Minimization of errors in discrete wavelet filtering of signals during ultrasonic measurements and testing

Error minimizing methods for discrete wavelet filtering of ultrasonic meter signals are considered. For this purpose, special model signals containing various measuring pulses are generated. The psi function of the Daubechies 28 wavelet is used to generate the pulses. Noise is added to the generated pulses. A comparative analysis of the two filtering algorithms is performed. The first algorithm is to limit the amount of detail of the wavelet decomposition coefficients in relation to signal interference. The minimum value of the root mean square error of wavelet decomposition signal deviation which is restored at each level from the initial signal without noise is determined. The second algorithm uses a separate threshold for each level of wavelet decomposition to limit the magnitude of the detail coefficients that are proportional to the standard deviation. Like in the first algorithm, the task is to determine the level of wavelet decomposition at which the minimum standard error is achieved. A feature of both algorithms is an expanded base of discrete wavelets ‒ families of Biorthogonal, Coiflet, Daubechies, Discrete Meyer, Haar, Reverse Biorthogonal, Symlets (106 in total) and threshold functions garotte, garrote, greater, hard, less, soft (6 in total). The model function uses random variables in both algorithms, so the averaging base is used to obtain stable results. Given features of algorithm construction allowed to reveal efficiency of ultrasonic signal filtering on the first algorithm presented in the form of oscilloscopic images. The use of a separate threshold for limiting the number of detail coefficients for each level of discrete wavelet decomposition using the given wavelet base and threshold functions has reduced the filtering error.

Generation of Chow Parameters and Reduced Variables Through Nearest Neighbor Relations in Threshold Networks

Generation of useful variables and features is an important issue throughout the machine learning, artificial intelligence, and applied fields for their efficient computations. In this paper, the nearest neighbor relations are proposed for the minimal generation and the reduced variables of the functions in the threshold networks. First, the nearest neighbor relations are shown to be minimal and inherited for threshold functions and they play an important role in the iterative generation of the Chow parameters. Further, they give a solution for the Chow parameters problem. Second, convex cones are made of the nearest neighbor relations for the generation of the reduced variables. Then the edges of convex cones are compared for the discrimination of variables. Finally, the reduced variables based on the nearest neighbor relations are shown to be useful for documents classification.

A Note on Numerical Representations of Nested System of Strict Partial Orders

This note provides two numerical representations of a nested system of strict partial orders. The first representation is based on utility and threshold functions. We generalize the threshold representation of menu-dependent preferences by allowing the threshold to depend not only on the menu but also on the pair of alternatives under comparison. The threshold function can be interpreted as the distance between alternatives. The second representation is based on the aggregation of multi-dimensional preference. This representation describes a decision-making procedure where multiple criteria are gradually aggregated into an overall assessment.

Hybrid Model for Time Series of Complex Structure with ARIMA Components

A hybrid model for the time series of complex structure (HMTS) was proposed. It is based on the combination of function expansions in a wavelet series with ARIMA models. HMTS has regular and anomalous components. The time series components, obtained after expansion, have a simpler structure that makes it possible to identify the ARIMA model if the components are stationary. This allows us to obtain a more accurate ARIMA model for a time series of complicated structure and to extend the area for application. To identify the HMTS anomalous component, threshold functions are applied. This paper describes a technique to identify HMTS and proposes operations to detect anomalies. With the example of an ionospheric parameter time series, we show the HMTS efficiency, describe the results and their application in detecting ionospheric anomalies. The HMTS was compared with the nonlinear autoregression neural network NARX, which confirmed HMTS efficiency.

Similar masking effects of natural backgrounds on detection performances in humans, macaques, and macaque-V1 population responses

Visual systems evolve to process the stimuli that arise in the organism's natural environment and hence to fully understand the neural computations in the visual system it is important to measure behavioral and neural responses to natural visual stimuli. Here we measured psychometric and neurometric functions and thresholds in the macaque monkey for detection of a windowed sine‐wave target in uniform backgrounds and in natural backgrounds of various contrasts. The neurometric functions and neurometric thresholds were obtained by near‐optimal decoding of voltage‐sensitive‐dye‐imaging (VSDI) responses at the retinotopic scale in primary visual cortex (V1). Results were compared with previous human psychophysical measurements made under the same conditions. We found that human and macaque behavioral thresholds followed the generalized Weber's law as function of contrast, and that both the slopes and the intercepts of the threshold functions match each other up to a single scale factor. We also found that the neurometric thresholds followed the generalized Weber's law and that the neurometric slopes and intercepts matched the behavioral slopes and intercepts up to a single scale factor. We conclude that human and macaque ability to detect targets in natural backgrounds are affected in the same way by background contrast, that these effects are consistent with population decoding at the retinotopic scale by down‐stream circuits, and that the macaque monkey is an appropriate animal model for gaining an understanding of the neural mechanisms in humans for detecting targets in natural backgrounds. Finally, we discuss limitations of the current study and potential next steps.

Graph Models for Backbone Sets and Limited Packings in Networks

Here, a graph-theoretic approach is applied to some problems in networks, for example in wireless sensor networks (WSNs) where some sensor nodes should be selected to behave as a backbone/dominating set to support routing communications in an efficient and fault-tolerant way. Four different types of multiple domination (k-, k-tuple, α‎- and α‎-rate domination) are considered and recent upper bounds for cardinality of these types of dominating sets are discussed. Randomized algorithms are presented for finding multiple dominating sets whose expected size satisfies the upper bounds. Limited packings in networks are studied, in particular the k-limited packing number. One possible application of limited packings is a secure facility location problem when there is a need to place as many resources as possible in a given network subject to some security constraints. The last section is devoted to two general frameworks for multiple domination: <r,s>-domination and parametric domination. Finally, different threshold functions for multiple domination are considered.

Method of Constructing a Nonlinear Approximating Scheme of a Complex Signal: Application Pattern Recognition

A method for identification of structures of a complex signal and noise suppression based on nonlinear approximating schemes is proposed. When we do not know the probability distribution of a signal, the problem of identifying its structures can be solved by constructing adaptive approximating schemes in an orthonormal basis. The mapping is constructed by applying threshold functions, the parameters of which for noisy data are estimated to minimize the risk. In the absence of a priori information about the useful signal and the presence of a high noise level, the use of the optimal threshold is ineffective. The paper introduces an adaptive threshold, which is assessed on the basis of the posterior risk. Application of the method to natural data has confirmed its effectiveness.

Optimization of threshold functions over streams

A common stream processing application is alerting, where the data stream management system (DSMS) continuously evaluates a threshold function over incoming streams. If the threshold is crossed, the DSMS raises an alarm. The threshold function is often calculated over two or more streams, such as combining temperature and humidity readings to determine if moisture will form on a machine and therefore cause it to malfunction. This requires taking a temporal join across the input streams. We show that for the broad class of functions called quasiconvex functions, the DSMS needs to retain very few tuples per-data-stream for any given time interval and still never miss an alarm. This surprising result yields a large memory savings during normal operation. That savings is also important if one stream fails, since the DSMS would otherwise have to cache all tuples in other streams until the failed stream recovers. We prove our algorithm is optimal and provide experimental evidence that validates its substantial memory savings.