Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

Laparoscopic colorectal resections performed over a seven-years period in a single Italian Centre

Introduction. Laparoscopic approach for treatment of colorectal lesion is gaining acceptance gradually. Evidence from numerous randomised controlled trials has shown the short-term benefits of laparoscopic colon resection over open surgery, and its long-term outcomes also does not differ considerably from those of open surgery. This study aims at a retrospective analysis of operative and short term outcomes of patients. Patients and methods. All laparoscopic colon and rectal resections performed between September 2004 and September 2011 were included. The clinical parameters, operative parameters and short-term outcome details of laparoscopic colorectal surgery patients were collected from the retrospectively reviewed database. Results. A total of 347 patients, median age 71 years (range 32 to 96), underwent laparoscopic resection of the colon and rectum. The median Body Mass Index (BMI) was 26.5. The majority of the procedures were performed for malignant disease (97,1%) and the most common procedure was right colectomy (41%). The median duration of surgery was 202,3 minutes, with conversion to open surgery in 40 patients (11.5%). Complications occurred in 23 patients (6.6%). The median length of hospital stay was 8.9 days. In patients with malignant disease, the median number of lymph nodes removed was 14.9. Conclusion. Our results show that laparoscopic approach for colon-rectal lesions is safe, feasible and produces favourable results. The most important aspect of surgery for malignant disease is the ability to remove radically the disease. However all data are still related to the experience of the operator.

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

D3M: multicast listener mobility support mechanisms over distributed mobility anchoring architectures

The explosion in mobile data traffic is a driver for future network operator technologies, given its large potential to affect both network performance and generated revenue. The concept of distributed mobility management (DMM) has emerged in order to overcome efficiency-wise limitations in centralized mobility approaches, proposing not only the distribution of anchoring functions but also dynamic mobility activation sensitive to the applications needs. Nevertheless, there is not an acceptable solution for IP multicast in DMM environments, as the first proposals based on MLD Proxy are prone to tunnel replication problem or service disruption. We propose the application of PIM-SM in mobility entities as an alternative solution for multicast support in DMM, and introduce an architecture enabling mobile multicast listeners support over distributed anchoring frameworks in a network-efficient way. The architecture aims at providing operators with flexible options to provide multicast mobility, supporting three modes: the first one introduces basic IP multicast support in DMM; the second improves subscription time through extensions to the mobility protocol, obliterating the dependence on MLD protocol; and the third enables fast listener mobility by avoiding potentially slow multicast tree convergence latency in larger infrastructures, by benefiting from mobility tunnels. The different modes were evaluated by mathematical analysis regarding disruption time and packet loss during handoff against several parameters, total and tunneling packet delivery cost, and regarding packet and signaling overhead.

A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Fractional differential equations with dependence on the Caputo-Katugampola derivative

In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.

Fiber scaffolds of poly (glycerol-dodecanedioate) and its derivative via electrospinning for neural tissue engineering

Peripheral nerves have demonstrated the ability to bridge gaps of up to 6 mm. Peripheral Nerve System injury sites beyond this range need autograft or allograft surgery. Central Nerve System cells do not allow spontaneous regeneration due to the intrinsic environmental inhibition. Although stem cell therapy seems to be a promising approach towards nerve repair, it is essential to use the distinct three-dimensional architecture of a cell scaffold with proper biomolecule embedding in order to ensure that the local environment can be controlled well enough for growth and survival. Many approaches have been developed for the fabrication of 3D scaffolds, and more recently, fiber-based scaffolds produced via the electrospinning have been garnering increasing interest, as it offers the opportunity for control over fiber composition, as well as fiber mesh porosity using a relatively simple experimental setup. All these attributes make electrospun fibers a new class of promising scaffolds for neural tissue engineering. Therefore, the purpose of this doctoral study is to investigate the use of the novel material PGD and its derivative PGDF for obtaining fiber scaffolds using the electrospinning. The performance of these scaffolds, combined with neural lineage cells derived from ESCs, was evaluated by the dissolvability test, Raman spectroscopy, cell viability assay, real time PCR, Immunocytochemistry, extracellular electrophysiology, etc. The newly designed collector makes it possible to easily obtain fibers with adequate length and integrity. The utilization of a solvent like ethanol and water for electrospinning of fibrous scaffolds provides a potentially less toxic and more biocompatible fabrication method. Cell viability testing demonstrated that the addition of gelatin leads to significant improvement of cell proliferation on the scaffolds. Both real time PCR and Immunocytochemistry analysis indicated that motor neuron differentiation was achieved through the high motor neuron gene expression using the metabolites approach. The addition of Fumaric acid into fiber scaffolds further promoted the differentiation. Based on the results, this newly fabricated electrospun fiber scaffold, combined with neural lineage cells, provides a potential alternate strategy for nerve injury repair.^

