On the regularization of feature fusion and mapping for fast MR multi-contrast imaging via iterative networks

Multi-contrast (MC) Magnetic Resonance Imaging (MRI) of the same patient usually requires long scanning times, despite the images sharing redundant information. In this work, we propose a new iterative network that utilizes the sharable information among MC images for MRI acceleration. The proposed network has reinforced data fidelity control and anatomy guidance through an iterative optimization procedure of Gradient Descent, leading to reduced uncertainties and improved reconstruction results. Through a convolutional network, the new method incorporates a learnable regularization unit that is capable of extracting, fusing, and mapping shareable information among different contrasts. Specifically, a dilated inception block is proposed to promote multi-scale feature extractions and increase the receptive field diversity for contextual information incorporation. Lastly, an optimal MC information feeding protocol is built through the design of a complementary feature extractor block. Comprehensive experiments demonstrated the superiority of the proposed network, both qualitatively and quantitatively.     

One-pot sonochemical synthesis of 1,3-thiazolidin-4-ones using nano-CdZr4(PO4)6 as a robust heterogeneous catalyst

An efficient three-component synthesis of 1,3-thiazolidin-4-ones is described by one-pot condensation of aldehydes, aniline and thioglycolic acid with nano-CdZr₄(PO₄)₆ as a robust heterogeneous catalyst under ultrasonic irradiation. Use of simple and readily available starting materials, experimental simplicity, applying the sonochemical methodology as an efficient method and innocuous means of activation in synthetic chemistry are some advantages of this protocol.     

Sonochemical synthesis of a new nano-sized cerium(III) supramolecular compound; Precursor for nanoceria

Using a sonochemical method, nanoparticles of a new Ce(III) supramolecular compound, (NAMH⁺)₂[Ce₄(pydc)₆(pydcH)₂(H₂O)₈]·8H₂O (1), (H₂pydc = 2,6-pyridinedicarboxylic acid, NAM = nicotinamide), have been synthesized. Compound 1 was characterized by scanning electron microscopy (SEM), X-ray powder diffraction (XRPD), FT-IR spectroscopy and elemental analyses, and its structure was determined by X-ray crystallography. It has been revealed that its structure consists of tetra-nuclear building units that extend to a 3D supramolecular network via non-covalent interactions mainly hydrogen bonding. The thermal stability of complex 1 both for its crystals and nanostructures has been studied by the thermal gravimetric (TG) method and compared with each other. The role of ultrasound irradiation power and the concentration of initial reactants on the size and morphology of the nano-structured complex 1, has been investigated. Ceria nanoparticles were obtained upon the calcination of complex 1 at 800 °C under atmospheric air. Furthermore, the fluorescent properties of complex 1 at room temperature were studied.     

Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n − 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n − r)-dimensional DFV.     

Set-up for time-resolved step-scan FTIR spectroscopy of noncyclic reactions

We have established a novel technique, which allows the application of time-resolved step-scan FTIR difference spectroscopy on noncyclic reactions. Cyclic reactions are ideally suited for the step-scan technique. However, it is difficult to apply the step-scan technique to noncyclic reactions, because the investigated process has to be repeated at about 1000 sampling positions of the interferogram. Consequently, to investigate noncyclic systems the sample has to be renewed at every sampling position. In the presented novel approach the IR-beam and the excitation laser-beam are focused to a very small diameter of 200 μm. Thereby, only a small segment of the sample, which has an overall diameter of 15 mm, is excited and probed. By moving the sample, which is mounted on an x-y-stage, to different nonexcited segments the reaction can be repeated until a complete interferogram data set is recorded. In so far as the typically used flow cells are concerned their optical pathlength is too large to perform difference spectroscopy. We use 4 μm thin films to depress the water background absorption of biological samples. As test, the well known photo-cyclic reactions of bacteriorhodopsin are measured. No systematic errors appear in the difference spectra. Because of intensity loss by the IR-microscope the signal-to-noise ratio is about 5 times less as compared to conventional step-scan measurements. For the first time, the technique is then applied to a noncyclic reaction, the photolysis of caged ATP. The successful performance with 10 μs time-resolution now opens the door for many new applications of step-scan FTIR measurements to noncyclic reactions.     

Clusters in a group: Decision making in the vector space formulation of the analytic hierarchy process

For a large group that might have a clustered structure, we discuss and implement an algorithm to group individuals into natural clusters using a convenient similarity measure. The cohesiveness of a homogeneous group or cluster is also investigated.     

Submodularity and the traveling salesman problem

In this paper we investigate the relationship between traveling salesman tour lengths and submodular functions. This work is motivated by the one warehouse multi-retailer inventory/distribution problem with traveling salesman tour vehicle routing costs. Our goal is to find a submodular function whose values are close to those of optimal tour lengths through a central warehouse and a group of retailers. Our work shows that a submodular approximation to traveling salesman tour lengths whose error is bounded by a constant does not exist. However, we present heuristics that have errors which grow slowly with the number of retailers for the traveling salesman problem in the Euclidean plane. Furthermore, we perform computational tests that show that our submodular approximations of traveling salesman tour lengths have smaller errors than our theoretical worst case analysis would lead us to believe.     

Géométrie des espaces de Banach ayant des approximations de l'identité contractantes

Let a, c ≥ 0 and let B be a compact set of scalars. We introduce property M^* (a, B, c) of Banach spaces X which is a geometric property of Banach spaces generalizing property (M^*) due to Kalton. Using M^*(a, B, c) with max ¦B¦ + c > 1, we characterize intrinsically a large class of shrinking approximations of the identity, including those related to M-, u-, and h-ideals of compact operators. We also show that the existence of these approximations of the identity is separably determined. As an application, we study ideals of compact and approximable operators. In particular, this provides an alternative unified and easier approach to the theories of M-, u-, and h-ideals of compact operators.