Multipoint secant and interpolation methods with nonmonotone line search for solving systems of nonlinear equations

Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the information about the Jacobian matrix gathered at the previous iterations, these methods are especially efficient in the case of expensive functions. They are known to be local and superlinearly convergent. We combine these methods with the nonmonotone line search proposed by Li and Fukushima (2000), and study global and superlinear convergence of this combination. Results of numerical experiments are presented. They indicate that the multipoint secant and interpolation methods tend to be more robust and efficient than Broyden's method globalized in the same way

Unscrambling Structured Chirality with Structured Light at the Nanoscale Using Photoinduced Force

We show that the gradient force generated by the near field of a chiral nanoparticle carries information about its chirality. On the basis of this physical phenomenon we propose a new microscopy technique that enables the prediction of spatial features of chirality of nanoscale samples by exploiting the photoinduced optical force exerted on an achiral tip in the vicinity of the test specimen. The tip-sample interactive system is illuminated by structured light to probe both the transverse and longitudinal (with respect to the beam propagation direction) components of the sample's magnetoelectric polarizability as the manifestation of its sense of handedness, i.e., chirality. We specifically prove that although circularly polarized waves are adequate to detect the transverse polarizability components of the sample, they are unable to probe the longitudinal component. To overcome this inadequacy and probe the longitudinal chirality, we propose a judiciously engineered combination of radially and azimuthally polarized beams as optical vortices possessing pure longitudinal electric and magnetic field components along their vortex axis, respectively. The proposed technique may benefit branches of science such as stereochemistry, biomedicine, physical and material science, and pharmaceutics

Unscrambling Structured Chirality with Structured Light at Nanoscale Using Photo-induced Force

We introduce a microscopy technique that facilitates the prediction of spatial features of chirality of nanoscale samples by exploiting photo-induced optical force exerted on an achiral tip in the vicinity of the test specimen. The tip-sample interactive system is illuminated by structured light to probe both the transverse and longitudinal (with respect to the beam propagation direction) components of the sample magnetoelectric polarizability as the manifestation of its sense of handedness, i.e., chirality. We specifically prove that although circularly polarized waves are adequate to detect the transverse polarizability components of the sample, they are unable to probe the longitudinal component. To overcome this inadequacy, we propose a judiciously engineered combination of radially and azimuthally polarized beams, as optical vortices possessing pure longitudinal electric and magnetic field components along their vortex axis, respectively, hence probing longitudinal chirality. The proposed technique may benefit branches of science like stereochemistry, biomedicine, physical and material science, and pharmaceutic

Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force

We propose a high-resolution microscopy technique for enantiospecific detection of chiral samples down to sub-100-nm size based on force measurement. We delve into the differential photoinduced optical force ΔF exerted on an achiral probe in the vicinity of a chiral sample when left and right circularly polarized beams separately excite the sample-probe interactive system. We analytically prove that ΔF is entangled with the enantiomer type of the sample enabling enantiospecific detection of chiral inclusions. Moreover, we demonstrate that ΔF is linearly dependent on both the chiral response of the sample and the electric response of the tip and is inversely related to the quartic power of probe-sample distance. We provide physical insight into the transfer of optical activity from the chiral sample to the achiral tip based on a rigorous analytical approach. We support our theoretical achievements by several numerical examples highlighting the potential application of the derived analytic properties. Lastly, we demonstrate the sensitivity of our method to enantiospecify nanoscale chiral samples with chirality parameter on the order of 0.01 and discuss how the sensitivity of our proposed technique can be further improved

Brain Natriuretic Peptides in Screening of Syncope with Cardiac Origin; a Commentary

