Principal eigenvector field segmentation for reproducible diffusion tensor tractography of white matter structures

The study was aimed to test the feasibility of utilizing an algorithmically determinable stable fiber mass (SFM) map obtained by an unsupervised principal eigenvector field segmentation (PEVFS) for automatic delineation of 18 white matter (WM) tracts: (1) corpus callosum (CC), (2) tapetum (TP), (3) inferior longitudinal fasciculus (ILF), (4) uncinate fasciculus (UNC), (5) inferior fronto-occipital fasciculus (IFO), (6) optic pathways (OP), (7) superior longitudinal fasciculus (SLF), (8) arcuate fasciculus (AF), (9) fornix (FX), (10) cingulum (CG), (11) anterior thalamic radiation (ATR), (12) superior thalamic radiation (STR), (13) posterior thalamic radiation (PTR), (14) corticospinal/corticopontine tract (CST/CPT), (15) medial lemniscus (ML), (16) superior cerebellar peduncle (SCP), (17) middle cerebellar peduncle (MCP) and (18) inferior cerebellar peduncle (ICP). Diffusion tensor imaging (DTI)-derived fractional anisotropy (FA) and the principal eigenvector field have been used to create the SFM consisting of a collection of linear voxel structures which are grouped together by color-coding them into seven natural classes to provide PEVFS signature segments which greatly facilitate the selection of regions of interest (ROIs) for fiber tractography using just a single mouse click, as compared with a manual drawing of ROIs in the classical approach. All the 18 fiber bundles have been successfully reconstructed, in all the subjects, using the single ROIs provided by the SFM approach, with their reproducibility characterized by the fact that the ROI selection is user independent. The essentially automatic PEVFS method is robust, efficient and compares favorably with the classical ROI methods for diffusion tensor tractography (DTT).     

Implantation of the 111In/Cd Probe as InO− Ion for Radioisotope Tracer Studies

A radioisotope ion implanter has been developed using a cesium-sputtering, negative ion source, which offers versatility and sustained operation. Employing the molecular ¹¹¹In¹⁶O⁻ ion, μCi activities of the radioisotope probe ¹¹¹In/Cd have been implanted into different material hosts. The implanted tracer activity has been shown to be sufficient for LTNO, NMRON and PAC. A new NMRON resonance for ¹¹¹InAg was observed at 75.08 MHz. In₂O₃ powder performed well as the radioisotope carrier in the ion source, with the ratio of radioisotope and parasitic ion current being typically 4 × 10⁻⁴.     

Higher-Order $(F,\alpha, \beta, \rho, d, E) $-Convexity in Fractional Programming

In this paper we define higher order $(F,\alpha, \beta, \rho,d, E)$-convex function with respect to $E$-differentiable function $K$ and obtain optimality conditions for nonlinear programming problem (NP) from the concept of higher order $(F,\alpha, \beta, \rho,d)$-convexity. Here, we establish Mond-Weir and Wolfe duality for (NP) and utilize these duality in nonlinear fractional programming problem.     

Fenugreek hydrogel–agarose composite entrapped gold nanoparticles for acetylcholinesterase based biosensor for carbamates detection

A biosensor was fabricated to detect pesticides in food samples. Acetylcholinesterase was immobilized in a novel fenugreek hydrogel–agarose matrix with gold nanoparticles. Transparent thin films with superior mechanical strength and stability were obtained with 2% fenugreek hydrogel and 2% agarose. Immobilization of acetylcholinesterase on the membrane resulted in high enzyme retention efficiency (92%) and a significantly prolonged shelf life of the enzyme (half-life, 55 days). Transmission electron microscopy revealed that, gold nanoparticles (10–20 nm in diameter) were uniformly dispersed in the fenugreek hydrogel–agarose–acetylcholinesterase membrane. This immobilized enzyme-gold nanoparticle dip-strip system detected various carbamates, including carbofuran, oxamyl, methomyl, and carbaryl, with limits of detection of 2, 21, 113, and 236 nM (S/N = 3), respectively. Furthermore, the fabricated biosensor exhibited good testing capabilities when used to detect carbamates added to various fruit and vegetable samples.     

