On the Independent Set Interdiction Problem

The purpose of the independent set interdiction problem in the weighted graph $G$ is to determine a set of vertices $R^*$ such that the weight of the maximum independent set in $G-R^*$ is minimized. We define an approximate solution for this problem. Then, an upper bound for the relative error of this problem is obtained. We show that the limit of the relative error of the independent set interdiction problem in some subclasses of the generalized Petersen graphs is zero as the number of vertices tends to infinity

Two proofs from Āzarkhor Ashtāz Goshnasp

One of the Iranian scientists of the fourth and fifth centuries AH is Āzarkhor Asht\={a}z Goshnasp. His name is only mentioned in the works of the prominent Iranian scientist, Ab\={u} Rayh\={a}n al-B\={i}r\={u}n\={i}. In this paper, we will explain \={A}zarkhor's two proofs on the first theorem of the book ``al-Estekhr\={a}j al-Awt\={a}r" that given by Ab\={u} Rayh\={a}n. This theorem is called ``Theorem of the broken chord" and these two proofs are the only mathematical legacy left by \={A}zarkhor

Some codes and designs invariant under the groups S7S_7 and S8S_8

We use the Key-Moori Method 1 and examine 1-designs and codes from the representations of the alternating group $A_7$. It is shown that a self-dual symmetric 2-$(35,18,9)$ design and an optimal even binary $[21,14,4]$ LCD code are found such that they are invariant under the full automorphism groups $S_8$ and $S_7$, respectively. Moreover, designs with parameters 1-$(21,l,k_{1,l})$ and 1-$(35,l,k_{2,l})$ are obtained, where $\omega$ is a codeword, $l=wt(\omega)$, $k_{1,l}=l|\omega^{S_7}|/21$ and $k_{2,l}=l|\omega^{S_7}|/35$. It is seen that there exist a 2-$(21,5,12)$ design with the full automorphism group $S_7$ among these 1-designs

Short-term changes in median nerve neural tension after a suboccipital muscle inhibition technique in subjects with cervical whiplash: A randomised controlled trial.

Objectives To assess the immediate effect of a suboccipital muscle inhibition (SMI) technique on: (a) neck pain, (b) elbow extension rangeof motion during the upper limb neurodynamic test of the median nerve (ULNT-1), and (c) grip strength in subjects with cervical whiplash;and determine the relationships between key variables.Design Randomised, single-blind, controlled clinical trial.Setting Faculty of Nursing, Physiotherapy and Podiatry, University of Seville, Spain.Participants Forty subjects {mean age 34 years [standard deviation (SD) 3.6]} with Grade I or II cervical whiplash and a positive responseto the ULNT-1 were recruited and distributed into two study groups: intervention group (IG) (n = 20) and control group (CG) (n = 20).Interventions The IG underwent the SMI technique for 4 minutes and the CG received a sham (placebo) intervention. Measures were collectedimmediately after the intervention.Main outcome measures The primary outcome was elbow range of motion during the ULNT-1, measured with a goniometer. The secondaryoutcomes were self-perceived neck pain (visual analogue scale) and free-pain grip strength, measured with a digital dynamometer.Results The mean baseline elbow range of motion was 116.0◦(SD 10.2) for the CG and 130.1◦(SD 7.8) for the IG. The within-groupcomparison found a significant difference in elbow range of motion for the IG [mean difference −15.4◦, 95% confidence interval (CI) −20.1to −10.6; P = 0.01], but not for the CG (mean difference −4.9◦, 95% CI −11.8 to 2.0; P = 0.15). In the between-group comparison, thedifference in elbow range of motion was significant (mean difference −10.5◦, 95% CI −18.6 to −2.3; P = 0.013), but the differences in gripstrength (P = 0.06) and neck pain (P = 0.38) were not significant.Conclusion The SMI technique has an immediate positive effect on elbow extension in the ULNT-1. No immediate effects on self-perceivedcervical pain or grip strength were observed

