Propagation of Random Errors by the Discrete Wavelet Transform Algorithm

The paper presents considerations concerning the transfer of random errors from the input to the output of the Discrete Wavelet Transform (DWT) algorithm. The concept of determining an uncertainty of its output data based on the probabilistic error description has been presented. The DWT is discussed as the product of the vector of input quantities and the matrix of algorithm coefficients. Calculations of the uncertainty of a single output result of the algorithm are described with assumption that the input quantities are burdened by random errors of known distributions. Theoretical considerations have been verified by simulation experiments using the Monte Carlo method. Determining the uncertainty at the DWT output is possible due to the specific properties of transferring random errors by linear and additive algorithms.

An open-source R-package and web application for high-quality probabilistic predictions in hydrology

<p>Probabilistic predictions provide crucial information regarding the uncertainty of hydrological predictions, which are a key input for risk-based decision-making. However, they are often excluded from hydrological modelling applications because suitable probabilistic error models can be both challenging to construct and interpret, and the quality of results are often reliant on the objective function used to calibrate the hydrological model.</p><p>We present an open-source R-package and an online web application that achieves the following two aims. Firstly, these resources are easy-to-use and accessible, so that users need not have specialised knowledge in probabilistic modelling to apply them. Secondly, the probabilistic error model that we describe provides high-quality probabilistic predictions for a wide range of commonly-used hydrological objective functions, which it is only able to do by including a new innovation that resolves a long-standing issue relating to model assumptions that previously prevented this broad application.  </p><p>We demonstrate our methods by comparing our new probabilistic error model with an existing reference error model in an empirical case study that uses 54 perennial Australian catchments, the hydrological model GR4J, 8 common objective functions and 4 performance metrics (reliability, precision, volumetric bias and errors in the flow duration curve). The existing reference error model introduces additional flow dependencies into the residual error structure when it is used with most of the study objective functions, which in turn leads to poor-quality probabilistic predictions. In contrast, the new probabilistic error model achieves high-quality probabilistic predictions for all objective functions used in this case study.</p><p>The new probabilistic error model and the open-source software and web application aims to facilitate the adoption of probabilistic predictions in the hydrological modelling community, and to improve the quality of predictions and decisions that are made using those predictions. In particular, our methods can be used to achieve high-quality probabilistic predictions from hydrological models that are calibrated with a wide range of common objective functions.</p>

RAP Model—Enabling Cross-Layer Analysis and Optimization for System-on-Chip Resilience

The Resilience Articulation Point (RAP) model aims to provision a probabilistic fault abstraction and error propagation concept for various forms of variability related faults in deep sub-micron CMOS technologies at the semiconductor material or device levels. RAP assumes that each of such physical faults will eventually manifest as a single- or multi-bit binary signal inversion or out-of-specification delay in a signal transition between bit values. When probabilistic error functions for specific fault origins are known at the bit or signal level, knowledge about the unit of design and its environment allow the transformation of the bit-related error functions into characteristic higher layer representations, such as error functions for data words, finite state machine (FSM) states, IP macro-interfaces, or software variables. Thus, design concerns can be investigated at higher abstraction layers without the necessity to further consider the full details of lower levels of design. This chapter introduces the ideas of RAP based on examples of particle strike, noise and voltage drop induced bit errors in SRAM cells. Furthermore, we show by different examples how probabilistic bit flips are systematically abstracted and propagated towards instruction and data vulnerability at MPSoC architecture level, and how RAP can be applied for dynamic testing and application-level optimizations in an autonomous robot scenario.

Practical probabilistic and graphical formulations of long-read polyploid haplotype phasing

Resolving haplotypes in polyploid genomes using phase information from sequencing reads is an important and challenging problem. We introduce two new mathematical formulations of polyploid haplotype phasing: (1) the min-sum max tree partition (MSMTP) problem, which is a more flexible graphical metric compared to the standard minimum error correction (MEC) model in the polyploid setting, and (2) the uniform probabilistic error minimization (UPEM) model, which is a probabilistic analogue of the MEC model. We incorporate both formulations into a long-read based polyploid haplotype phasing method called flopp. We show that flopp compares favorably to state-of-the-art algorithms—up to 30 times faster with 2 times fewer switch errors on 6x ploidy simulated data.