Arbres de Markov Triplet et fusion de Dempster–Shafer

The hidden Markov chains (HMC) (X,Y) have been recently generalized to triplet Markov chains (TMC), which enjoy the same capabilities of restoring a hidden process X from the observed process Y. The posterior distribution of X can be viewed, in an HMC, as a particular case of the so called “Dempster–Shafer fusion” (DS fusion) of the prior Markov with a probability q defined from the observation Y=y. As such, when we place ourselves in the Dempster–Shafer theory of evidence by replacing the probability distribution of X by a mass function M having an analogous Markov form (which gives again the classical Markov probability distribution in a particular case), the result of DS fusion of M with q generalizes the conventional posterior distribution of X. Although this result is not necessarily a Markov distribution, it has been recently shown that it is a TMC, which renders traditional restoration methods applicable. The aim of this Note is to present some generalizations of the latter result: (i) more general HMCs can be considered; (ii) q, which can possibly be a mass function Q, is itself a result of the DS fusion; and (iii) all these results are finally specified in the hidden Markov trees (HMT) context, which generalizes the HMC one. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Homomo rphisms of the g roup $$L^1_s$$ into the g roup $$L^1_ r$$ fo r r ≤ 3

We determine all homomorphisms of the differential group L¹_sL^1_s with arbitrary s ≥ 2 into the group L¹_rL^1_r for r ≤  3.     

Quadratic harnesses, -commutations, and orthogonal martingale polynomials

We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a -commutation relation. This implies that quadratic harnesses are essentially determined uniquely by five numerical constants. Explicit recurrences for the orthogonal martingale polynomials are derived in several cases of interest.

     

Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate

We discuss dynamics of a slow quantum phase transition in a spin-1 Bose-Einstein condensate. We analytically determine the scaling properties of the system magnetization and verify them with numerical simulations in a one dimensional model.     

Terahertz emission from collapsing field domains during switching of a gallium arsenide bipolar transistor

Broadband pulsed THz emission with peak power in the sub-mW range has been observed experimentally during avalanche switching in a gallium arsenide bipolar junction transistor at room temperature, while significantly higher total generated power is predicted in simulations. The emission is attributed to very fast oscillations in the conductivity current across the switching channels, which appear as a result of temporal evolution of the field domains generated in highly dense electron-hole plasma. This plasma is formed in turn by powerful impact ionization in multiple field domains of ultrahigh amplitude.     

Microwave frequency modulation in CW EPR at W-band using a loop-gap resonator

Loop-gap resonator (LGR) technology has been extended to W-band (94GHz). One output of a multiarm Q-band (35GHz) EPR bridge was translated to W-band for sample irradiation by mixing with 59 GHz; similarly, the EPR signal was translated back to Q-band for detection. A cavity resonant in the cylindrical TE011 mode suitable for use with 100 kHz field modulation has also been developed. Results using microwave frequency modulation (FM) at 50 kHz as an alternative to magnetic field modulation are described. FM was accomplished by modulating a varactor coupled to the 59 GHz oscillator. A spin-label study of sensitivity was performed under conditions of overmodulation and gamma2H1(2)T1T2<1. EPR spectra were obtained, both absorption and dispersion, by lock-in detection at the fundamental modulation frequency (50 kHz), and also at the second and third harmonics (100 and 150 kHz). Source noise was deleterious in first harmonic spectra, but was very low in second and third harmonic spectra. First harmonic microwave FM was transferred to microwave modulation at second and third harmonics by the spins, thus satisfying the "transfer of modulation" principle. The loaded Q-value of the LGR with sample was 90 (i.e., a bandwidth between 3 dB points of about 1 GHz), the resonator efficiency parameter was calculated to be 9.3 G at one W incident power, and the frequency deviation was 11.3 MHz p-p, which is equivalent to a field modulation amplitude of 4 G. W-band EPR using an LGR is a favorable configuration for microwave FM experiments.     

Stereochemistry of rHint1 hydrolase assisted cleavage of P-N bond in nucleoside 5'-O-phosphoramidothioates

The Hint-1 hydrolase assisted cleavage of the P-N bond in adenosine-5'-O-[N-(tryptophanylamide)]phosphoramidothioate proceeds with retention of configuration at the phosphorus atom which is consistent with the formation of a covalent enzyme-substrate complex.     

Complexes between some lysine-containing peptides and crown ethers--electrospray ionization mass spectrometric study

The complexes between lysine-containing peptides (M) and crown ethers (CEs, 18C6, 15C5, 12C4) have been studied by the electrospray ionization (ESI) mass spectrometry. The maximum number of CEs attached has been found to be the same as that of the alkyl-amino side chains of lysine and as that of the protons attached. Examination of the breakdown plots of the abundances of the ions observed against the cone voltage (CV) has shown that mass spectrometric fragmentation pathways of [M + nH + (CE)n]+n may involve a loss of a neutral CE molecule as well as protonated one. The decrease in the CE cavity (the use of 12C4 or 15C5 instead of 18C6) leads to a dramatic lowering in the stability of the complexes in the gas phase but not in solution. Attachment of a CE to peptides increases their hydrophobicity, and therefore proceeds with lower efficiency in water than in methanol.