Fixed points for fuzzy quasi-contractions in fuzzy metric spaces endowed with a graph

[EN] In this paper, we introduce the notion of G-fuzzy H-quasi-contractions using directed graphs in the setting of fuzzy metric spaces endowed with a graph and we show that this new type of contraction generalizes a large number of different types of contractions. Subsequently, we investigate some results concerning the existence of fixed points for this class of contractions under two different conditions in M-complete fuzzy metric spaces endowed with a graph. Our main results of the work significantly generalize many known comparable results in the existing literature. Examples are given to support the usability of our results and to show that they are improvements of some known ones.Dinarvand, M. (2020). Fixed points for fuzzy quasi-contractions in fuzzy metric spaces endowed with a graph. Applied General Topology. 21(2):177-194. https://doi.org/10.4995/agt.2020.11369OJS177194212S. M. A. Aleomraninejad, Sh. Rezapour and N. Shahzad, Some fixed point results on a metric space with a graph, Topology Appl. 159, no. 3 (2012), 659-663. https://doi.org/10.1016/j.topol.2011.10.013A. Amini-Harandi and D. Mihet, Quasi-contractive mappings in fuzzy metric spaces, Iranian J. Fuzzy Syst. 12, no. 4 (2015), 147-153.F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. Stiint. Univ. ''Ovidius" Constanta Ser. Mat. 20, no. 1 (2012), 31-40. https://doi.org/10.2478/v10309-012-0003-xF. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal. 75 (2012), 3895-3901. https://doi.org/10.1016/j.na.2012.02.009J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976. https://doi.org/10.1007/978-1-349-03521-2S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci. 25 (1972), 727-730.Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45, no. 2 (1974), 267-273. https://doi.org/10.2307/2040075M. Dinarvand, Fixed point results for $(varphi,psi)$-contractions in metric spaces endowed with a graph, Mat. Vesn. 69, no. 1 (2017), 23-38.M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets Syst. 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canadian Math. Bull. 16 (1973), 201-206. https://doi.org/10.4153/CMB-1973-036-0J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 136, no. 4 (2008), 1359-1373. https://doi.org/10.1090/S0002-9939-07-09110-1R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71-76. https://doi.org/10.2307/2316437I. Kramosil and J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetica 11, no. 5 (1975), 336-344.A. Petrusel and I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134, no. 2 (2006), 411-418. https://doi.org/10.1090/S0002-9939-05-07982-7S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. 5 (1972), 26-42.B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290. https://doi.org/10.1090/S0002-9947-1977-0433430-4S. Shukla, Fixed point theorems of G-fuzzy contractions in fuzzy metric spaces endowed with a graph, Commun. Math. 22 (2014), 1-12. https://doi.org/10.1186/1687-1812-2014-127D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222 (2013), 108-114. https://doi.org/10.1016/j.fss.2013.01.012L. A. Zadeh, Fuzzy Sets, Inform. Control, 10, no. 1 (1960), 385-389

Creation of Nanorobots: Both State-of-the-Science and State-of-the-Art

Over the last decade, remarkable achievements in nanofabrication technology has led to the development of hybrid intelligent systems including the nanomechanical devices powered by the chemical energy sources or biomolecular motors. In this context, nanorobotics has emerged as a highly-advanced technology for designing the fully functional smart devices or robots at nano scale. Development of these highly-controlled and functional nanostructures for sensing, information processing, signaling, and actuation may provide remarkable breakthroughs in medicine such as the improved imaging or targeted therapeutic interventions. Besides the detection and destroying the toxic materials and ecosystem restoration, the stimuli-responsive nanorobots may be used for the diagnosis or treatment of cardiac disorders, traumatic injuries, diabetes, and bacterial or viral infections. These molecular tools with nanoscale resolution facilitates early diagnosis in cancer and precise localization of anticancer agents leading to the minimal side effects. Nanorobots may easily traverse the human body and repair the cells or assist an improper functioning organ. These tiny devices integrated with wireless locomotion, external or internal power supply, artificial intelligence, and smart sensors may also be used for targeted delivery of genes or drugs into the single cells or tissues, tele-operation, or patient monitoring. Indeed, development of the medical nanorobots with a wide range of capabilities is a proof of concept and art in modern science and a breakthrough in nanotechnology which has been highlighted in the present manuscript

