Adaptive instant record signals applied to detection with time reversal operator decomposition

Time reversal arrays are becoming common tools whether for detection or tomography. These applications require the measurement of the response from the array to one or several receivers. The most natural way to record the impulse responses for several sources is to generate pulses successively from each emitting point and record simultaneously the signals from the receivers. However, this method is very time consuming or inefficient in terms of signal-to-noise ratio. To overcome this limitation quasi-orthogonal pseudonoise signals like Kasami sequences can be used. For guided wave propagation, a very high degree of orthogonality between the signal is necessary to allow an accurate measure of the whole multipath structure of the transfer function. Hence, in this work, we propose a new family of pseudo-orthogonal signals that is adapted to the environment and more specifically, to highly dispersive media. These adaptive instant records signals are used experimentally to detect targets using the time reversal operator decomposition method. The accuracy of the 15 x 15 transfer functions acquired simultaneously, and therefore the detection capability, are demonstrated in an experimental ultrasonic waveguide as a small-scale model of shallow water propagation including bottom absorption and reverberation.     

Continuous Limits of Classical Repeated Interaction Systems

We consider the physical model of a classical mechanical system (called “small system”) undergoing repeated interactions with a chain of identical small pieces (called “environment”). This physical setup constitutes an advantageous way of implementing dissipation for classical systems; it is at the same time Hamiltonian and Markovian. This kind of model has already been studied in the context of quantum mechanical systems, where it was shown to give rise to quantum Langevin equations in the limit of continuous time interactions (Attal and Pautrat in Ann Henri Poincaré 7:59–104, 2006), but it has never been considered for classical mechanical systems yet. The aim of this article is to compute the continuous limit of repeated interactions for classical systems and to prove that they give rise to particular stochastic differential equations (SDEs) in the limit. In particular, we recover the usual Langevin equations associated with the action of heat baths. In order to obtain these results, we consider the discrete-time dynamical system induced by Hamilton’s equations and the repeated interactions. We embed it into a continuous-time dynamical system and compute the limit when the time step goes to 0. This way, we obtain a discrete-time approximation of SDE, considered as a deterministic dynamical system on the Wiener space, which is not exactly of the usual Euler scheme type. We prove the L ^p and almost sure convergence of this scheme. We end up with applications to concrete physical examples such as a charged particle in a uniform electric field or a harmonic interaction. We obtain the usual Langevin equation for the action of a heat bath when considering a damped harmonic oscillator as the small system.     

Nonsmooth nonconvex optimization approach to clusterwise linear regression problems

Clusterwise regression consists of finding a number of regression functions each approximating a subset of the data. In this paper, a new approach for solving the clusterwise linear regression problems is proposed based on a nonsmooth nonconvex formulation. We present an algorithm for minimizing this nonsmooth nonconvex function. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate a good starting point for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or near global solution to the problem when the data sets are sufficiently dense. The algorithm is compared with the multistart Späth algorithm on several publicly available data sets for regression analysis.     

Characterization Theorem for Best Polynomial Spline Approximation with Free Knots,Variable Degree and Fixed Tails

In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov–Rubinov. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation.     

Mobilité conformationnelle et migration des liaisons π dans le [24]annulène

Conformational Mobility and Migration of the π Bonds of the [24]annulene. The configuration and the conformation of [24]annulene have been determined after a detailed analysis of its ¹H-NMR spectrum recorded at −95°. At this temperature, molecular dynamics is practically frozen, and the spectrum can be correctly simulated considering eight magnetic sites with the relevant couplings. The [24]annulene exhibits alternation of the double and the single bonds with the CTTTCTTTCTTT sequence (C=cis, T=trans) expressing the connectivity of the double bonds. The signal of the 9 protons pointing inside the ring is 7.72 ppm at lower field than the signal of the 15 outer protons; this indicates a marked paramagnetic ring current. Molecular dynamics is revealed by the dependence of the spectrum upon the temperature; the simulation of the line shape of these spectra indicates that the [24]annulene in solution exists as an equilibrium of two conformers A and B ( B / A ≤0.05), both having the same configuration. Each of these conformers undergoes two isodynamic processes: a migration of the π bonds on the adjacent single bonds (bond shift) described by V and a conformational mobility described by K. The two conformers interconvert extremely rapidely. Conformer A complies with C_3h symmetry, conformer B with C₃ symmetry. The enthalpy, entropy, and free energy of activation for the processes described by V and K in the major conformer A have been determined: these processes are slower than those observed in [16]annulene. From their values, we could deduce that the resonance energy in the [24]-7³annulene is negative and of the order of −9 to −10 kcal⋅mol⁻¹.     

