A statistical approach to the inverse problem in magnetoencephalography

Magnetoencephalography (MEG) is an imaging technique used to measure the magnetic field outside the human head produced by the electrical activity inside the brain. The MEG inverse problem, identifying the location of the electrical sources from the magnetic signal measurements, is ill-posed, that is, there are an infinite number of mathematically correct solutions. Common source localization methods assume the source does not vary with time and do not provide estimates of the variability of the fitted model. Here, we reformulate the MEG inverse problem by considering time-varying locations for the sources and their electrical moments and we model their time evolution using a state space model. Based on our predictive model, we investigate the inverse problem by finding the posterior source distribution given the multiple channels of observations at each time rather than fitting fixed source parameters. Our new model is more realistic than common models and allows us to estimate the variation of the strength, orientation and position. We propose two new Monte Carlo methods based on sequential importance sampling. Unlike the usual MCMC sampling scheme, our new methods work in this situation without needing to tune a high-dimensional transition kernel which has a very high cost. The dimensionality of the unknown parameters is extremely large and the size of the data is even larger. We use Parallel Virtual Machine (PVM) to speed up the computation.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS716 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterisations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained.Comment: LaTex 18 pages, to appear in J. Math. Phys. (To compile, need pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty

Dynamics of strong and radiative decays of Ds-mesons in the hadrogenesis conjecture

The positive parity scalar D$_{s0}^*$(2317) and axial-vector D$_{s1}^*$(2460) charmed strange mesons are generated by coupled-channel dynamics through the s-wave scattering of Goldstone bosons off the pseudoscalar and vector D(D$_s$)-meson ground states. The specific masses of these states are obtained as a consequence of the attraction arising from the Weinberg-Tomozawa interaction in the chiral Lagrangian. Chiral corrections to order Q$_\chi^2$ are calculated and found to be small. The D$_{s0}^*$(2317) and D$_{s1}^*$(2460) mesons decay either strongly into the isospin-violating $\pi^0$D$_s$ and $\pi^0$D$_s^*$ channels or electromagnetically. We show that the $\pi^0$-$\eta$ and (K$^0$D$^+$-K$^+$D$^0$) mixings act constructively to generate strong widths of the order of 140 keV and emphasize the sensitivity of this value to the $KD$ component of the states. The one-loop contribution to the radiative decay amplitudes of scalar and axial-vector states is calculated using the electromagnetic Lagrangian to chiral order Q$_\chi^2$. We show the importance of taking into account processes involving light vector mesons explicitly in the dynamics of electromagnetic decays. The radiative width are sensitive to both $\eta D_s$ and $KD$ components, hence providing information complementary to the strong widths on the positive parity $D_s$-meson structure.Comment: 4 pages, Invited Contribution to QNP09, Beijing, September 21-26, 200

Distributed Clustering in Cognitive Radio Ad Hoc Networks Using Soft-Constraint Affinity Propagation

Absence of network infrastructure and heterogeneous spectrum availability in cognitive radio ad hoc networks (CRAHNs) necessitate the self-organization of cognitive radio users (CRs) for efficient spectrum coordination. The cluster-based structure is known to be effective in both guaranteeing system performance and reducing communication overhead in variable network environment. In this paper, we propose a distributed clustering algorithm based on soft-constraint affinity propagation message passing model (DCSCAP). Without dependence on predefined common control channel (CCC), DCSCAP relies on the distributed message passing among CRs through their available channels, making the algorithm applicable for large scale networks. Different from original soft-constraint affinity propagation algorithm, the maximal iterations of message passing is controlled to a relatively small number to accommodate to the dynamic environment of CRAHNs. Based on the accumulated evidence for clustering from the message passing process, clusters are formed with the objective of grouping the CRs with similar spectrum availability into smaller number of clusters while guaranteeing at least one CCC in each cluster. Extensive simulation results demonstrate the preference of DCSCAP compared with existing algorithms in both efficiency and robustness of the clusters

Dynamics of strong and radiative decays of Ds mesons

The positive parity scalar D$_{s0}^*$(2317) and axial-vector D$_{s1}^*$(2460) charmed strange mesons are generated by coupled-channel dynamics through the s-wave scattering of Goldstone bosons off the pseudoscalar and vector D(D$_s$)-meson ground states. The attraction leading to the specific masses of these states reflects the chiral symmetry breaking scale which characterizes the Weinberg-Tomozawa interaction in the chiral Lagrangian. Chiral corrections to order Q$_\chi^2$ are calculated and found to be small. The D$_{s0}^*$(2317) and D$_{s1}^*$(2460) mesons decay either strongly into the isospin-violating $\pi^0$D$_s$ and $\pi^0$D$_s^*$ channels or electromagnetically. We show that the $\pi^0$-$\eta$ and (K$^0$D$^+$-K$^+$D$^0$) mixings act constructively to generate strong widths of the order of 140 keV. The one-loop contribution to the radiative decay amplitudes of scalar and axial-vector states is calculated using the electromagnetic Lagrangian to chiral order Q$_\chi^2$. We show the importance of taking into account processes involving light vector mesons explicitly in the dynamics of electromagnetic decays to obtain a satisfactory description of the available data.Comment: Contribution to the Meson 2008 Conference, June 6-10, Cracow, Polan

Intrinsic interface exchange coupling of ferromagnetic nanodomains in a charge ordered manganite

We present a detailed magnetic study of the Pr1/3Ca2/3MnO3 manganite, where we observe the presence of small ferromagnetic (FM) domains (diameter ~ 10A) immersed within the charge-ordered antiferromagnetic (AFM) host. Due to the interaction of the FM nanodroplets with a disordered AFM shell, the low-temperature magnetization loops present exchange bias (EB) under cooling in an applied magnetic field. Our analysis of the cooling field dependence of the EB yields an antiferromagnetic interface exchange coupling comparable to the bulk exchange constant of the AFM phase. We also observe training effect of the EB, which is successfully described in terms of a preexisting relaxation model developed for other classical EB systems. This work provides the first evidence of intrinsic interface exchange coupling in phase separated manganites.Comment: 7 pages, 6 figure

Transient response under ultrafast interband excitation of an intrinsic graphene

The transient evolution of carriers in an intrinsic graphene under ultrafast excitation, which is caused by the collisionless interband transitions, is studied theoretically. The energy relaxation due to the quasielastic acoustic phonon scattering and the interband generation-recombination transitions due to thermal radiation are analyzed. The distributions of carriers are obtained for the limiting cases when carrier-carrier scattering is negligible and when the intercarrier scattering imposes the quasiequilibrium distribution. The transient optical response (differential reflectivity and transmissivity) on a probe radiation and transient photoconductivity (response on a weak dc field) appears to be strongly dependent on the relaxation and recombination dynamics of carriers.Comment: 9 pages, 8 figure

Transient magnetoconductivity of photoexcited electrons

Transient magnetotransport of two-dimensional electrons with partially-inverted distribution excited by an ultrashort optical pulse is studied theoretically. The time-dependent photoconductivity is calculated for GaAs-based quantum wells by taking into account the relaxation of electron distribution caused by non-elastic electron-phonon interaction and the retardation of the response due to momentum relaxation and due to a finite capacitance of the sample. We predict large-amplitude transient oscillations of the current density and Hall field (Hall oscillations) with frequencies corresponding to magnetoplasmon range, which are initiated by the instability owing to the absolute negative conductivity effect.Comment: 21 pages, 6 fig