Resveratrol: More than a phytochemical

In recent years, alternative and complementary medicine including the plant-based drugs with antioxidant and neuroptotective effects has attracted a growing interest. Resveratrol, a polyphenolic compound which is found in various plant species, has emerged as a promising nutraceutical with therapeutic potentials in neuropsychiatric, cardiometabolic and cancer diseases, also aging. The abundance of research providing promising findings about the multi-spectrum therapeutic applications of resveratrol and its encouraging potential to treat or prevent chronic and age-related disorders has raised a considerable number of clinical trials. Recently, resveratrol is implicated the biology of nerve growth factor (NGF), a critical player in the maintenance of neuronal growth and function. Furthermore, resveratrol affects the endocannabinoid signalling (eCBs) which exerts modulatory effects in the survival signalling pathways, neural plasticity, and a variety of neuroinflammatory and neurodegenerative processes. The therapeutic effects of this ubiquitous signalling system in Alzheimer`s disease, epilepsy, multiple sclerosis, mood and movement disorders, spinal cord injury, and stroke have been well-documented. In the present review, the implication of NGF and eCBs in the mechanism of action of resveratrol, that may be of therapeutic significance in neurological and non-neurological disorders, is highlighted. Biomed Rev 2015; 26: 13-21

Application of Carbon Nanotubes for Controlled Release of Growth Factors or Endocannabinoids: A Breakthrough in Biomedicine

Carbon nanotubes, the nanostructures with immense potential in various scientific fields such as the regenerative medicine, have emerged as innovative nanosreservoirs with multimodal functionality and application in theranostic sessions. The superior mechanical properties, high thermoelectrical conductivities, or improved solubility and biocompatibility have made CNTs as suitable candidates for biosensing, high-resolution imaging, tissue-engineering, and delivery of a variety of compounds with poor solubility or short half-life. These advanced nanovectors which promote neuronal growth and functional connectivity, have shown great theranostic potential in the central nervous system disorders. Several pioneering works have shown the ability of CNTs for controlled release of drugs or growth factors into the brain. Over the last decade the neurotropic and metabotrophic effects of nerve-growth factor, brain-derived neurothropic factor and endocannabinoid system and their involvement in the mechanism of action of a wide variety of drugs have been the focus of intense research. In order to overcome the rapid degradation and/or non-specific distribution of nerve-growth factor or endocanabinoids, conjugation with CNTs has led to the prolonged effects of these modulating factors. Based on their unique properties, the appropriate application of functionalized CNTs may indeed revolutionize the current biomedical interventions that has been highlighted in the present review

Nanoparticles reshape the biomedical industry

Over the last decades, increasing interest has been attracted towards the nanotechnology which provide a set of promising research tools and theranostic approaches. Tremendous research efforts in nanofabrication technology have led to the production of biocompatible nanostructures and advanced carriers with various configurations for protection of the loaded biomolecules or drugs against the metabolism or excretion. Furthermore, controlled delivery and targeted therapy may result in the improved therapeutic effects against a variety of diseases and reduced adverse effects of drugs. The efficiency of protein drugs may be negatively affected by their limited transportation within the body and short half-lives. Application of nanoparticles may significantly improve the pharmacological profiles of protein drugs. In neurology, high-resolution imaging techniques, nanoengineered materials capable of interaction with the nervous systems, and nanopharmaceuticals with minimal toxicity and improved bioavailability may be of great theranostic significance. This may provide remarkable breakthroughs in the pharmaceutical industry and health-care system. In the present review, the significance of nanotechnology and modeling approaches in health-care system has been highlighted

FIXED POINTS OF ALMOST CONTRACTIVE TYPE MAPPINGS IN PARTIALLY ORDERED B-METRIC SPACES AND APPLICATIONS TO QUADRATIC INTEGRAL EQUATIONS

The purpose of this paper is to present a new class of almost contractive mappings called almost generalized $(\psi,\varphi,\theta)_{s}$-contractive mappings and to establish some fixed point and common fixed point results for this class of mappings in partially ordered $b$-metric spaces. Our main results of the paper significantly generalize and improve many well known comparable results in the recent literature. Moreover, some examples and an application to the existence of a solution for a class of nonlinear quadratic integral equations is given here to illustrate the usability of the obtained results

The fabrication of potentiometric membrane sensors and their applications

Ionophore-incorporated PVC-membrane sensors are well-established analytical tools routinely used for the selective and direct measurement of a wide variety of different ions in complex biological and environmental samples. The key ingredient of such plasticized PVC-members is the involved ionophore, defining the selectivity of the electrodes complex formation with the cation of interest. In the past few years, the development of new ion-selective electrodes for various ions has been reported inthe literature