Sustainable tourism practices through the eyes of the tourist: a case study of a tour operator

This internship report aim was to find out the importance of sustainable tourism practices from a tourist point of view. The research study and internship took place at Back-Roads Touring - a tour operator (based in London) that specializes in small group touring for seniors travellers from Australia, New Zealand, USA and Canada. Google Forms online questionnaire was used in order to answer the objectives of the study. In total 1322 clients received an online questionnaire out of which 182 filled in the survey. The study had four objectives, however the main focus was to find out which tourism practices ( out of 15 choices) were the most important to the respondents during a Back-Roads Tour and which tourism options (using the same 15 choices) the respondents identify as sustainable tourism options ( objective 2 and 3). The results showed that the respondents valued the most small group touring and having an experienced tour leader, which are the core practices of the company. Furthermore, the respondents were not seeking for more sustainable tourism practices neither willing to donate money to local charities/non- profit organizations. This finding shows that the clients are content with a current model of a tour, are willing to return, however price and quality will be play a key role in the decision. The respondents´ lack of wish to support or donate money to charities /non-profit organizations, could be due to the fact that most of the clients were from middle class thus they did not have enough disposable income. Moreover, one of the objectives of this study was to find out if the clients valued sustainable tourism certification. The results showed that the respondents’ were not aware of the sustainable tourism certification that the company obtained, however slightly over half of the respondents said that the knowledge of the certification has positively influenced them to travel again with a company.

A bioengineered nisin derivative, M21A, in combination with food grade additives eradicates biofilms of Listeria monocytogenes

The burden of foodborne disease has large economic and social consequences worldwide. Despite strict regulations, a number of pathogens persist within the food environment, which is greatly contributed to by a build-up of resistance mechanisms and also through the formation of biofilms. Biofilms have been shown to be highly resistant to a number of antimicrobials and can be extremely difficult to remove once they are established. In parallel, the growing concern of consumers regarding the use of chemically derived antimicrobials within food has led to a drive toward more natural products. As a consequence, the use of naturally derived antimicrobials has become of particular interest. In this study we investigated the efficacy of nisin A and its bioengineered derivative M21A in combination with food grade additives to treat biofilms of a representative foodborne disease isolate of Listeria monocytogenes. Investigations revealed the enhanced antimicrobial effects, in liquid culture, of M21A in combination with citric acid or cinnamaldehyde over its wild type nisin A counterpart. Subsequently, an investigation was conducted into the effects of these combinations on an established biofilm of the same strain. Nisin M21A (0.1 μg/ml) alone or in combination with cinnamaldehyde (35 μg/ml) or citric acid (175 μg/ml) performed significantly better than combinations involving nisin A. All combinations of M21A with either citric acid or cinnamaldehyde eradicated the L. monocytogenes biofilm (in relation to a non-biofilm control). We conclude that M21A in combination with available food additives could further enhance the antimicrobial treatment of biofilms within the food industry, simply by substituting nisin A with M21A in current commercial products such as Nisaplin® (Danisco, DuPont).

Applying Least Absolute Shrinkage Selection Operator and Akaike Information Criterion Analysis to Find the Best Multiple Linear Regression Models between Climate Indices and Components of Cow’s Milk

This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new), and respiratory rate predictor RRP) with three main components of cow’s milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p-value < 0.001 and R2 (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.

Effect of edible coatings with essential oils on the quality of red raspberries over shelf-life

The objective of the present work was to develop stategies for raising the shelf-life of red raspberries (Rubus idaeus L.). The quality of red raspberries over shelf-life after coated with alginate plus Brazilian Citrus essential oils was evaluated. Edible coatings did not significantly influence the firmness loss, soluble solids content (SCC), and brightness of fruits over time, when compared to control, nevertheless all edible coatings with essential oils induced higher weight loss than those samples in which the essential oils were not incorporated. Fruits coated with alginate plus lime essential oil (0.2%) or orange essential oil (0.1%) after 15 days of storage had less red skin, but were darker than the remaining samples. The less red colour verified in these samples was also coincident with the lower concentration of anthocyanins at the end of the experiment as well as the lower capacity for scavenging ABTS free radicals or quenching singlet oxygen. The edible coatings supplemented with the essential oil of orange either at 0.1 % or 0.2 % were very efficient to control the yeasts and moulds growth after 15 days of storage. To control the development of aerobic mesophilic bacteria the use of essential oil of lemon 0.2% and essential oil of orange 0.1% were the most efficient. The essential oils used in the edible coatings did not significantly change the sensorial properties of the fruit. Cyanidin-3-O-sophoroside, cyanidin-3-O-glucosylrutinoside, cyanidin-3-O-xylosylrutinoside, cyanidin-3-O-glucoside, cyanidin-3-O-rutinoside, pelargonidin-3-O-sophoroside, pelargonidin-3-O-glucosylrutinoside, pelargonidin 3-O-glucoside, pelargonidin 3-O-rutinoside were found in raspberries fruits. An unknown cyanidin derivative was also found in all samples, constituting 27.4% of total anthocyanin content.

