A signal subspace approach for modeling the hemodynamic response function in fMRI

Many fMRI analysis methods use a model for the hemodynamic response function (HRF). Common models of the HRF, such as the Gaussian or Gamma functions, have parameters that are usually selected a priori by the data analyst. A new method is presented that characterizes the HRF over a wide range of parameters via three basis signals derived using principal component analysis (PCA). Covering the HRF variability, these three basis signals together with the stimulation pattern define signal subspaces which are applicable to both linear and nonlinear modeling and identification of the HRF and for various activation detection strategies. Analysis of simulated fMRI data using the proposed signal subspace showed increased detection sensitivity compared to the case of using a previously proposed trigonometric subspace. The methodology was also applied to activation detection in both event-related and block design experimental fMRI data using both linear and nonlinear modeling of the HRF. The activated regions were consistent with previous studies, indicating the ability of the proposed approach in detecting brain activation without a priori assumptions about the shape parameters of the HRF. The utility of the proposed basis functions in identifying the HRF is demonstrated by estimating the HRF in different activated regions.     

Mating Siegel quadratic polynomials

Let be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers and . Using a new degree Blaschke product model for the dynamics of and an adaptation of complex a priori bounds for renormalization of critical circle maps, we prove that can be realized as the mating of two Siegel quadratic polynomials with the corresponding rotation numbers and .

     

Soluble and thermally stable polyamides bearing 1,1′-thiobis(2-naphthoxy) groups

A new-type of sulfide containing diacid (1,1′-thiobis(2-naphthoxy acetic acid)) was synthesized from 2-naphthol in three steps. Reaction of 2-naphthol with sulfur dichloride afforded 1,1′-thiobis(2-naphthol) (TBN). 1,1′-Thiobis(2-naphthoxy acetic ester) (TBNAE) was successfully synthesized by refluxing the TBN with methylcholoroacetate in the presence of potassium carbonate. The related diacid was synthesized by basic solution reduction of TBNAE. The obtained diacid was fully characterized and used to prepare novel thermally stable poly(sulfide ether amide)s via polyphosphorylation reaction with different aromatic diamines. The properties of these new polyamides were investigated and compared with similar polyamides. These polyamides showed inherent viscosities in the range of 0.39-0.87 dL g⁻¹ in N,N-dimethylacetamide (DMAc) at 30 °C and at a concentration of 0.5 g dL⁻¹. All the polyamides were readily soluble in a variety of polar solvents such as DMAc and tetrahydrofuran (THF). These polyamides showed glass transition temperature (T_g) between 241-268 °C. Thermogravimetric analysis measurement revealed the decomposition temperature at 10% weight loss (T₁₀) ranging from 441- 479 °C in argon atmosphere.     

One‐pot Green Procedure for Synthesis of Tetrahydrobenzo[a]xanthene‐11‐one Catalyzed by Brønsted Ionic Liquids under Solvent‐free Conditions

An efficient one‐pot condensation of β‐naphthol, aldehydes and cyclic 1,3‐dicarbonyl compound has been achieved with ionic liquids as catalyst, thus a variety of 8,9,10,12‐tetrahydrobenzo[a]xanthen‐11‐one derivatives were prepared in good yields. The present approach offers several advantages such as shorter reaction times, good yields and mild reaction conditions.     

Pentafluorophenylammonium triflate as a mild and new organocatalyst for acylation of alcohols, phenols, and amines under solvent-free condition

A simple, inexpensive, environmentally friendly and efficient route for the acylation of a number of alcohols, phenols and amines using pentafluorophenylammonium triflate (PFPAT) as a catalyst is described. PFPAT organocatalyst is air-stable, cost-effective, easy to handle, and easily removed from the reaction mixtures.     

Effect of carbon fiber volume fraction on 6H to 4H-SiC polytype transformation

In this study, polycrystalline α-SiC composed of 55.7?wt.% 6H-SiC, 35.1?wt.% 4H-SiC with different volume fractions of carbon fibers (0–5–10–15–20%) was successfully sintered by spark plasma sintering technique at 2000°C and 35?MPa of applied pressure. The micrographs obtained from scanning electron microscopy revealed that the sintered samples were composed of equiaxed SiC grains. Results indicated that the presence of carbon fibers retarded the SiC densification process, decreased their relative densities and increased their porosity. Additionally, according to quantitative phase analysis by the Rietveld method during the sintering step, it was found that the 6H to 4H transformation has taken place. Increasing the carbon fibers content accelerated this trend as the sample containing 20?vol.% carbon fiber was consisted of 85.5?wt.% 4H-SiC.     

A note on quasi-Gorenstein rings

In this paper, after giving a criterion for a Noetherian local ring to be quasi-Gorenstein, we obtain some sufficient conditions for a quasi-Gorenstein ring to be Gorenstein. In the course, we provide a slight generalization of a theorem of Evans and Griffith. Received: 16 February 2008     

Synthesis and characterization of polydiacetylene films and nanotubes

We report here the synthesis and characterization of polydiacetylene (PDA) films and nanotubes using layer-by-layer (LBL) chemistry. 10,12-Docosadiyndioic acid (DCDA) monomer was self-assembled on flat surfaces and inside of nanoporous alumina templates. UV irradiation of DCDA provided polymerized-DCDA (PDCDA) films and nanotubes. We have used zirconium-carboxylate interlayer chemistry to synthesize PDCDA multilayers on flat surfaces and in nanoporous template. PDCDA multilayers were characterized using optical (UV-vis, fluorescence, ellipsometry, FTIR) spectroscopies, ionic current-voltage ( I- V) analysis, and scanning electron microscopy. Ellipsometry, FTIR, electronic absorption and emission spectroscopies showed a uniform DCDA deposition at each deposition cycle. Our optical spectroscopic analysis indicates that carboxylate-zirconium interlinking chemistry is robust. To explain the disorganization in the alkyl portion of PDCDA multilayer films, we propose carboxylate-zirconium interlinkages act as "locks" in between PDCDA layers which restrict the movement of alkyl portion in the films. Because of this locking, the induced-stresses in the polymer chains can not be efficiently relieved. Our ionic resistance data from I- V analysis correlate well with calculated resistance at smaller number of PDCDA layers but significantly deviated for thicker PDCDA nanotubes. These differences were attributed to ion-blocking because some of the PDCDA nanotubes were totally closed and the nonohmic and permselective ionic behaviors when the diameter of the pores approaches the double-layer thickness of the solution inside of the nanotubes.     

Synthesis of new di‐ and tetraazadibenzosulfoxide macrocycolic compounds

Novel macrocyclic di and tetraamide compounds have been synthesized by the reaction of 2‐2′‐sulfoxide‐bis‐(4‐methyl phenoxy) aceticester or aceticacid chloride) (obtained from corresponding bisphenol) with appropriate diamines. Also the results of the presence of base as template are discussed and compared.