One-level reformulation of the bilevel Knapsack problem using dynamic programming

In this paper, we consider the Bilevel Knapsack Problem (BKP), which is a hierarchical optimization problem in which the feasible set is determined by the set of optimal solutions for a parametric Knapsack Problem. We introduce a new reformulation of the BKP into a one-level integer programming problem using dynamic programming. We propose an algorithm that allows the BKP to be solved exactly in two steps. In the first step, a dynamic programming algorithm is used to compute the set of follower reactions to leader decisions. In the second step, an integer problem that is equivalent to the BKP is solved using a branch-and-bound algorithm. Numerical results are presented to show the performance of our method.     

Blocked-micropores,surface functionalized,bio-compatible and silica-coated iron oxide nanocomposites as advanced MRI contrast agent

Quasi-critical fluctuations occur close to critical points or close to continuous phase transitions. In three-dimensional systems, precision tuning is required to access the fluctuation regime. Lowering the dimensionality enhances the parameter space for quasi-critical fluctuations considerably. This enables one to make use of novel properties emerging in fluctuating systems, such as giant susceptibilities, Casimir forces or novel quasi-particle interactions. Examples are discussed ranging from simple metal–adsorbate systems to unconventional superconductivity in iron-based superconductors.     

Power enhancement with super-Gaussian sliding-frequency guiding filters

I show with numerical simulations that higher-order sliding filters, especially super-Gaussian filters, can produce dramatic power enhancement of optical solitons, similar to that of dispersion-managed solitons. This approach should allow smaller timing jitter without sacrificing the signal-to-noise ratio.     

Paramagnetic liposomes: inner versus outer membrane relaxivity of DPPC liposomes incorporating lipophilic gadolinium complexes

Proton relaxometric properties of unilamellar DPPC liposomes embedding an amphiphilic paramagnetic chelate (Gd-DTPA-BC(14)A) in both layers of the phospholipid membrane or only in the external one are compared. The results show that the membrane's water permeability is able to quench the effect of the paramagnetic complexes located in the internal layer of DPPC liposomes, leading thus to an apparent lower global relaxivity.     

Synthesis and Characterization of Various Benzyl Diethylenetriaminepentaacetic Acids (dtpa) and Their Paramagnetic Complexes,Potential Contrast Agents for Magnetic Resonance Imaging

Four derivatives of diethylenetriaminepentaacetic acid (=3,6,9‐tris(carboxymethyl)‐3,6,9‐triazaundecanedioic acid (H₅dtpa)), potential contrast agents for magnetic resonance imaging (MRI), carrying benzyl groups at various positions of the parent structure were synthesized and characterized by a thorough multinuclear NMR study, i.e., the (S)‐ and (R)‐stereoisomers 1a and 1b of 4‐benzyl‐3,6,9‐tris(carboxymethyl)‐3,6,9‐triazaundecanedioic acid (H₅[(S)‐(4‐Bz)dtpa] and H₅[(R)‐(4‐Bz)dtpa], the diamide derivative N,N″‐bis[(benzylcarbamoyl)methyl]diethylenetriamine‐N,N′,N″‐triacetic acid (=3,9‐bis[2‐(benzylamino)‐2‐oxoethyl]‐6‐(carboxymethyl)‐3,6,9‐triazaundecanedioic acid; H₃[dtpa(BzA)₂]; 2 ), and the diester derivative N,N″‐bis{[(benzyloxy)carbonyl]methyl}diethylenetriamine‐N,N′,N″‐triacetic acid (=3,9‐bis[2‐(benzyloxy)‐2‐oxoethyl]‐6‐(carboxymethyl)‐3,6,9‐triazaundecanedioic acid; H₃[dtpa(BzE)₂]; 3 ). From the ¹⁷O‐NMR chemical shift of H₂O induced by their dysprosium complexes with ligands 1 – 3 , it was concluded that only one H₂O molecule is contained in the first coordination sphere of these lanthanide complexes. The rotational correlation times (τ_R) of the complexes were estimated from the ²H‐NMR longitudinal relaxation rate of the deuterated diamagnetic lanthanum complexes. The exchange time of the coordinated H₂O molecule (τ_M) was studied through the temperature dependence of the ¹⁷O‐NMR transverse relaxation rate. As compared to [Gd(dtpa)]²⁻, the H₂O‐exchange rate is faster for [Gd{(S)‐(4‐Bz)dtpa}]²⁻ and [Gd{(R)‐(4‐Bz)dtpa}]²⁻‐, slower for [Gd{dtpa(BzA)₂}], and almost identical for [Gd{dtpa(BzE)₂}]. The analysis of the ¹H‐relaxivity of the gadolinium complexes recorded from 0.02 to 300 MHz established that i) the relaxivity of [Gd{dtpa(BzE)₂}] is similar to that of [Gd(dtpa)]²⁻, ii) the slightly slower molecular rotation of [Gd{dtpa(BzA)₂}] induces a mild enhancement of its relaxivity, and iii) the marked increase of relaxivity of [Gd{(S)‐(4‐Bz)dtpa}]²⁻ and [Gd{(R)‐(4‐Bz)dtpa}]²⁻ mainly results from an apparently shorter distance between the gadolinium ion and the H₂O protons of the coordinated H₂O molecule.     

