Computing power indices: Multilinear extensions and new characterizations

Johnston [Johnston, R.J., 1978. On the measurement of power: some reactions to Laver. Environment and Planning A 10, 907–914], Deegan and Packel [Deegan, J., Packel, E.W., 1979. A new index of power for simple n-person games. International Journal of Game Theory 7, 113–123], and Holler [Holler, M.J., 1982. Forming coalitions and measuring voting power. Political Studies 30, 262–271] proposed three power indices for simple games: Johnston index, Deegan–Packel index, and the Public Good Index. In this paper, methods to compute these indices by means of the multilinear extension of the game are presented. Furthermore, a new characterization of the Public Good Index is given. Our methods are applied to two real-world examples taken from the political field.     

In situ study of the thermoresponsive behavior of micropatterned hydrogel films by imaging ellipsometry

A patterned hydrogel was immobilized on a polymer substrate by low-pressure argon plasma treatment using a masking technique. The polymer sample showed a thermoresponsive aggregation behavior in the region of 35-37 degrees C. The micropatterned, thermoresponsive hydrogel film has been characterized with imaging ellipsometry. The characterization was carried out on the dry film as well as on a swollen sample in water. The thermoresponsive behavior was studied in deionized water by temperature-dependent measurements in a solid-liquid cell. Through imaging ellipsometry, it was possible to distinguish the different regions of interest on a micrometer scale and to follow the swelling of the hydrogel part as a function of the temperature. It was possible to visualize the swelling as 3D profiles of Delta at various temperatures. Long-term changes of the sample could also be detected, which cannot be picked up by conventional ellipsometry.     

Determination of acyclovir in plasma by high performance liquid chromatography with UV detection. Method development and method validation

A HJPLC method for the determination of acyclovir in plasma is described. The method is simple and sensitive enough for bioequiva-lence studies, where a large number of plasma samples with low acyclovir concertration are involved. The procedure is based on the deproteinization of plasma with perchloric acid and separation of acyclovir on a Hypersil ODS Column at pH 5.6 with UV detection. The calibration standards are linear up to at least 4000 ng/mL and the limit of quantification is 10 ng/mL.     

A general procedure for the synthesis of stereochemically pure conduritol derivatives practical also for solid-phase chemistry

A straightforward synthetic protocol apt to synthesize a library constituted by all conduritol stereoisomers in solution phase is described and successfully applied to some polymer-supported substrates. During the solid-phase sequence, an unprecedented rearrangement of a resin-bound sulfone performed under the Ramberg-B?cklund conditions appears of particular interest. Upon treatment with Me(3)Si-I, thiepanes supported on resin are found to undergo regio- and stereospecific ring contraction to a six-membered ring system with traceless cleavage from the solid support.     

Changes in cerebral activity after decreased upper-limb hypertonus: an EMG-fMRI study

Objective

Whereas several studies have used functional magnetic resonance imaging (fMRI) to investigate motor recovery, whether therapy to decrease post-stroke hypertonus alters central motor patterns remains unclear. In this study, we used continuous electromyography (EMG)-fMRI to investigate possible changes in movement-related brain activation in patients receiving Botulinum toxin (BoNT-A) for hand-muscle hypertonus after chronic stroke.

Methods

We studied eight stroke patients all of whom had hemiparesis and associated upper-limb hypertonus. All patients underwent an fMRI-EMG recording and clinical-neurological assessment before BoNT-A and 5 weeks thereafter. The handgrip motor task during imaging was fixed across both patients and controls. The movements were metronome paced, movement amplitude and force were controlled with a plastic orthosis, dynamometer and EMG recording. An age-matched control group was recruited from among healthy volunteers underwent the same fMRI-EMG recording.

Results

Before BoNT-A, while patients moved the paretic hand, fMRI detected wide bilateral activation in the sensorymotor areas (SM1), in the supplementary motor area (SMA) and cerebellum. After BoNT-A blood oxygenation level-dependent (BOLD) activation decreased in ipsilateral and contralateral motor areas and became more lateralized. BOLD activation decreased also in ipsilateral cerebellar regions and in the SMA.

Conclusion

Changes in peripheral upper-limb hypertonus after BoNT-A were associated to an improvement in active movements and more lateralized and focalized activation of motor areas. The clinical and EMG-fMRI coregistration technique we used to study hand-muscle hypertonus in patients receiving BoNT-A after chronic stroke should be useful in future studies seeking improved strategies for post-stroke neurorehabilitation.     

Well-Posedness for Nonlinear Wave Equation with Potentials Vanishing at Infinity

The main purpose of this paper is to prove global well-posedness in some scale-invariant weighted Besov spaces and Strichartz spaces for the nonlinear wave equation with competing nonlinearities which have time depending potentials decaying at infinity. We discuss also some new frequency localized estimates in non-isotropic Lebesgue spaces.     

Bases of Feigin–Stoyanovsky’s type subspaces for $$C_\ell ^{(1)}$$

In this paper, we construct combinatorial bases of Feigin–Stoyanovsky’s type subspaces of standard modules for level k affine Lie algebra \(C_\ell ^{(1)}\). We prove spanning by using annihilating field \(x_\theta (z)^{k+1}\) of standard modules. In the proof of linear independence, we use simple currents and intertwining operators whose existence is given by fusion rules.     

Maps from M2({\mathbb{F}}) to M3({\mathbb{F}}) that are multiplicative with respect to the Jordan triple product

We characterize the Jordan triple product preserving maps M₂( ${\mathbb{F}}$ ) to M₃( ${\mathbb{F}}$ ) for algebraically closed fields ${\mathbb{F}}$ , char ${\mathbb{F} \neq 2}$ .     

On bipartite graphs with small number of laplacian eigenvalues greater than two and three

All connected bipartite graphs with exactly two Laplacian eigenvalues greater than two are determined. Besides, all connected bipartite graphs with exactly one Laplacian eigenvalue greater than three are determined.