Expressions for Rényi and Shannon entropies for bivariate distributions

Exact forms of Rényi and Shannon entropies are determined for 27 continuous bivariate distributions, including the Kotz type distribution, truncated normal distribution, distributions with normal and centered normal conditionals, natural exponential distribution, Freund's exponential distribution, Marshall and Olkin's exponential distribution, exponential mixture distribution, Arnold and Strauss's exponential distribution, McKay's gamma distribution, distribution with gamma conditionals, gamma exponential distribution, Dirichlet distribution, inverted beta distribution, distribution with beta conditionals, beta stacy distribution, Cuadras and Augé's distribution, Farlie Gumbel Morgenstern distribution, logistic distribution, Pearson type VII distribution, Pearson type II distribution, distribution with Cauchy conditionals, bilateral Pareto distribution, Muliere and Scarsini's Pareto distribution, distribution with Pareto conditionals and the distribution with Gumbel conditionals. We believe that the results presented here will serve as an important reference for scientists and engineers in many areas.     

Protection switching and local area network emulation in passive optical networks

This paper proposes and experimentally demonstrates an automatic-protection-switching (APS) mechanism against distribution fiber breaks in passive optical networks (PONs). The protection of optical-network units (ONUs) that are located at the customer premises is carried out by monitoring the distribution fiber using the traffic that is transported among the customers in the PON. This configuration emulates a local area network (LAN) over the existing PON while facilitating the switching of signal transmissions to a predetermined protection path in an event of a distribution fiber break. As failure detection and APS are performed independently by each ONU in a distributed manner, the processing complexities and delays are reduced at the central office (CO). The restoration of the traffic transported between the CO and an ONU in the event of the distribution fiber break is performed by interconnecting adjacent ONUs and carrying out signal transmissions via an independent but interconnected ONU. Such a protection mechanism enables multiple adjacent ONUs to be simultaneously protected by a single ONU utilizing its maximum available bandwidth. This paper experimentally verifies the feasibility of the proposed protection mechanism in conjunction with two different LAN-emulation schemes with a 1.25-Gb/s upstream baseband transmission to the CO and a 155-Mb/s LAN data transmission on a radio-frequency carrier. The experimental results obtained from both schemes are compared, and the power budgets are calculated to analyze the scalability of each scheme.     

Closed Form Solutions for the Probability of Error for EG Combiners

Elementary expressions are derived for the probabilities of error of general equal gain combiner (EGC) over Rayleigh fading channels. The computational effort is significantly reduced     

Laser-free operation of customer unit with local area network emulation in passive optical networks facilitated by reflective semiconductor optical amplifier

A scheme for upstream access and local area networking among customers in a passive optical network facilitated through a single reflective semiconductor optical amplifier placed in customer premises is proposed and experimentally demonstrated. Upstream access is performed by wavelength seeding the reflective semiconductor optical amplifier while the broadband amplified spontaneous emission spectra was used for the transmission of the local area network traffic     

Influence of hydrology on water quality and trophic state of irrigation reservoirs in Sri Lanka

Many reservoirs provide multiple benefits to people around the world, in addition to primary uses such as irrigation. Thus, reservoir management should address their multiple uses. The water quality of ten irrigation reservoirs in Sri Lanka was examined in the present study with the objective of better understanding the effects of hydrological regimes on reservoir water quality and trophic state. Basic limnological parameters pertinent to the nutrient loads to, and trophic state of, the reservoirs were collected from June 2013 to February 2016. The sampling period was arbitrarily divided into two periods of approximately similar duration (period 1 = June 2013–September 2014; period 2 = October 2014–February 2016) to investigate whether or not there was a seasonal variation in the water quality parameters. Although temporal and spatial variations were observed, most water quality parameters were within the levels acceptable for drinking water standards. The 10 reservoirs were also ordinated by principal component analysis (PCA) on the basis of the water quality parameters of the two sampling periods in a two‐dimensional score plot. Reservoirs in the first principal component (PC1) axis were represented by negative scores attributable to the dissolved oxygen concentration and pH and, to a lesser extent, by electrical conductivity and chlorophyll‐a concentration. Positive scores in PC1 were represented by reservoirs with a score loading attributable to alkalinity, nitrate concentration, Secchi depth, temperature and seston weight and, to a lesser extent, from the total phosphorus concentration. There was a significant negative correlation of PC1 scores with relative reservoir water‐level fluctuation (RRLF; the ratio of mean reservoir water‐level amplitude to mean reservoir depth). Furthermore, Carlson's trophic index also were influenced by RRLF, although not by hydraulic retention time (HRT), indicating allochthonous nutrient inputs into the irrigation reservoirs were mainly governed by RRLF, but not by HRT. Thus, the results of the present study provide useful insights into achieving desirable reservoir water quality through the manipulation of the hydrological regime.     

Hantush’s M(α, β) and M*(α, β) are Generalized Incomplete Exponential Functions

It is pointed out that Hantush’s M(α, β) and M*(α, β) functions, two functions that arise with respect to groundwater pumping modeling, are particular cases of the generalized incomplete exponential functions known in the mathematics/statistics literature. Some relevant computational issues are discussed.     

Rates of convergence of extremes for mixed exponential distributions

The limiting distributions of the extremes of mixed exponential distributions and the associated rates of convergence are derived. The practical values of the results are illustrated by a numerical study.     

Relationship of bull fertility with daughter fertility and production traits in Holstein dairy cattle

The phenotypic and genetic correlations between fertility ratings of AI bulls for conception rate and their estimated breeding values for daughters' fertility and production traits were calculated. Genetic correlations between fertility ratings of bulls for conception and heifer fertility traits (age at first breeding, age at last breeding, and number of insemination per conception) were negative and ranged from -.04 to -.23, indicating daughters of bulls with high fertility ratings were younger at first breeding and required fewer services to conceive. In general, genetic correlations between fertility ratings of bulls for conception rate and cow fertility traits (days from calving to first breeding, days open, and number of inseminations per conception) and production traits (breed class average milk and fat and fat percentage) in the first two lactations were also moderate to high and in the favorable direction. Although heritability of both male and female fertility is low, these data indicate that heavy use of sires with high fertility ratings could have a mild positive effect on both male and female fertility. Evidence is also found to indicate that in this breed, selection for increased milk yield should not impair genetic ability of cows to reproduce.     

On Outage Probability of Selection Cooperation

An exact and elementary expression is derived for the outage probability of selection cooperation. Its performance is compared versus known approximations. Some better approximations are proposed.