The effect of triphala lavender tablets on the treatment of children with attention deficit/hyperactivity disorder

Background: Attention deficit/hyperactivity disorder (ADHD) is a common psychiatric disorder in the children. The purpose of this study was to evaluate the efficacy of Triphala Lavender tablets as an adjuvant therapy along with methylphenidate on the treatment of children with attention deficit/hyperactivity disorder. Methods: In this clinical trial study that was done in Isfahan Province, Iran, in 2016, 44 children with attention deficit/hyperactivity disorder were enrolled according to inclusion (aged between 6 to 12 years) and exclusion (failure to follow up) criteria. The patients were randomly divided into two group as intervention (treated with methylphenidate and Triphala lavender tablets) and placebo (treated with methylphenidate and placebo). Patients were treated for 8 weeks. The assessment tool was Attention Deficit/Hyperactivity Disorder Rating Scale-IV (ADHD-RS-IV), which was used at the onset, and 2, 4, and 8 weeks after the intervention. Findings: The ADHD-RS-IV scores significantly decreased in both groups after intervention (P < 0.001 for both). In addition, the ADHD-RS-IV in the intervention group was significantly lower than placebo group at the 4th week after the intervention (P = 0.042); but there was no significant difference between the two groups in ADHD-RS-IV at onset, and 2 and 8 weeks after the intervention (P > 0.050 for all). Conclusion: The use of Triphala Lavender tablets as an adjuvant therapy may be effective in patients with attention deficit/hyperactivity disorder, but due to limited study about the role of Triphala Lavender tablets in treatment of these patients, we need future studies with larger sample sizes and longer time. © 2018, Isfahan University of Medical Sciences(IUMS). All rights reserved

On-chip polyelectrolyte coating onto magnetic droplets-towards continuous flow assembly of drug delivery capsules

Polyelectrolyte (PE) microcapsules for drug delivery are typically fabricated via layer-by-layer (LbL) deposition of PE layers of alternating charge on sacrificial template microparticles, which usually requires multiple incubation and washing steps that render the process repetitive and time-consuming. Here, ferrofluid droplets were explored for this purpose as an elegant alternative of templates that can be easily manipulated via an external magnetic field, and require only a simple microfluidic chip design and setup. Glass microfluidic devices featuring T-junctions or flow focusing junctions for the generation of oil-based ferrofluid droplets in an aqueous continuous phase were investigated. Droplet size was controlled by the microfluidic channel dimensions as well as the flow rates of the ferrofluid and aqueous phases. The generated droplets were stabilised by a surface active polymer, polyvinylpyrrolidone (PVP), and then guided into a chamber featuring alternating, co-laminar PE solutions and wash streams, and deflected across them by means of an external permanent magnet. The extent of droplet deflection was tailored by the flow rates, the concentration of magnetic nanoparticles in the droplets, and the magnetic field strength. PVP-coated ferrofluid droplets were deflected through solutions of polyelectrolyte and washing streams using several iterations of multilaminar flow designs. This culminated in an innovative "Snakes-and-Ladders" inspired microfluidic chip design that overcame various issues of the previous iterations for the deposition of layers of anionic poly(sodium-4-styrene sulfonate) (PSS) and cationic poly(fluorescein isothiocyanate allylamine hydrochloride) (PAH-FITC) onto the droplets. The presented method demonstrates a simple and rapid process for PE layer deposition in <30 seconds, and opens the way towards rapid layer-by-layer assembly of PE microcapsules for drug delivery applications.The authors thank the Royal Embassy of Saudi Arabia Cultural Bureau in London and Albaha University in Saudi Arabia for funding. J.G.-P., E.B. and I.O. acknowledge financial support from the Spanish Ministry of Economy and Competitiveness (project CTQ2015-66078-R (MINECO/FEDER) and FPI postgraduate research grant (BES-2013-064415). The authors thank Dr Stephen Clark for fabrication of the microfluidic devices