculae, etc.) with a higher rotation than the solar plasma. The rotation rate latitudinal gradients of the SBCS and the subphotospheric layers are very similar. The SBCS motion shows an acceleration of about 0.005 deg/day/month during the declining phase of solar cycle 23, whereas the angular velocity of subsurface layers does not display any evident variation with time, except for the well known torsional oscillation pattern. Finally, both subphotospheric and coronal rotations of the southern hemisphere are predominantly larger than those of the northern hemisphere. At latitudes where the north-south asymmetry of the angular velocity increases (decreases) with activity for the SBCS, it decreases (increases) for subphotospheric layers.Comment: 6pages, 8 figures, Accepted for publication in Astronomy and Astrophysic