Isometric multipliers of a vector valued Beurling algebra on a discrete semigroup

Let (S,ω) be a weighted abelian semigroup, let M _ω (S) be the semigroup of ω-bounded multipliers of S, and let \(\mathcal {A}\) be a strictly convex commutative Banach algebra with identity. It is shown that T is an onto isometric multiplier of \(\ell ^{1}(S,\omega , \mathcal {A})\) if and only if there exists an invertible σ ∈ M _ω (S), a unitary point \(a \in \mathcal {A}\), and a k>0 such that \(T(f)= ka{\sum }_{x \in S} f(x)\delta _{\sigma (x)}\) for each \(f={\sum }_{x \in S}f(x)\delta _{x} \in \ell ^{1}(S,\omega ,\mathcal {A})\). It is also shown that an isomorphism from \(\ell ^{1}(S_{1},\omega _{1},\mathcal {A})\) onto \(\ell ^{1}(S_{2},\omega _{2}, \mathcal {B})\) induces an isomorphism from \(M(\ell ^{1}(S_{1},\omega _{1},\mathcal {A}))\), the set of all multipliers of \(\ell ^{1}(S_{1},\omega _{1},\mathcal {A})\), onto \(M(\ell ^{1}(S_{2},\omega _{2},\mathcal {B}))\).     

Approximation of quadrilaterals by rational quadrilaterals in the plane

Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain diophantine equations. We look at a number of such questions including the question of approximating arbitrary triangles and quadrilaterals by those with rational sides, diagonals and areas. We transform these problems into questions on the existence of infinitely many rational solutions on a two parameter family of quartic curves. This is further transformed to a two parameter family of elliptic curves to deduce our main result concerning density of points on a line which are at a rational distance from three collinear points (Theorem 4). We deduce from this a new proof of density of rational quadrilaterals in the space of all quadrilaterals (Theorem 39). The other main result (Theorem 3) of this article is on the density of rational triangles which is related to analyzing rational points on the unit circle. Interestingly, this enables us to deduce that parallelograms with rational sides and area are dense in the class of all parallelograms. We also give a criterion for density of certain sets in topological spaces using local product structure and prove the density Theorem 6 in the appendix section. An application of this proves the density of rational points as stated in Theorem 31.     

An innovative extensional viscometer for low-viscosity and low-elasticity liquids

A spinline-type extensional viscometer is described in which an innovative method of tensile stress measurement is employed. A limited amount of liquid flows through a vertical capillary at a constant flow rate under the influence of a constant pressure head. The drainage time decreases when the liquid stream leaving the capillary is stretched by the application of vacuum. These drainage times are measured in a manner similar to that used for intrinsic viscosity measurements. The measured difference in drainage times, with and without stretching, is trivially related to the extensional stress at the capillary exit, and this provides a very simple method of accurately determining fluid stretching forces having a magnitude as low as 10^-4 N; stresses at other axial locations in the stretched liquid jet are obtained by means of a force balance in the usual manner. The validity of the proposed technique is demonstrated by obtaining the expected results for a Newtonian oil having a shear viscosity of 56.2 mPa-s. Also presented are preliminary data on polyethylene oxide-in-water solutions having an even lower shear viscosity.     

Non-linear studies of orthotropic shallow spherical shells on elastic foundation

Governing non-linear integro-differential equations for cylindrically orthotropic shallow spherical shells resting on linear Winkler-Pasternak elastic foundations, undergoing moderately large deformations are presented. Three problems, namely, non-linear static deflection response, non-linear dynamic deflection response and dynamic snap-through buckling of orthotropic shells have been investigated. The influences of material orthotropy, foundation parameters and shell-material damping on the deflection response are determined for the clamped and the simply- supported immovable edge conditions accurately. Orthotropy, foundation interaction and material damping play significant roles in improving the load carrying capacity of the shell structures.     

A visual strip sensor for determination of iron

A visual strip has been developed for sensing iron in different aqueous samples like natural water and fruit juices. The sensor has been synthesized by UV-radiation induced graft polymerization of acrylamide monomer in microporous poly(propylene) base. For physical immobilization of iron selective reagent, the in situ polymerization of acrylamide has been carried out in the presence of 1,10-phenanthroline. The loaded strip on interaction with Fe(II) in aqueous solution turned into orange red color and the intensity of the color was found to be directly proportional to the amount of Fe(II) in the aqueous sample. The minimal sensor response with naked eye was found for 50 ng mL⁻¹ of Fe in 15 min of interaction. However, as low as 20 ng mL⁻¹ Fe could be quantified using a spectrophotometer. The detection limit calculated using the 3s/S criteria, where ‘s’ is the standard deviation of the absorbance of blank reagent loaded strip and ‘S’ is the slope of the linear calibration plot, was 1.0 ng mL⁻¹. The strip was applied to measure Fe in a variety of samples such as ground water and fruit juices.