On the relaxed area of maps from the plane to itself taking three values

In this thesis we address two different problems; the first and the main one is the study of the relaxed area functional A(u, \u3a9) of the graph of vector maps u 08 L1(\u3a9; R^k) on an open set \u3a9 82 R^n, mainly for n = k = 2. In particular we are interested in estimating from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three C^2-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to \u201cfill the hole\u201d in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections. Moreover we investigate the possibility of adopting similar techniques to study the same problem in more general and different settings for instance when u has several (finite or infinite) triple junctions, or when n = 3, or when R^{2 72} is endowed by a Riemannian metric. An interesting open problem that we plan to address in the future, is to investigate the lower bound inequality; this seems to involve a strong use of geometric measure theory and Cartesian currents. The second part of the thesis is devoted to the problem of characterizing arbitrary codimensional smooth manifolds M with boundary embedded in R^n using the square distance function and the signed distance function from M and from its boundary. The results are localized in an open set

H5N1 Clade 2.2 Polymorphism Tracing Identifies Influenza Recombination and Potential Vaccine Targets

Highly pathogenic Influenza A H5N1 was first identified in Guangdong Province in 1996, followed by human cases in Hong Kong in 1997 1. The number of confirmed human cases now exceeds 300 and the associated Case Fatality Rate exceeds 60% 2. The genetic diversity of the serotype continues to increase. Four distinct clades or sub-clades have been linked to human cases 3.4. The gradual genetic changes identified in the sub-clades have been attributed to copy errors by viral encoded polymerases that lack an editing function, thereby resulting in antigenic drift 5. We traced polymorphism acquisition in Clade 2.2 sequences. We report here the concurrent acquisition of the same polymorphism by multiple, genetically distinct, Clade 2.2 sub-clades in Egypt, Russia and Ghana. These changes are not easily explained by the current theory of “random mutation” through copy error, and are more easily explained by recombination with a common source. This conclusion is supported by additional polymorphisms shared by Clade 2.2 isolates in Egypt, Nigeria and Germany including aggregation of regional polymorphisms from each of these areas into a single Nigerian human hemagglutinin gene

Isolation of avian influenza H5N1 virus from vaccinated commercial layer flock in Egypt

Uninterrupted transmission of highly pathogenic avian influenza virus (HPAIV) H5N1 of clade 2.2.1 in Egypt since 2006 resulted in establishment of two main genetic clusters. The 2.2.1/C group where all recent human and majority of backyard origin viruses clustered together, meanwhile the majority of viruses derived from vaccinated poultry in commercial farms grouped in 2.2.1.1 clade. In the present investigation, an HPAIV H5N1 was isolated from twenty weeks old layers chickens that were vaccinated with a homologous H5N1 vaccine at 1, 7 and 16 weeks old. At twenty weeks of age, birds showed cyanosis of comb and wattle, decrease in egg production and up to 27% mortality. Examined serum samples showed low antibody titer in HI test (Log2 3.2 ± 4.2). The hemagglutinin (HA) and neuraminidase (NA) genes of the isolated virus were closely related to viruses in 2.2.1/C group isolated from poultry in live bird market (LBM) and backyards or from infected people. Conspicuous mutations in the HA and NA genes including a deletion within the receptor binding domain in the HA globular head region were observed. Despite repeated vaccination of layer chickens using a homologous H5N1 vaccine, infection with HPAIV H5N1 resulted in significant morbidity and mortality. In endemic countries like Egypt, rigorous control measures including enforcement of biosecurity, culling of infected birds and constant update of vaccine virus strains are highly required to prevent circulation of HPAIV H5N1 between backyard birds, commercial poultry, LBM and humans

Dynamics and Control of Satellite Relative Motion in Proximity Operations

In this dissertation, the development of relative navigation, guidance, and control algorithms of an autonomous space rendezvous and docking system are presented. These algorithms are based on innovative formulations of the relative motion equations that are completely explicit in time. The navigation system uses an extended Kalman filter based on these formulations to estimate the relative position and velocity of the chaser vehicle with respect to the target vehicle and the chaser attitude and gyro biases. This filter uses the range and angle measurements of the target relative to the chaser from a simulated LIDAR system, along with the star tracker and gyro measurements of the chaser. The corresponding measurement models, process noise matrix, and other filter parameters are provided. The guidance and control algorithms are based on the glideslope used in the past for rendezvous and proximity operations of the Space Shuttle with other vehicles. These algorithms are used to approach, flyaround, and to depart from a target vehicle in elliptic orbits. The algorithms are general and able to translate the chaser vehicle in any direction, decelerate while approaching the target vehicle, and accelerate when moving away. Numerical nonlinear simulations that illustrate the relative navigation, attitude estimation, guidance, and control algorithm\u27s, as well as performance and accuracy are evaluated in the research study

Improving the physicochemical and antioxidative properties of fermented goat milk using carob molasses and some probiotic strains