Calix[4]arenes as Molecular Platforms for Magnetic Resonance Imaging (MRI) Contrast Agents

The novel amphipilic conjugate of a calix[4]arene with four Gd–1,4,7,10‐ tetra(carboxymethyl)‐1,4,7,10‐tetraazacyclododecane (DOTA) chelates has potential as a magnetic resonance imaging contrast agent, both in its monomeric and in its micellar form. The system, illustrated here with its nuclear magnetic relaxation profile, shows good relaxivities, thanks to its high rigidity.

     

Sharp parameter bounds for certain maximal point lenses

Starting from an $n$ -point circular gravitational lens having $3n+1$ images, Rhie (ArXiv Astrophysics e-prints, 2003) used a perturbation argument to construct an $(n+1)$ -point lens producing $5n$ images. In this work we give a concise proof of Rhie’s result, and we extend the range of parameters in Rhie’s model for which maximal lensing occurs. We also study a slightly different construction given by Bayer and Dyer (Gen Relativ Gravit 39(9):1413–1418, 2007) arising from the $(3n+1)$ -point lens. In particular, we extend their results and give sharp parameter bounds for their lens model. By a substitution of variables and parameters we show that both models are equivalent in a certain sense.     

Hydrogels Incorporating GdDOTA: Towards Highly Efficient Dual T(1) /T(2) MRI Contrast Agents

Do not tumble dry: Gadolinium-DOTA encapsulated into polysaccharide nanoparticles (GdDOTA?NPs) exhibited high relaxivity (r(1) =101.7?s(-1) mM(-1) per Gd(3+) ion at 37?°C and 20?MHz). This high relaxation rate is due to efficient Gd loading, reduced tumbling of the Gd complex, and the hydrogel nature of the nanoparticles. The efficacy of the nanoparticles as a T(1) /T(2) dual-mode contrast agent was studied in C6 cells.     

Ferromagnetic Mn-doped Si0.3Ge0.7 nanodots self-assembled on Si(100)

Densely packed epitaxial Mn-doped Si(0.3)Ge(0.7) nanodots self-assembled on Si(100) have been obtained. Their structural properties were studied using reflection high-energy electron diffraction, energy dispersive x-ray diffraction, atomic force microscopy, extended x-ray absorption fine structure measurements and high-resolution transmission electron microscopy. Mn(5)Ge(1)Si(2) crystallites embedded in Si(0.3)Ge(0.7) were found. They exhibit a ferromagnetic behaviour with a Curie temperature of about 225?K.     

The highest water exchange rate ever measured for a Gd(III) chelate

The complex [Gd(L)(H2O)]3- (H(6)L =N,N'-bis(6-carboxy-2-pyridylmethyl)ethylenediamine-N,N'-methylenephosphonic acid) displays the highest water exchange rate ever measured for a Gd(III) chelate (k(298)(ex)= 8.8 x 10(8) s(-1)), which is attributed to the flexibility of the metal coordination environment.