A unifying theorem for Newton’s method on spaces with a convergence structure

We present a semilocal convergence theorem for Newton’s method (NM) on spaces with a convergence structure. Using our new idea of recurrent functions, we provide a tighter analysis, with weaker hypotheses than before and with the same computational cost as for Argyros (1996, 1997, 1997, 2007) [1], [2], [3] and [5], Meyer (1984, 1987, 1992) [13], [14] and [15]. Numerical examples are provided for solving equations in cases not covered before.     

Simultaneous Determination of 1,4‐Benzodiazepines and Tricyclic Antidepressants in Saliva after Sequential SPE Elution by the Same HPLC Conditions

A new method has been described to determine both benzodiazepines (six) and tricyclic antidepressants (four) simultaneously in saliva by HPLC with a UV detector set at 240 nm using cholchicine as the internal standard. A careful specific sequential solid‐phase elution was optimized and performed to elute benzodiazepines using a mixture of methanol‐acetonitrile (1:1 v/v) followed by the elution of tricyclic antidepressants with methanol. Separation of the compounds was performed on a Kromasil column (250 × 4 mm, 5 μm) by a gradient eluents consisting of 0.05 M CH₃COONH₄‐acetonitrile‐methanol (55:15:30 v/v/v). The results were linear for both benzodiazepines and tricyclic antidepressants up to 20 ng μL^‐1 with the correlation coefficients greater than 0.998. The sensitivity limits, LOD and LOQ were 0.08‐0.34 ng μL^‐1 and 0.28‐1.13 ng μL^‐1, respectively. The method is simple, fast and reliable with good specificity and sensitivity, will be suitable for use in a clinical setting, where there is a concomitant use of 1,4‐benzodiazepines and tricyclic antidepressants.     

A constrained approach to multiscale stochastic simulation of chemically reacting systems

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems.     

Practical synthesis of (2'R)-2'-deoxy-2'-C-methyluridine by highly diastereoselective homogeneous hydrogenation

Diastereoselective hydrogenation of 2'-deoxy-2'-exo-methyleneuridine was carried out under homogeneous conditions using a low loading of a chiral Rh catalyst. This, coupled with improvements in the synthesis of the substrate, allowed the smooth pilot plant preparation of the title compound on >10 kg scale.     

A high-throughput microfluidic assay to study neurite response to growth factor gradients

Studying neurite guidance by diffusible or substrate bound gradients is challenging with current techniques. In this study, we present the design, fabrication and utility of a microfluidic device to study neurite guidance under chemogradients. Experimental and computational studies demonstrated the establishment of a steep gradient of guidance cue within 30 min and stable for up to 48 h. The gradient was found to be insensitive to external perturbations such as media change and movement of device. The effects of netrin-1 (0.1-10 μg mL(-1)) and brain pulp (0.1 μL mL(-1)) were evaluated for their chemoattractive potential on neurite turning, while slit-2 (62.5 or 250 ng mL(-1)) was studied for its chemorepellant properties. Hippocampal or dorsal root ganglion (DRG) neurons were seeded into a micro-channel and packed onto the surface of a 3D collagen gel. Neurites grew into the matrix in three dimensions, and a gradient of guidance cue was created orthogonal to the direction of neurite growth to impact guidance. The average turning angle of each neurite was measured and averaged across multiple devices cultured under similar conditions to quantify the effect of guidance cue gradient. Significant positive turning towards gradient was measured in the presence of brain pulp and netrin-1 (1 μg mL(-1)), relative to control cultures which received no external guidance cue (p < 0.001). Netrin-1 released from transfected fibroblasts had the most positive turning effect of all the chemoattractive cues tested (p < 0.001). Slit-2 exhibited strong chemorepellant characteristics on both hippocampal and DRG neurite guidance at 250 ng mL(-1) concentration. Slit-2 also showed similar behavior on DRG neuron invasion into 3D collagen gel (p < 0.01 relative to control cultures). Taken together, the results suggest the utility of this microfluidic device to generate stable chemogradients for studying neurobiology, cell migration and proliferation, matrix remodeling and co-cultures with other cell lines, with potential applications in cancer biology, tissue engineering and regenerative medicine.     

Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions

We extend the applicability of the Gauss–Newton method for solving singular systems of equations under the notions of average Lipschitz–type conditions introduced recently in Li et al. (J Complex 26(3):268–295, 2010). Using our idea of recurrent functions, we provide a tighter local as well as semilocal convergence analysis for the Gauss–Newton method than in Li et al. (J Complex 26(3):268–295, 2010) who recently extended and improved earlier results (Hu et al. J Comput Appl Math 219:110–122, 2008; Li et al. Comput Math Appl 47:1057–1067, 2004; Wang Math Comput 68(255):169–186, 1999). We also note that our results are obtained under weaker or the same hypotheses as in Li et al. (J Complex 26(3):268–295, 2010). Applications to some special cases of Kantorovich–type conditions are also provided in this study.     

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.     

Nonvanishing at spatial extremity solutions of the defocusing nonlinear Schrödinger equation

We show local existence of certain type of solutions for the Cauchy problem of the defocusing nonlinear Schrödinger equation with pure power nonlinearity, in various cases of open sets, unbounded or bounded. These solutions do not vanish at the boundary or at infinity. We also show, in certain cases, that these solutions are unique and global.     

Cytoprotective Mechanisms of DJ-1: Implications in Cardiac Pathophysiology

DJ-1 was originally identified as an oncogene product while mutations of the gene encoding DJ-1/PARK7 were later associated with a recessive form of Parkinson’s disease. Its ubiquitous expression and diversity of function suggest that DJ-1 is also involved in mechanisms outside the central nervous system. In the last decade, the contribution of DJ-1 to the protection from ischemia-reperfusion injury has been recognized and its involvement in the pathophysiology of cardiovascular disease is attracting increasing attention. This review describes the current and gaps in our knowledge of DJ-1, focusing on its role in regulating cardiovascular function. In parallel, we present original data showing an association between increased DJ-1 expression and antiapoptotic and anti-inflammatory markers following cardiac and vascular surgical procedures. Future studies should address DJ-1’s role as a plausible novel therapeutic target for cardiovascular disease.     

Representation formulae of general solutions in the theory of hemitropic elasticity

We consider the steady state oscillation equations of the theoryof elasticity of hemitropic materials. We derive general representationformulae for the displacement and microrotation vectors by meansof six scalar metaharmonic functions. These formulae are veryconvenient and useful in many particular problems for domainswith concrete geometry. Here we consider two canonical transmissionproblems for piecewise homogeneous bodies with spherical interfacesand with the help of the representation formulae construct explicitsolutions in the form of absolutely and uniformly convergentseries. The representations can also be applied to multi-layeredbodies with spherical and cylindrical interfaces.