Domination Number of the Non-commuting Graph of Finite Groups

Let G be a non-abelian group. The non-commuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are adjacent whenever ab ≠ ba. A set S ⊆ V(Γ) of vertices in a graph Γ is a dominating set if every vertex v ∈ V(Γ) is an element of S or adjacent to an element of S. The domination number of a graph Γ denoted by γ(Γ), is the minimum size of a dominating set of Γ. </p><p>Here, we study some properties of the non-commuting graph of some finite groups. In this paper, we show that \gamma(\Gamma_G)<\frac{|G|-|Z(G)|}{2}. Also we charactrize all of groups G of order n with t = ∣Z(G)∣, in which $\gamma(\Gamma_{G})+\gamma(\overline{\Gamma}_{G})\in \{n-t+1,n-t,n-t-1,n-t-2\}.

Optimal Safety for Constrained Differential Inclusions using Nonsmooth Control Barrier Functions

For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs. Through the use of nonsmooth analysis tools, we show that a continuous optimal control law can be selected from a set-valued constraint capturing the system constraints and conditions guaranteeing safety using control barrier functions. Our results guarantee optimality and safety via a continuous state-feedback law designed using nonsmooth control barrier functions. An example pertaining to obstacle avoidance with a target illustrates our results and the associated benefits of using nonsmooth control barrier functions.Comment: Submitted to LCS

Cryptanalysis of RAPP, an RFID Authentication Protocol

Tian et al. proposed a novel ultralightweight RFID mutual authentication protocol [4] that has recently been analyzed in [1], [2], [5]. In this letter, we first propose a desynchronization attack that succeeds with probability almost 1, which improves upon the 0.25 given by the attack in [1]. We also show that the bad properties of the proposed permutation function can be exploited to disclose several bits of the tag’s secret (rather than just one bit as in [2]), which increases the power of a traceability attack. Finally, we show how to extend the above attack to run a full disclosure attack, which requires to eavesdrop less protocol runs than the attack described in [5] (i.e., 192 << 230)

Clinical and Molecular Study of NPC in Iran: Report of 5 Novel Mutations

How to Cite This Article: Tonekaboni SH, Aryani O, Karimzadeh P, Zaman T, Ashrafi M, Salehpour Sh, Dehghan Manshadi M, Khalili E, Houshmand M. Clinical and Molecular Study of NPC in Iran: Report of 5 Novel Mutations. Ir an J Child Neurol. 2015 Autumn;9:4(Suppl.1): 8-9.Pls see pdf

Preparation, characterization, and in ovo vaccination of dextran-spermine nanoparticle DNA vaccine coexpressing the fusion and hemagglutinin genes against Newcastle disease

Plasmid DNA (pDNA)-based vaccines have emerged as effective subunit vaccines against viral and bacterial pathogens. In this study, a DNA vaccine, namely plasmid internal ribosome entry site-HN/F, was applied in ovo against Newcastle disease (ND). Vaccination was carried out using the DNA vaccine alone or as a mixture of the pDNA and dextran-spermine (D-SPM), a nanoparticle used for pDNA delivery. The results showed that in ovo vaccination with 40 µg pDNA/egg alone induced high levels of antibody titer (P0.05). Higher antibody titer was observed in the group immunized with 40 µg pDNA/egg at 4 weeks postvaccination. The findings also showed that vaccination with 40 µg pDNA/egg alone was able to confer protection against Newcastle disease virus strain NDIBS002 in two out of seven SPF chickens. Although the chickens produced antibody titers 3 weeks after in ovo vaccination, it was not sufficient to provide complete protection to the chickens from lethal viral challenge. In addition, vaccination with pDNA/D-SPM complex did not induce high antibody titer when compared with naked pDNA. Therefore, it was concluded that DNA vaccination with plasmid internal ribosome entry site-HN/F can be suitable for in ovo application against ND, whereas D-SPM is not recommended for in ovo gene delivery.Ministry of Science, Technology and Innovations (MOSTI), Malaysia, for the research grant (ERGS/1-2012/5527122), and Institute of Bioscience, Higher Institution Centre of Excellence (IBS HICoE) grant from the Ministry of Higher Education, Government of Malaysi

Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page

The motion of a fluid-rigid disc system at the zero limit of the rigid disc radius

We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with the fluid, in the whole plane. The fluid motion is described by the Navier-Stokes equations and the motion of the rigid body by conservation laws of linear and angular momentum. We show that, assuming that the rigid disc is not allowed to rotate, as the radius of the disc goes to zero, the solution of this system converges, in an appropriate sense, to the solution of the Navier-Stokes equations describing the motion of only fluid in the whole plane. We also prove that the trajectory of the centre of the disc, at the zero limit of its radius, coincides with a fluid particle trajectory.Comment: 29 pages, 0 figure

In vivo Skin Penetration, Radical Protection, and Structural Changes after Topical Application of a Herbal Oil Cream Compared to Topical Calcipotriol in Mild to Moderate Psoriasis

Background: The chronicity of psoriasis often requires continuous topical treatment. Materials and Methods: Here, the radical protection of a cream containing various herbal oils was evaluated in vivo by electron paramagnetic resonance (EPR) spectroscopy and its skin penetration by Raman microscopy in intact and barrier-disturbed skin. Changes in skin barrier properties were evaluated after 4 weeks of daily topical application using in vivo laser scanning microscopy (LSM) and transepidermal water loss in 26 healthy volunteers. A randomized, controlled, double-blind, three-arm parallel clinical study evaluated the efficacy of the herbal oil cream compared to a 0.05% calcipotriol-containing cream and to a vehicle cream, in 135 patients with mild to moderate plaque psoriasis with the change in Psoriasis Area and Severity Index (PASI) from baseline to week 12 as the primary endpoint. Results: EPR spectroscopy disclosed a significantly higher radical formation in untreated than skin treated with the herbal oil cream (p ≤ 0.05). LSM measurements indicated a protective skin barrier effect in treated compared to untreated skin. In the clinical trial, the topical application of herbal oils showed a significant reduction of the PASI score compared to topical calcipotriol at week 12 (p = 0.016). The mean reduction in PASI was 49% for the herbal oil cream, 38% for calcipotriol, and 55% for the vehicle cream. The percentage of patients, who reached PASI 50 and 75 at any time point, was 55.9% and 29.4% for the herbal oil cream, 47.4% and 15.8% for calcipotriol, and 23 (60.5%) and 13 (34.2%) for the vehicle, respectively (p > 0.05). The vehicle, originally designed as a placebo, contained a main ingredient of the herbal oil cream and therefore showed corresponding results. Conclusion: The herbal oil cream demonstrated effectiveness in the treatment of mild to moderate plaque psoriasis

Metabolomics Reveals Differential Levels of Oral Metabolites in HIV-Infected Patients: Toward Novel Diagnostic Targets

The objective of the current study was to characterize the profile of oral metabolites in HIV-infected patients using metabolomics. Oral wash samples were collected from 12 HIV-infected and 12 healthy individuals (matched for age, sex, and ethnicity), processed, and analyzed by metabolomics. We detected 198 identifiable and 85 nonidentifiable metabolites; 27 identifiable metabolites were differentially present (12 increased, 15 decreased) in HIV-infected patients. Elevated metabolites included p-cresol sulfate, nucleotides (e.g., allantoin), and amino acids (e.g., phenylalanine, tryptophan), whereas decreased oral metabolites included fucose, fumarate, and N-acetylglucosamine. Pathway network analysis revealed the largest multinode network in healthy versus HIV-infected patients to involve carbohydrate biosynthesis and degradation. HIV-infected patients on antiretroviral therapy (ART) showed the largest number (12) of statistically significant metabolite correlation differences compared with healthy controls. Interestingly, the oral phenlyalanine:tyrosine ratio increased in ART-naive HIV-infected patients (mean ± SEM = 2.58 ± 0.87) compared with healthy individuals (1.33 ± 0.10, p = 0.062) or ART-experienced patients (1.78 ± 0.30, p = 0.441). This is the first study to reveal differential levels of oral metabolites in HIV-infected patients compared withj healthy volunteers, and that oral phenlyalanine:tyrosine ratio may be a useful marker for noninvasive monitoring of the immune status during HIV infection