Function Computation under Privacy, Secrecy, Distortion, and Communication Constraints

The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include (1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals’ observed sequences; (2) the information leakage to a fusion center with respect to the remote source is considered a new privacy leakage metric; (3) the function computed is allowed to be a distorted version of the target function, which allows the storage rate to be reduced compared to a reliable function computation scenario, in addition to reducing secrecy and privacy leakages; (4) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless and lossy single-function computation with two transmitting nodes, which recover previous results in the literature. For special cases, including invertible and partially invertible functions, and degraded measurement channels, exact lossless and lossy rate regions are characterized, and one exact region is evaluated as an example scenario.

Function Computation Under Privacy, Secrecy, Distortion, and Communication Constraints

The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include 1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals’ observed sequences; 2) the information leakage to a fusion center with respect to the remote source is considered as a new privacy leakage metric; 3) the function computed is allowed to be a distorted version of the target function, which allows to reduce the storage rate as compared to a reliable function computation scenario in addition to reducing secrecy and privacy leakages; 4) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless and lossy single-function computation with two transmitting nodes, which recover previous results in the literature. For special cases that include invertible and partially-invertible functions, and degraded measurement channels, exact lossless and lossy rate regions are characterized, and one exact region is evaluated for an example scenario.

Determination of best-fit isotherm model for the sorption of Lead (II) and Manganese (II) ions onto acid-activated shale using selected non-linear error functions

The focus of this research is to apply the selected error function equation to establish the equilibrium isotherm model that best describes the adsorption of Pb2+ and Mn2+ onto acid-activated shale. Data collected from the batch experiment were analyzed using selected isotherm models (Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Sips and Redlich-Peterson). To compute the isotherm parameters used in choosing the best-fit isotherm model, selected non-linear error functions, namely, error sum of the square, normalized standard deviation, hybrid error function, root mean square error and Marquardt’s percent standard deviation were employed. From the scanning electron microscope results, it was observed that the surface characteristics of the shale change considerably with calcination and acid treatment but the acid-treated shale shows better uneven porous surface characteristics. Error function computation shows that the Dubinin-Radushkevich isotherm model had the least sum of normalized error of 0.3623 for Pb2+ adsorption and 0.5465 for Mn2+ adsorption; hence, it was selected as the best isotherm model for explaining the sorption of Pb(II) and Mn(II) ions unto acid-activated shale.