Extension of the Kalman–Bucy Filter to Elementary Linear Systems with Fractional Brownian Noises

We investigate the optimal filtering problem in the simplest Gaussian linear system driven by fractional Brownian motions. At first we extend to this setting the Kalman–Bucy filtering equations which are well-known in the specific case of usual Brownian motions. Closed form Volterra type integral equations are derived both for the mean of the optimal filter and the variance of the filtering error. Then the asymptotic stability of the filter is analyzed. It is shown that the variance of the filtering error converges to a finite limit as the observation time tends to infinity. This revised version was published online in August 2006 with corrections to the Cover Date.     

Measurement of the generalized polarizabilities of the proton in virtual Compton scattering at Q2=0.92 and 1.76 GeV2

We report a virtual Compton scattering study of the proton at low c.m. energies. We have determined the structure functions P(LL)-P(TT)/epsilon and P(LT), and the electric and magnetic generalized polarizabilities (GPs) alpha(E)(Q2) and beta(M)(Q2) at momentum transfer Q(2)=0.92 and 1.76 GeV2. The electric GP shows a strong falloff with Q2, and its global behavior does not follow a simple dipole form. The magnetic GP shows a rise and then a falloff; this can be interpreted as the dominance of a long-distance diamagnetic pion cloud at low Q2, compensated at higher Q2 by a paramagnetic contribution from piN intermediate states.     

Frequency-selective quantitation of short-echo time 1H magnetic resonance spectra

Accurate and efficient filtering techniques are required to suppress large nuisance components present in short-echo time magnetic resonance (MR) spectra. This paper discusses two powerful filtering techniques used in long-echo time MR spectral quantitation, the maximum-phase FIR filter (MP-FIR) and the Hankel-Lanczos Singular Value Decomposition with Partial ReOrthogonalization (HLSVD-PRO), and shows that they can be applied to their more complex short-echo time spectral counterparts. Both filters are validated and compared through extensive simulations. Their properties are discussed. In particular, the capability of MP-FIR for dealing with macromolecular components is emphasized. Although this property does not make a large difference for long-echo time MR spectra, it can be important when quantifying short-echo time spectra.     

MAS NMR spectra of quadrupolar nuclei in disordered solids: the Czjzek model

Structural disorder at the scale of two to three atomic positions around the probe nucleus results in variations of the EFG and thus in a distribution of the quadrupolar interaction. This distribution is at the origin of the lineshape tailing toward high fields which is often observed in the MAS NMR spectra of quadrupolar nuclei in disordered solids. The Czjzek model provides an analytical expression for the joint distribution of the NMR quadrupolar parameters upsilon(Q) and eta from which a lineshape can be predicted. This model is derived from the Central Limit Theorem and the statistical isotropy inherent to disorder. It is thus applicable to a wide range of materials as we have illustrated for 27Al spectra on selected examples of glasses (slag), spinels (alumina), and hydrates (cement aluminum hydrates). In particular, when relevant, the use of the Czjzek model allows a quantitative decomposition of the spectra and an accurate extraction of the second moment of the quadrupolar product. In this respect, it is important to realize that only rotational invariants such as the quadrupolar product can make sense to describe the quadrupolar interaction in disordered solids.     

Fast reproducible identification and large-scale databasing of individual functional cognitive networks

Background  

Although cognitive processes such as reading and calculation are associated with reproducible cerebral networks, inter-individual variability is considerable. Understanding the origins of this variability will require the elaboration of large multimodal databases compiling behavioral, anatomical, genetic and functional neuroimaging data over hundreds of subjects. With this goal in mind, we designed a simple and fast acquisition procedure based on a 5-minute functional magnetic resonance imaging (fMRI) sequence that can be run as easily and as systematically as an anatomical scan, and is therefore used in every subject undergoing fMRI in our laboratory. This protocol captures the cerebral bases of auditory and visual perception, motor actions, reading, language comprehension and mental calculation at an individual level.     

Self-propelled droplets

Self-propelled droplets are a special kind of self-propelled matter that are easily fabricated by standard microfluidic tools and locomote for a certain time without external sources of energy. The typical driving mechanism is a Marangoni flow due to gradients in the interfacial energy on the droplet interface. In this article we review the hydrodynamic prerequisites for self-sustained locomotion and present two examples to realize those conditions for emulsion droplets, i.e. droplets stabilized by a surfactant layer in a surrounding immiscible liquid. One possibility to achieve self-propelled motion relies on chemical reactions affecting the surface active properties of the surfactant molecules. The other relies on micellar solubilization of the droplet phase into the surrounding liquid phase. Remarkable cruising ranges can be achieved in both cases and the relative insensitivity to their own ‘exhausts’ allows to additionally study collective phenomena.