Fermented goat milk samples, processed by adding 0, 2, and 4% carob molasses, and Bifidobacterium bifidum DSMZ or Lactobacillus helveticus CH5, were evaluated for their physicochemical, antioxidative, and sensory properties along with probiotic viability during storage. pH and viscosity gradually decreased over the storage period whereas their values increased with the increased amount of carob molasses. Bifidobacterium bifidum DSMZ or Lactobacillus helveticus CH5 kept higher viable numbers. Lactobacillus helveticus CH5 strain recorded higher viability. Increasing the added amount of carob molasses increased the total phenolic content, which in turn is reflected in the increase in antioxidant activity. Adding carob molasses participated in the partial masking of the goaty flavor and had no significant effect on the product’s acceptability, which was strongly influenced by the progress of cold storage. Therefore, fermented goat milk described by its enhanced physicochemical and antioxidative properties could be obtained by adding carob molasses and probiotics.<br/

Life history parameters of Yellowfin hind, Cephalopholis hemistiktos (Rí¼ppell, 1830) in the coast of United Arab Emirates

The life history parameters, including age, growth, mortality and recruitment of Yellowfin hind, Cephalopholis hemistiktos were studied in monthly collected samples from January to December 2018. Otolith was used for age determination. Mean size by the end of each year of life was estimated and showed that, the highest annual increment was identified at the end of the first year of life then gradually decreased with increase of fish age. The estimated von Bertalanffy growth parameters were L∞=43.51 cm, K=0.26 per year, t0=-0.74 year. Asymptotic weight W∞ was estimated as 1375.23 g. The length-weight relationship was W=0.0126 L3.0746 with R2=0.94 for both sexes. The instantaneous rates of total mortality and natural mortality were estimated as 0.77 and 0.49 per year, respectively. The gonado-somatic index showed increasing from April to August with a peak in June for both sexes. Size at first capture (Lc)was estimated as 24.30 cm, which was smaller than the mean size at first sexual maturity 25.31 cm. The value of fishing mortality (F=0.28y-1) was slightly higher than the optimum (Fopt=0.25y-1) and smaller than the limit (Flimit=0.33y-1) biological reference point, indicating that species was exploited within sustainable limit. Estimated parameters and the relative yield-per-recruit analysis showed that this species is not over-exploited

Distributional Probabilistic Model Checking

Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect to the expected value of these quantities, which can mask important aspects of the full probability distribution such as the possibility of high-risk, low-probability events or multimodalities. We propose a distributional extension of probabilistic model checking, applicable to discrete-time Markov chains (DTMCs) and Markov decision processes (MDPs). We formulate distributional queries, which can reason about a variety of distributional measures, such as variance, value-at-risk or conditional value-at-risk, for the accumulation of reward until a co-safe linear temporal logic formula is satisfied. For DTMCs, we propose a method to compute the full distribution to an arbitrary level of precision, based on a graph analysis and forward analysis of the model. For MDPs, we approximate the optimal policy with respect to expected value or conditional value-at-risk using distributional value iteration. We implement our techniques and investigate their performance and scalability across a range of benchmark models. Experimental results demonstrate that our techniques can be successfully applied to check various distributional properties of large probabilistic models.Comment: 20 pages, 2 pages appendix, 5 figures. Submitted for review. For associated Github repository, see https://github.com/davexparker/prism/tree/ing

Optimization of driving mode switching strategy for a multimode plug-in hybrid electric vehicle

Hybrid electric vehicles have become increasingly popular recently. Switching from internal combustion engine to battery as a clean source of energy is considered as a solution to reduce city pollution due to vehicle emissions. PHEV is a viable balance between the two sources of energy to achieve higher fuel economy with lower emissions. For a multimode PHEV, the car switches among three operation modes; namely electric mode, series mode, and parallel mode to maximize fuel economy based on the driving conditions. In this work, minimization of fuel consumption is used to optimize the mode switching strategy for a PHEV. The study is conducted using a reference vehicle that resembles 2014 Honda Accord Plug-in Hybrid vehicle. Global optimization with constraints using pattern search method is utilized. Starting from a switching strategy with 〖MPG〗_e = 30, optimization increased fuel economy to 〖MPG〗_e = 51.4 for a combined cycle (FTW75 and HWFET). Optimization proved to be a feasible method to improve mode switching strateg

Relative motion guidance, navigation and control for autonomous orbital rendezvous

In this paper, the dynamics of the relative motion problem in a perturbed orbital environment are exploited based on Gauss’ variational equations. The relative coordinate frame (Hill frame) is studied to describe the relative motion. A linear high fidelity model is developed to describe the relative motion. This model takes into account primary gravitational and atmospheric drag perturbations. In addition, this model is used in the design of a control, guidance, and navigation system of a chaser vehicle to approach towards and to depart from a target vehicle in proximity operations. Relative navigation uses an extended Kalman filter based on this relative model to estimate the relative position and velocity of the chaser vehicle with respect to the target vehicle and the chaser attitude and gyros biases. This filter uses the range and angle measurements of the target relative to the chaser from a simulated Light Detection and Ranging (LIDAR) system, along with the star tracker and gyro measurements of the chaser. The corresponding measurement models, process noise matrix and other filter parameters are provided. Numerical simulations are performed to assess the precision of this model with respect to the full nonlinear model.The analyses include the navigations errors, trajectory dispersions, and attitude dispersions