Syncope is a serious problem with life-time prevalence of 35%. It is estimated that 1 -3% of referrals to emergency departments and in-patient admissions are due to syncope. The underlying conditions can be cardiac or neurologic. Considering the completely different circumstances ruling the encounters with cardiac and neurologic syncope, in recent years many attempts have beenmade to find the proper tool for differentiating cardiac and non-cardiac causes of syncope. The result of which is formation of some clinical decision rules including San Francisco Syncope Rule (SFSR), Osservatorio Epidemiologico sulla Sincope nel Lazio (OESIL),Evaluation of Guidelines in Syncope Study (EGSYS), risk stratification of syncope in the emergency department (Rose), and Boston Syncope Rules. The serum marker brain natriuretic peptide (BNP), which is becoming increasingly established in emergency departments for diagnosis of acute heart failure, can reflect thepresence of a structural heart disease. It seems that BNP could be considered as a screening tool in detection of syncope with cardiac origin. In a study by Wojtowicz J et al. who evaluated BNP in children and adolescents with syncope, there was no significant difference in terms of BNP level between the syncope andcontrol groups. In contrast, Zhang Q et al. concluded that serum BNP is helpful in differentiating cardiac (958.78 § 2443.41 pg/mL) and non-cardiac (31.05 § 22.64 pg/mL) syncope. Tanimoto K et al. considered the cut-off value of 40 pg/ml for BNP in differentiating cardiac and non-cardiac syncope and found that it had 82% sensitivity and 92% specificity. A significant difference was observed in BNP level of the cardiac group (514 pg/ml) compared to the non-cardiac ones (182 pg/ml) in Pfister et al. study. It seems that, more research is needed to clarify this relationship and the variables that might play the role of confounders in a causal inference.More studies on children are required because there is some controversy regarding this relationship. Running studies with accurate methodology, large sample sizes, and in a multicentric fashion could be helpful in this regard

Two-scale structure for giant field enhancement: combination of Rayleigh anomaly and colloidal plasmonic resonance

We demonstrate theoretically and experimentally a two-scale architecture able to achieve giant field enhancement by simultaneously exploiting both the Rayleigh anomaly and localized surface plasmon resonance. Metallic oligomers composed of colloidal nanospheres are well-known for the ability to strongly enhance the near-field at their plasmonic resonance. However, due to intrinsic nonlocality of the dielectric response of the metals along with their inherent loss, the achievable field enhancement has an ultimate constraint. In this paper we demonstrate that combining plasmonic resonance enhancements from oligomers, with feature size of tens of nanometers, with a Rayleigh anomaly caused by a 1-D set of periodic nanorods, having a period on the order of the excitation wavelength, provides a mean to produce enhancement beyond that constrained by losses in near field resonances. Metallic oligomers are chemically assembled in between the periodic set of nanorods that are fabricated using lithographic methods. The nanorod periodicity is investigated to induce the Rayleigh anomaly at the oligomers plasmonic resonance wavelength to further enhance the field in the oligomers hot spots. A thorough study of this structure is carried out by using an effective analytical-numerical model which is also compared to full-wave simulation results. Experimental results comparing enhancements in surface enhanced Raman scattering measurements with and without nanorods demonstrate the effectiveness of a Rayleigh anomaly in boosting the field enhancement. The proposed structure is expected to be beneficial for many applications ranging from medical diagnostics to sensors and solar cells

Clinical Study INF-and Ototoxicity

Introduction. INF-is a common drug for the treatment of hepatitis B and C. Although a variety of related complications are discussed, possible ototoxic effects of this mediation are not well described. Methods and Materials. In a before-after control study, 24 patients who received INF-for the treatment of hepatitis B and C and 30 normal controls were included. Subjective and objective ototoxicity evaluations via questionnaire, high frequency audiometry, and measuring transiently evoked otoacoustic emissions (TEOAEs) were performed one week before and one month after the prescription of the drug. Results. Subjective hearing complaint, tinnitus, and vertigo were seen in just 3 cases, which was not statistically significant ( = 0.083). In the frequency range of 4000 to 8000 Hz before (9.38 ± 1.0 and 10.7 ± 1.2, resp.) and after (17.9 ± 2.6 and 17.6 ± 2.6, resp.) one month of treatment, a significant difference ( = 0.083) was detected. Progressive decreases in amplitude of the OAE during TEOAE measurement in 1, 2, and 4 frequencies among 41.66%, 18.75 %, and 43.75% were observed, respectively. The hearing loss was seen more among older and male cases significantly. Conclusion. The results showed ototoxicity of INF-that may encourage planning hearing monitoring in patients receiving this drug