An algorithm to estimate anatomical connectivity between brain regions using diffusion MRI

The study of anatomical connectivity is essential for interpreting functional MRI data and for establishing how brain areas are linked together into networks to support higher-order functions. Diffusion-weighted MR images (DWI) and tractography provide a unique noninvasive tool to explore the connectional architecture of the brain. The identification of anatomical circuits associated with a specific function can be better accomplished by the joint application of diffusion and functional MRI. In this article, we propose a simple algorithm to identify the set of pathways between two regions of interest. The method is based upon running deterministic tractography from all possible starting positions in the brain and selecting trajectories that intersect both regions. We compare results from single-fiber tractography using diffusion tensor imaging and from multi-fiber tractography using reduced-encoding persistent angular structure (PAS) MRI on standard DWI datasets from healthy human volunteers. Our results show that, in comparison with single-fiber tractography, the multi-fiber technique reveals additional putative routes of connection. We demonstrate highly consistent results of the proposed technique over a cohort of 16 healthy subjects.     

Global compactness for a class of quasi-linear elliptic problems

We prove a global compactness result for Palais-Smale sequences associated with a class of quasi-linear elliptic equations on exterior domains.     

On the Dalgaard-Strulik Model with Logistic Population Growth Rate and Delayed-Carrying Capacity

Recently Dalgaard and Strulik have proposed (in Resour. Energy Econ. 33:782–797, 2011) an energy model of capital accumulation based on the mathematical framework developed by Solow-Swan and coupled with Cobb-Douglas production function (Solow in Q. J. Economics 70:65–94, 1956; Swan in Econ. Rec. 32(63):334–361, 1956). The model is based on a constant rate of population growth assumption. The present paper, according to the analysis performed by Yukalov et al. (Physica D 238:1752–1767, 2009), improves the Dalgaard-Strulik model by introducing a logistic-type equation with delayed carrying capacity which alters the asymptotic stability of the relative steady state. Specifically, by choosing the time delay as a bifurcation parameter, it turns out that the steady state loses stability and a Hopf bifurcation occurs when time delay passes through critical values. The results are of great interest in the applied and theoretical economics.     

Cubic Nonlinearity in Elastic Materials: Theoretical Prediction and Computer Modelling of New Wave Effects

Our object of interest is nonlinear interaction of waves in elastic materials. The new model of a material is proposed that takes into account the mechanism of simultaneous quadratic and cubic nonlinear deformations. Introduction of cubic nonlinearity into the model makes the general wave picture more complicated and creates new possibilities for the wave analysis. We present four possibilities for the evolution of profiles of plane harmonic waves. It is noted that quadratic and cubic nonlinearities emerge first of all in the second and third harmonics generation, respectively. Further, we discuss the results of computer modelling of the wave profile evolution. The influence of the progress of second and third harmonics on the wave profile evolution is studied separately. We study separately how second and third harmonics influence the evolution of the wave profile. We also investigate how the progress of harmonics depends on the initial frequency and amplitude. We find two distinct schemes of the evolution progress: the scheme (in) with four stages for the second harmonics and the scheme with three stages for the third harmonics. As a result the influence of both harmonics could be observed simultaneously, and such a case is demonstrated in the paper. Nevertheless this phenomenon is not necessarily present in every material which explains the absence of experimental observations of the third harmonics by this time.     

Total syntheses of anominine and tubingensin A

A divergent strategy for the total syntheses of the indole terpenoid anominine (1) and its natural congener tubingensin A (2) has been developed. The common intermediate 11 bearing all of the required stereogenic centers for both natural products was first assembled by employing a Ueno-Stork radical cyclization and a Sc(OTf)(3)-mediated Mukaiyama aldol reaction to form the key C-C bonds in a stereocontrolled manner. The route to anominine features a radical deoxygenation followed by an efficient side-chain installation, while the path to tubingensin A exploits a CuOTf-promoted 6π-electrocyclization/aromatization sequence to forge the central region of the pentacyclic scaffold.     

On Grover’s search algorithm from a quantum information geometry viewpoint

We present an information geometric characterization of Grover’s quantum search algorithm. First, we quantify the notion of quantum distinguishability between parametric density operators by means of the Wigner-Yanase quantum information metric. We then show that the quantum searching problem can be recast in an information geometric framework where Grover’s dynamics is characterized by a geodesic on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover’s algorithm. We also discuss possible deviations from Grover’s algorithm within this quantum information geometric setting.     

The triplex vaccine effects in mammary carcinoma: A nonlinear model in tune with SimTriplex

This paper deals with the mathematical modeling of the mammary carcinoma-immune system competition elicited by an external stimulus represented by three different protocols of the triplex vaccine [C. De Giovanni, et al., Immunoprevention of HER-2/neu transgenic mammary carcinoma through an interleukin 12-engineered allogeneic cell vaccine, Cancer Research 64 (2004) 4001-4009]. The presented model is composed of nonlinear ordinary differential equations based on parameters and cell populations. A qualitative analysis of the asymptotic behavior of the model and numerical simulations are able to depict preclinical experiments on transgenic mice in tune with the SimTriplex model [F. Pappalardo, F. Castiglione, P.L. Lollini, S. Motta, Modelling and simulation of cancer immunoprevention vaccine, Bioinformatics 21 (2005) 2891-2897]. The results are of great interest both in the applied and theoretical sciences.