Detecting Financial Fraud and Crimes in Capital Markets: a Study of Data-driven and Computational Approaches

Automatic surveillance of abnormal trading behaviours/patterns (ATPs) in capital markets is essential to protect the capital of legitimate traders from price distortion of finance assets. Detection of ATPs involves the finding of single (one trading order with large trading volume and long cancellation time, e.g. several minutes) or sequential (correlated multiple trading orders with small volume and short cancellation time, e.g. milliseconds) anomalies in trading data. However, accurate and timely identification of ATPs remains an open challenge due to high volume and high frequency data as well as unlabelled data. In this research, we have investigated anomaly detection approaches to address the challenges and filled the knowledge gap through the following four contributions: Firstly, we have performed a literature review and conducted a thorough benchmark evaluation on existing state-of-the-art anomaly detection algorithms (i.e. Artificial Neural Network- Auto Encoder, Isolation Forest, Local Outlier Factor (LOF), Histogram-based Outlier Score (HBOS), Angle-based Outlier Detection (ABOD), Principle Component Analysis (PCA) and K-Nearest Neighbors (KNN) ) using publicly available datasets from different domains such as health and finance. The experimental results show that Isolation Forest, HBOS and PCA are robust algorithms in terms of both high detection performance (Area Under the ROC Curve (AUC) = 0.95) and low computational time for large dataset. Secondly, as one of the major contributions of this research, we have proposed a novel generic unsupervised anomaly detection model, which can be applied to anomaly detection of both financial and non-financial datasets. The essence of the proposed model consists in partitioning a bounded D-dimensional space (e.g. the unit hyper-cube ID) by a sequence of random shapes, in which each data will be trapped either inside or outside, followed by probabilistic modelling of a pattern of falling inside or outside for a data point. Anomalous data which are rare and iv different from the rest of the dataset will be assigned a higher anomaly score. Thirdly, to investigate the robustness of the proposed anomaly detection model, we have performed a thorough sensitivity analysis under different hyper-parameters settings (i.e. the number of random shapes, shape of random shapes, etc.) and different publicly available datasets. The results show that the model performance stabilises as the number of random shapes increases. Furthermore, the shape of random shapes could affect the performance of the algorithm which needs to be optimised for a given dataset. Also, the results indicate that the algorithm’s computational time increases linearly with the number of random shapes which shows the robustness of the algorithm for detecting anomalies in a timely manner. Finally, we have applied the proposed algorithm on real Bitcoin prices as a case study and tested, evaluated and compared its performance with the benchmark algorithms such as Auto Encoder, Isolation Forest, LOF, HBOS, ABOD, PCA and KNN. The results show that the proposed algorithm achieves AUC = 0.94. Comparing to the benchmark algorithms, it also outperforms the existing algorithms by 8.5 percent increase while having low computational time

Thiolated chitosan nanoparticles as a delivery system for antisense therapy: evaluation against EGFR in T47D breast cancer cells

Thiolated chitosan has high transfection and mucoadhesive properties. We investigated the potential of two recently synthesized polymers: NAC-C (N-acetyl cysteine-chitosan) and NAP-C (N-acetyl penicillamine-chitosan) in anticancer drug delivery targeting epidermal growth factor receptor (EGFR). Doxorubicin (DOX) and antisense oligonucleotide (ASOND)-loaded polymer nanoparticles were prepared in water by a gelation process. Particle characterization, drug loading, and drug release were evaluated. To verify drug delivery efficiency in vitro experiments on a breast cancer cell line (T47D) were performed. EGFR gene and protein expression was analyzed by real time quantitative polymerase chain reaction and Western blotting, respectively. A loading percentage of 63% ± 5% for ASOND and 70% ± 5% for DOX was achieved. Drug release data after 15 hours showed that ASOND and DOX were completely released from chitosan-based particles while a lower and more sustained release of only 22% ± 8% was measured for thiolated particles. In a cytosol simulated release medium/reducing environment, such as found intracellularly, polymer-based nanoparticles dissociated, liberating approximately 50% of both active substances within 7 hours. ASOND-loaded polymer nanoparticles had higher stability and high mucoadhesive properties. The ASOND-loaded thiolated particles significantly suppressed EGFR gene expression in T47D cells compared with ASOND-loaded chitosan particles and downregulated EGFR protein expression in cells. This study could facilitate future investigations into the functionality of NAP-C and NAC-C polymers as an efficient ASOND delivery system in vitro and in vivo