Distributed optimization and games over networks: a system theoretical perspective

Several decision and control tasks involve networks of cyber-physical systems that need to be coordinated and controlled according to a fully-distributed paradigm involving only local communications without any central unit. This thesis focuses on distributed optimization and games over networks from a system theoretical perspective. In the addressed frameworks, we consider agents communicating only with neighbors and running distributed algorithms with optimization-oriented goals. The distinctive feature of this thesis is to interpret these algorithms as dynamical systems and, thus, to resort to powerful system theoretical tools for both their analysis and design. We first address the so-called consensus optimization setup. In this context, we provide an original system theoretical analysis of the well-known Gradient Tracking algorithm in the general case of nonconvex objective functions. Then, inspired by this method, we provide and study a series of extensions to improve the performance and to deal with more challenging settings like, e.g., the derivative-free framework or the online one. Subsequently, we tackle the recently emerged framework named distributed aggregative optimization. For this setup, we develop and analyze novel schemes to handle (i) online instances of the problem, (ii) ``personalized'' optimization frameworks, and (iii) feedback optimization settings. Finally, we adopt a system theoretical approach to address aggregative games over networks both in the presence or absence of linear coupling constraints among the decision variables of the players. In this context, we design and inspect novel fully-distributed algorithms, based on tracking mechanisms, that outperform state-of-the-art methods in finding the Nash equilibrium of the game.

Ihwg-μnir: A Miniaturised Near-infrared Gas Sensor Based On Substrate-integrated Hollow Waveguides Coupled To A Micro-nir-spectrophotometer.

A miniaturised gas analyser is described and evaluated based on the use of a substrate-integrated hollow waveguide (iHWG) coupled to a microsized near-infrared spectrophotometer comprising a linear variable filter and an array of InGaAs detectors. This gas sensing system was applied to analyse surrogate samples of natural fuel gas containing methane, ethane, propane and butane, quantified by using multivariate regression models based on partial least square (PLS) algorithms and Savitzky-Golay 1(st) derivative data preprocessing. The external validation of the obtained models reveals root mean square errors of prediction of 0.37, 0.36, 0.67 and 0.37% (v/v), for methane, ethane, propane and butane, respectively. The developed sensing system provides particularly rapid response times upon composition changes of the gaseous sample (approximately 2 s) due the minute volume of the iHWG-based measurement cell. The sensing system developed in this study is fully portable with a hand-held sized analyser footprint, and thus ideally suited for field analysis. Last but not least, the obtained results corroborate the potential of NIR-iHWG analysers for monitoring the quality of natural gas and petrochemical gaseous products.

Estimated Disability-adjusted Life Years Averted By Long-term Provision Of Long Acting Contraceptive Methods In A Brazilian Clinic.

