Dynamic filtering of static dipoles in magnetoencephalography

We consider the problem of estimating neural activity from measurements of the magnetic fields recorded by magnetoencephalography. We exploit the temporal structure of the problem and model the neural current as a collection of evolving current dipoles, which appear and disappear, but whose locations are constant throughout their lifetime. This fully reflects the physiological interpretation of the model. In order to conduct inference under this proposed model, it was necessary to develop an algorithm based around state-of-the-art sequential Monte Carlo methods employing carefully designed importance distributions. Previous work employed a bootstrap filter and an artificial dynamic structure where dipoles performed a random walk in space, yielding nonphysical artefacts in the reconstructions; such artefacts are not observed when using the proposed model. The algorithm is validated with simulated data, in which it provided an average localisation error which is approximately half that of the bootstrap filter. An application to complex real data derived from a somatosensory experiment is presented. Assessment of model fit via marginal likelihood showed a clear preference for the proposed model and the associated reconstructions show better localisation

The Effect of the LISA Response Function on Observations of Monochromatic Sources

The Laser Interferometer Space Antenna (LISA) is expected to provide the largest observational sample of binary systems of faint sub-solar mass compact objects, in particular white-dwarfs, whose radiation is monochromatic over most of the LISA observational window. Current astrophysical estimates suggest that the instrument will be able to resolve about 10000 such systems, with a large fraction of them at frequencies above 3 mHz, where the wavelength of gravitational waves becomes comparable to or shorter than the LISA arm-length. This affects the structure of the so-called LISA transfer function which cannot be treated as constant in this frequency range: it introduces characteristic phase and amplitude modulations that depend on the source location in the sky and the emission frequency. Here we investigate the effect of the LISA transfer function on detection and parameter estimation for monochromatic sources. For signal detection we show that filters constructed by approximating the transfer function as a constant (long wavelength approximation) introduce a negligible loss of signal-to-noise ratio -- the fitting factor always exceeds 0.97 -- for f below 10mHz, therefore in a frequency range where one would actually expect the approximation to fail. For parameter estimation, we conclude that in the range 3mHz to 30mHz the errors associated with parameter measurements differ from about 5% up to a factor of 10 (depending on the actual source parameters and emission frequency) with respect to those computed using the long wavelength approximation.Comment: replacement version with typos correcte

Conchoidal transform of two plane curves

The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in \PP^2 \times \PP^2. We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve $C$ we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.Comment: 18 pages Revised version: slight title change, improved exposition, fixed proof of Theorem 5.3 Accepted for publication in Appl. Algebra Eng., Commun. Comput

Free energy landscape of mechanically unfolded model proteins: extended Jarzinsky versus inherent structure reconstruction

The equilibrium free energy landscape of off-lattice model heteropolymers as a function of an internal coordinate, namely the end-to-end distance, is reconstructed from out-of-equilibrium steered molecular dynamics data. This task is accomplished via two independent methods: by employing an extended version of the Jarzynski equality (EJE) and the inherent structure (IS) formalism. A comparison of the free energies estimated with these two schemes with equilibrium results obtained via the umbrella sampling technique reveals a good quantitative agreement among all the approaches in a range of temperatures around the ``folding transition'' for the two examined sequences. In particular, for the sequence with good foldability properties, the mechanically induced structural transitions can be related to thermodynamical aspects of folding. Moreover, for the same sequence the knowledge of the landscape profile allows for a good estimation of the life times of the native configuration for temperatures ranging from the folding to the collapse temperature. For the random sequence, mechanical and thermal unfolding appear to follow different paths along the landscape.Comment: Latex manuscript, 20 pages, 23 figures, submitted to Physical Review