Phosphonated Near‐Infrared Fluorophores for Biomedical Imaging of Bone

The conventional method for creating targeted contrast agents is to conjugate separate targeting and fluorophore domains. A new strategy is based on the incorporation of targeting moieties into the non‐delocalized structure of pentamethine and heptamethine indocyanines. Using the known affinity of phosphonates for bone minerals in a model system, two families of bifunctional molecules that target bone without requiring a traditional bisphosphonate are synthesized. With peak fluorescence emissions at approximately 700 or 800 nm, these molecules can be used for fluorescence‐assisted resection and exploration (FLARE) dual‐channel imaging. Longitudinal FLARE studies in mice demonstrate that phosphonated near‐infrared fluorophores remain stable in bone for over five weeks, and histological analysis confirms their incorporation into the bone matrix. Taken together, a new strategy for creating ultra‐compact, targeted near‐infrared fluorophores for various bioimaging applications is described.     

Elongated Bacterial Pili as a Versatile Alignment Medium for NMR Spectroscopy

In NMR spectroscopy, residual dipolar couplings (RDCs) have emerged as one of the most exquisite probes of biological structure and dynamics. The measurement of RDCs relies on the partial alignment of the molecule of interest, for example by using a liquid crystal as a solvent. Here, we establish bacterial type 1 pili as an alternative liquid-crystalline alignment medium for the measurement of RDCs. To achieve alignment at pilus concentrations that allow for efficient NMR sample preparation, we elongated wild-type pili by recombinant overproduction of the main structural pilus subunit. Building on the extraordinary stability of type 1 pili against spontaneous dissociation and unfolding, we show that the medium is compatible with challenging experimental conditions such as high temperature, the presence of detergents, organic solvents or very acidic pH, setting it apart from most established alignment media. Using human ubiquitin, HIV-1 TAR RNA and camphor as spectroscopic probes, we demonstrate the applicability of the medium for the determination of RDCs of proteins, nucleic acids and small molecules. Our results show that type 1 pili represent a very useful alternative to existing alignment media and may readily assist the characterization of molecular structure and dynamics by NMR.     

Experimental and theoretical investigations of the sulfite-based polyoxometalate cluster redox series: alpha- and beta-[Mo(18)O(54)(SO(3))(2)](4-/5-/6-)

The synthesis, isolation and structural characterization of the sulfite polyoxomolybdate clusters alpha-(D(3h))(C(20)H(44)N)(4){alpha-[Mo(18)O(54)(SO(3))(2)]}CH(3)CN and beta-(D(3d))(C(20)H(44)N)(4){beta-[Mo(18)O(54)(SO(3))(2)]}CH(3)CN is presented. Voltammetric studies in acetonitrile (0.1 M Hx(4)NClO(4), Hx(4)N=tetra-n-hexylammonium) reveal the presence of an extensive series of six one-electron reduction processes for both isomers. Under conditions of bulk electrolysis, the initial [Mo(18)O(54)(SO(3))(2)](4-/5-) and [Mo(18)O(54)(SO(3))(2)](5-/6-) processes produce stable [Mo(18)O(54)(SO(3))(2)](5-) and [Mo(18)O(54)(SO(3))(2)](6-) species, respectively, and the same reduced species may be produced by photochemical reduction. Spectroelectrochemical data imply that retention of structural form results upon reduction, so that both alpha and beta isomers are available at each of the 4-, 5-, and 6-redox levels. However, the alpha isomer is the thermodynamically favored species in both the one- and two-electron-reduced states, with beta-->alpha isomerization being detected in both cases on long time scales (days). EPR spectra also imply that increasing localization of the unpaired electron occurs over the alpha- and beta-[Mo(18)O(54)(SO(3))(2)](5-) frameworks as the temperature approaches 2 K where the EPR spectra show orthorhombic symmetry with different g and hyperfine values for the alpha and beta isomers. Theoretical studies support the observation that it is easier to reduce the alpha cluster than the beta form and also provide insight into the driving force for beta-->alpha isomerization in the reduced state. Data are compared with that obtained for the well studied alpha-[Mo(18)O(54)(SO(4))(2))](4-) sulfate cluster.