Covariant Magnetic Connection Hypersurfaces

In the single fluid, nonrelativistic, ideal-Magnetohydrodynamic (MHD) plasma description magnetic field lines play a fundamental role by defining dynamically preserved "magnetic connections" between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D {\it magnetic connection hypersurfaces} in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when ${\bf E} \cdot {\bf B} = 0$.Comment: 10 pages no figure

Genetic diagnosis as a tool for personalized treatment of Duchenne muscular dystrophy

Accurate definition of genetic mutations causing Duchenne muscular dystrophy (DMD) has always been relevant in order to provide genetic counseling to patients and families, and helps to establish the prognosis in the case where the distinction between Duchenne, Becker, or intermediate muscular dystrophy is not obvious. As molecular treatments aimed at dystrophin restoration in DMD are increasingly available as commercialized drugs or within clinical trials, genetic diagnosis has become an indispensable tool in order to determine eligibility for these treatments. DMD patients in which multiplex ligation-dependent probe amplification (MLPA) or similar techniques show a deletion suitable to exon skipping of exons 44, 45, 51, or 53, may be currently treated with AONs targeting these exons, in the context of clinical trials, or, as is the case for exon 51 skipping in the United States, with the first commercialized drug (eteplirsen). Patients who test negative at MLPA, but in whom DMD gene sequencing shows a nonsense mutation, may be amenable for treatment with stop codon readthrough compounds such as ataluren. Novel molecular approaches such as CRISPR-Cas9 targeting of specific DMD mutations are still in the preclinical stages, but appear promising. In conclusion, an accurate genetic diagnosis represents the entrance into a new scenario of personalized medicine in DMD

Generalised relativistic Ohm's laws, extended gauge transformations and magnetic linking

Generalisations of the relativistic ideal Ohm's law are presented that include specific dynamical features of the current carrying particles in a plasma. Cases of interest for space and laboratory plasmas are identified where these generalisations allow for the definition of generalised electromagnetic fields that transform under a Lorentz boost in the same way as the real electromagnetic fields and that obey the same set of homogeneous Maxwell's equations

An Action Principle for Relativistic MHD

A covariant action principle for ideal relativistic magnetohydrodynamics (MHD) in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al., which uses a noncanonical bracket to effect constrained variations of an action functional. Various implications and extensions of this action principle are also discussed. Two significant by-products of this formalism are the introduction of a new divergence-free 4-vector variable for the magnetic field, and a new Lie-dragged form for the theory

Multi-Lag Term Structure Models with Stochastic Risk Premia.

The purpose of this paper is to propose discrete-time term structure models where the historical dynamics of the factor (xt) is given, in the univariate case, by a Gaussian AR(p) process, and, in the multivariate case, by a Gaussian n-dimensional VAR(p) process. The factor (xt) is considered as a latent or an observable variable and, in the second case, (xt) is given by the short rate (in the scalar setting) or by a vector of several yields (in the multivariate setting). We consider an exponential-affine stochastic discount factor (SDF) with a stochastic factor risk correction coefficient defined, at time t, as an affine function of Xt = (xt, . . . , xt?p+1)0 and, consequently, the yield-to-maturity formula at time t is an affine function of the p most recent lagged values of xt+1. We study the Gaussian AR(p) and the Gaussian VAR(p) Factor-Based Term Structure Models. We investigate, under the risk-neutral and the S-forward probability, the Moving Average (or discrete-time Heath, Jarrow and Morton) representation of the yield and short-term forward rate processes. This representation gives the possibility to exactly replicate the currently-observed yield curve. We also study the problem of matching the theoretical and currently-observed market term structure by means of the Extended AR(p) approach.Discrete-time Affine Term Structure Models ; Stochastic Discount Factor, Gaussian VAR(p) processes ; Stochastic risk premia ; Moving Average or discrete-time HJM representations ; Exact Fitting of the currently-observed yield curve.

Switching VARMA Term Structure Models - Extended Version.

The purpose of the paper is to propose a global discrete-time modeling of the term structure of interest rates able to capture simultaneously the following important features : (i) an historical dynamics of the factor driving term structure shapes involving several lagged values, and switching regimes; (ii) a specification of the stochastic discount factor (SDF) with time-varying and regime dependent risk-premia; (iii) explicit or quasi explicit formulas for zero-coupon bond and interest rate derivative prices; (iv) the positivity of the yields at each maturity. The first family of models we develop is given by the Switching Autoregressive Normal (SARN) and the Switching Vector Autoregressive Normal (SVARN) Factor-Based Term Structure Models of order p. The second family of models we study is given by the Switching Autoregressive Gamma (SARG) and the Switching Vector Autoregressive Gamma (SVARG) Factor-Based Term Structure Models of order p. Regime shifts are described by a Markov chain with (historical) non-homogeneous transition probabilities.Affine Term Structure Models ; Stochastic Discount Factor ; Car processes ; Switching Regimes ; VARMA processes ; Lags ; Positivity ; Derivative Pricing.

Pressure anisotropy and small spatial scales induced by velocity shear

Non-Maxwellian metaequilibria can exist in low-collisionality plasmas as evidenced by satellite and laboratory measurements. By including the full pressure tensor dynamics in a fluid plasma model, we show that a sheared velocity field can provide an effective mechanism that makes an initial isotropic state anisotropic and agyrotropic. We discuss how the propagation of magneto-elastic waves can affect the pressure tensor anisotropization and its spatial filamentation which are due to the action of both the magnetic field and flow strain tensor. We support this analysis by a numerical integration of the nonlinear equations describing the pressure tensor evolution.Comment: 5 pages, 3 Figure