Magneto-elastic effects and magnetization plateaus in two dimensional systems

We show the importance of both strong frustration and spin-lattice coupling for the stabilization of magnetization plateaus in translationally invariant two-dimensional systems. We consider a frustrated spin-1/2 Heisenberg model coupled to adiabatic phonons under an external magnetic field. At zero magnetization, simple structures with two or at most four spins per unit cell are stabilized, forming dimers or $2 \times 2$ plaquettes, respectively. A much richer scenario is found in the case of magnetization $m=1/2$, where larger unit cells are formed with non-trivial spin textures and an analogy with the corresponding classical Ising model is detectable. Specific predictions on lattice distortions and local spin values can be directly measured by X-rays and Nuclear Magnetic Resonance experiments.Comment: 4 pages and 4 figure

Anisotropic dynamics of a vicinal surface under the meandering step instability

We investigate the nonlinear evolution of the Bales-Zangwill instability, responsible for the meandering of atomic steps on a growing vicinal surface. We develop an asymptotic method to derive, in the continuous limit, an evolution equation for the two-dimensional step flow. The dynamics of the crystal surface is greatly influenced by the anisotropy inherent to its geometry, and is characterized by the coarsening of undulations along the step direction and by the elastic relaxation in the mean slope direction. We demonstrate, using similarity arguments, that the coalescence of meanders and the step flow follow simple scaling laws, and deduce the exponents of the characteristic length scales and height amplitude. The relevance of these results to experiments is discussed.Comment: 10 pages, 7 figures; submitted to Phys. Rev.

Volume elements and torsion

We reexamine here the issue of consistency of minimal action formulation with the minimal coupling procedure (MCP) in spaces with torsion. In Riemann-Cartan spaces, it is known that a proper use of the MCP requires that the trace of the torsion tensor be a gradient, $T_\mu=\partial_\mu\theta$, and that the modified volume element $\tau_\theta = e^\theta \sqrt{g} dx^1\wedge...\wedge dx^n$ be used in the action formulation of a physical model. We rederive this result here under considerably weaker assumptions, reinforcing some recent results about the inadequacy of propagating torsion theories of gravity to explain the available observational data. The results presented here also open the door to possible applications of the modified volume element in the geometric theory of crystalline defects.Comment: Revtex, 8 pages, 1 figure. v2 includes a discussion on $\lambda$-symmetr

On the relativistic L-S coupling

The fact that the Dirac equation is linear in the space and time derivatives leads to the coupling of spin and orbital angular momenta that is of a pure relativistic nature. We illustrate this fact by computing the solutions of the Dirac equation in an infinite spherical well, which allows to go from the relativistic to the non-relativistic limit by just varying the radius of the well.Comment: LateX2e, 12 pages, 1 figure, accepted in Eur. J. Phy

Is the Cepheus E Outflow driven by a Class 0 Protostar?

New early release observations of the Cepheus E outflow and its embedded source, obtained with the Spitzer Space Telescope, are presented. We show the driving source is detected in all 4 IRAC bands, which suggests that traditional Class 0 classification, although essentially correct, needs to accommodate the new high sensitivity infrared arrays and their ability to detected deeply embedded sources. The IRAC, MIPS 24 and 70 microns new photometric points are consistent with a spectral energy distribution dominated by a cold, dense envelope surrounding the protostar. The Cep E outflow, unlike its more famous cousin the HH 46/47 outflow, displays a very similar morphology in the near and mid-infrared wavelengths, and is detected at 24 microns. The interface between the dense molecular gas (where Cep E lies) and less dense interstellar medium, is well traced by the emission at 8 and 24 microns, and is one of the most exotic features of the new IRAC and MIPS images. IRS observations of the North lobe of the flow confirm that most of the emission is due to the excitation of pure H2 rotational transitions arising from a relatively cold (Tex~700 K) and dense (N{H}~9.6E20 cm-2 molecular gas.Comment: 14 pages (pre-print format), including 6 figures. Published in ApJ Special Spitzer Issue (2004

Time Optimal Unitary Operations

Extending our previous work on time optimal quantum state evolution, we formulate a variational principle for the time optimal unitary operation, which has direct relevance to quantum computation. We demonstrate our method with three examples, i.e. the swap of qubits, the quantum Fourier transform and the entangler gate, by choosing a two-qubit anisotropic Heisenberg model.Comment: 4 pages, 1 figure. References adde