What is the contribution of the provision, at no cost for users, of long acting reversible contraceptive methods (LARC; copper intrauterine device [IUD], the levonorgestrel-releasing intrauterine system [LNG-IUS], contraceptive implants and depot-medroxyprogesterone [DMPA] injection) towards the disability-adjusted life years (DALY) averted through a Brazilian university-based clinic established over 30 years ago. Over the last 10 years of evaluation, provision of LARC methods and DMPA by the clinic are estimated to have contributed to DALY averted by between 37 and 60 maternal deaths, 315-424 child mortalities, 634-853 combined maternal morbidity and mortality and child mortality, and 1056-1412 unsafe abortions averted. LARC methods are associated with a high contraceptive effectiveness when compared with contraceptive methods which need frequent attention; perhaps because LARC methods are independent of individual or couple compliance. However, in general previous studies have evaluated contraceptive methods during clinical studies over a short period of time, or not more than 10 years. Furthermore, information regarding the estimation of the DALY averted is scarce. We reviewed 50 004 medical charts from women who consulted for the first time looking for a contraceptive method over the period from 2 January 1980 through 31 December 2012. Women who consulted at the Department of Obstetrics and Gynaecology, University of Campinas, Brazil were new users and users switching contraceptive, including the copper IUD (n = 13 826), the LNG-IUS (n = 1525), implants (n = 277) and DMPA (n = 9387). Estimation of the DALY averted included maternal morbidity and mortality, child mortality and unsafe abortions averted. We obtained 29 416 contraceptive segments of use including 25 009 contraceptive segments of use from 20 821 new users or switchers to any LARC method or DMPA with at least 1 year of follow-up. The mean (± SD) age of the women at first consultation ranged from 25.3 ± 5.7 (range 12-47) years in the 1980s, to 31.9 ± 7.4 (range 16-50) years in 2010-2011. The most common contraceptive chosen at the first consultation was copper IUD (48.3, 74.5 and 64.7% in the 1980s, 1990s and 2000s, respectively). For an evaluation over 20 years, the cumulative pregnancy rates (SEM) were 0.4 (0.2), 2.8 (2.1), 4.0 (0.4) and 1.3 (0.4) for the LNG-IUS, the implants, copper IUD and DMPA, respectively and cumulative continuation rates (SEM) were 15.1 (3.7), 3.9 (1.4), 14.1 (0.6) and 7.3 (1.7) for the LNG-IUS, implants, copper IUD and DMPA, respectively (P < 0.001). Over the last 10 years of evaluation, the estimation of the contribution of the clinic through the provision of LARC methods and DMPA to DALY averted was 37-60 maternal deaths; between 315 and 424 child mortalities; combined maternal morbidity and mortality and child mortality of between 634 and 853, and 1056-1412 unsafe abortions averted. The main limitations are the number of women who never returned to the clinic (overall 14% among the four methods under evaluation); consequently the pregnancy rate could be different. Other limitations include the analysis of two kinds of copper IUD and two kinds of contraceptive implants as the same IUD or implant, and the low number of users of implants. In addition, the DALY calculation relies on a number of estimates, which may vary in different parts of the world. LARC methods and DMPA are highly effective and women who were well-counselled used these methods for a long time. The benefit of averting maternal morbidity and mortality, child mortality, and unsafe abortions is an example to health policy makers to implement more family planning programmes and to offer contraceptive methods, mainly LARC and DMPA, at no cost or at affordable cost for the underprivileged population. This study received partial financial support from the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), grant # 2012/12810-4 and from the National Research Council (CNPq), grant #573747/2008-3. B.F.B., M.P.G., and V.M.C. were fellows from the scientific initiation programme from FAPESP. Since the year 2001, all the TCu380A IUD were donated by Injeflex, São Paulo, Brazil, and from the year 2006 all the LNG-IUS were donated by the International Contraceptive Access Foundation (ICA), Turku, Finland. Both donations are as unrestricted grants. The authors declare that there are no conflicts of interest associated with this study.

Effects Of Partial Inhibition Of Respiratory Complex I On H2o 2 Production By Isolated Brain Mitochondria In Different Respiratory States.

The aim of this work was to characterize the effects of partial inhibition of respiratory complex I by rotenone on H2O2 production by isolated rat brain mitochondria in different respiratory states. Flow cytometric analysis of membrane potential in isolated mitochondria indicated that rotenone leads to uniform respiratory inhibition when added to a suspension of mitochondria. When mitochondria were incubated in the presence of a low concentration of rotenone (10 nm) and NADH-linked substrates, oxygen consumption was reduced from 45.9 ± 1.0 to 26.4 ± 2.6 nmol O2 mg(-1) min(-1) and from 7.8 ± 0.3 to 6.3 ± 0.3 nmol O2 mg(-1) min(-1) in respiratory states 3 (ADP-stimulated respiration) and 4 (resting respiration), respectively. Under these conditions, mitochondrial H2O2 production was stimulated from 12.2 ± 1.1 to 21.0 ± 1.2 pmol H2O2 mg(-1) min(-1) and 56.5 ± 4.7 to 95.0 ± 11.1 pmol H2O2 mg(-1) min(-1) in respiratory states 3 and 4, respectively. Similar results were observed when comparing mitochondrial preparations enriched with synaptic or nonsynaptic mitochondria or when 1-methyl-4-phenylpyridinium ion (MPP(+)) was used as a respiratory complex I inhibitor. Rotenone-stimulated H2O2 production in respiratory states 3 and 4 was associated with a high reduction state of endogenous nicotinamide nucleotides. In succinate-supported mitochondrial respiration, where most of the mitochondrial H2O2 production relies on electron backflow from complex II to complex I, low rotenone concentrations inhibited H2O2 production. Rotenone had no effect on mitochondrial elimination of micromolar concentrations of H2O2. The present results support the conclusion that partial complex I inhibition may result in mitochondrial energy crisis and oxidative stress, the former being predominant under oxidative phosphorylation and the latter under resting respiration conditions.