PRELIMINARY DESIGN OF ANALOG DISCRETE UNIFORM NOISE GENERATOR

The paper presents the basic idea of ​​the construction of an analog discrete uniform noise generator. The source of noise is a carbon resistor, the noise is linearly strongly amplified and limited to around zero. The probability density function (PDF) of the carbon resistor thermal noise in that region is square. By narrowing the symmetric allowable gap (interval) around zero, PDF of the noise approaches a uniform distribution. The factor of deviation from the uniform distribution is correctly and precisely defined. This quantity has been shown to be practically negligible. In addition, the paper discusses the application of the proposed ditheter noise, both in the two-bit and in the multi-bit stochastic digital measurement method (SDMM). It has been shown that noise is more suitable for application in multi-bit SDMM, because it is less sensitive to deviations from the uniform distribution. Commercially available track-and-hold circuits provide at least an order of magnitude wider bandwidth of the described generator compared to the standard solution that uses numerical random number generator and a corresponding D/A converter. However, the realization of such a generator requires hard engineering work, and therefore goes beyond the scope of this paper.

Comparison robust data smoothing algorithms with wavelet filter for denoising sonic log signals

Well logging is an essential approach to making geophysical surveys and petrophysical measurements and plays a key role to interpret downhole conditions. But, well logging signals usually contain noise that distorts results and causes ambiguous interpretations. In this paper, the wavelet filter and robust data smoothing algorithms are tested for denoising synthetic sonic log and field sonic log data. Robust data smoothing algorithms include Gaussian, RLOESS (Robust locally estimating scatterplot smoothing), and RLOWESS (Robust locally weighted scatterplot smoothing) methods. Uniform and normal distribution noise applied to synthetic model and results revealed that the wavelet filter performs better than data smoothing algorithms for denoising uniform distribution noise. However, the RLOESS removed uniform noise acceptably. But, for normal distribution noise, the wavelet filter disrupts and data smoothing algorithms, specifically RLOESS attenuated noise perfectly. Due to the noise nature of field sonic log data, wavelet filter completely disrupts, but data smoothing algorithms removed the noise of field data more efficiently, particularly RLOESS. So, we can express that RLOESS is a perfect algorithm for denoising sonic log signals, regardless of noise nature.

Estimation and computations for Gaussian mixtures with uniform noise under separation constraints

In this paper we study a finite Gaussian mixture model with an additional uniform component that has the role to catch points in the tails of the data distribution. An adaptive constraint enforces a certain level of separation between the Gaussian mixture components and the uniform component representing noise and outliers in the tail of the distribution. The latter makes the proposed tool particularly useful for robust estimation and outlier identification. A constrained ML estimator is introduced for which existence and consistency is shown. One of the attractive features of the methodology is that the noise level is estimated from data. We also develop an EM-type algorithm with proven convergence. Based on numerical evidence we show how the methods developed in this paper are useful for several fundamental data analysis tasks: outlier identification, robust location-scale estimation, clustering, and density estimation.

An information theoretic method to resolve millisecond-scale spike timing precision in a comprehensive motor program

Sensory inputs in nervous systems are often encoded at the millisecond scale in a temporally precise code. There is now a growing appreciation for the prevalence of precise timing encoding in motor systems. Animals from moths to birds control motor outputs using precise spike timing, but we largely do not know at what scale timing matters in these circuits due to the difficulty of recording a complete set of spike-resolved motor signals and relatively few methods for assessing spike timing precision. We introduce a method to estimate spike timing precision in motor circuits using continuous MI estimation at increasing levels of added uniform noise. This method can assess spike timing precision at fine scales for encoding rich motor output variation. We demonstrate the advantages of this approach compared to a previously established discrete information theoretic method of assessing spike timing precision. We use this method to analyze a data set of simultaneous turning (yaw) torque output and EMG recordings from the 10 primary muscles of Manduca sexta as tethered moths visually tracked a robotic flower moving with a 1 Hz sinusoidal trajectory. We know that all 10 muscles in this motor program encode the majority of information about yaw torque in spike timings, but we do not know whether individual muscles receive information encoded at different levels of precision. Using the continuous MI method, we demonstrate that the scale of temporal precision in all motor units in this insect flight circuit is at the sub-millisecond or millisecond-scale, with variation in precision scale present between muscle types. This method can be applied broadly to estimate spike timing precision in sensory and motor circuits in both invertebrates and vertebrates.

Quantum-assisted associative adversarial network: applying quantum annealing in deep learning

Generative models have the capacity to model and generate new examples from a dataset and have an increasingly diverse set of applications driven by commercial and academic interest. In this work, we present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted by the discriminator. A quantum processor can be used to sample from the model to train the Boltzmann machine. This novel hybrid quantum-classical algorithm joins a growing family of algorithms that use a quantum processor sampling subroutine in deep learning, and provides a scalable framework to test the advantages of quantum-assisted learning. For the latent space model, fully connected, symmetric bipartite and Chimera graph topologies are compared on a reduced stochastically binarized MNIST dataset, for both classical and quantum sampling methods. The quantum-assisted associative adversarial network successfully learns a generative model of the MNIST dataset for all topologies. Evaluated using the Fréchet inception distance and inception score, the quantum and classical versions of the algorithm are found to have equivalent performance for learning an implicit generative model of the MNIST dataset. Classical sampling is used to demonstrate the algorithm on the LSUN bedrooms dataset, indicating scalability to larger and color datasets. Though the quantum processor used here is a quantum annealer, the algorithm is general enough such that any quantum processor, such as gate model quantum computers, may be substituted as a sampler.

Multi-Objective Surrogate-Assisted Stochastic Optimization for Engine Calibration

A surrogate assisted optimization approach is an attractive way to reduce the total computational budget for obtaining optimal solutions. This makes it special for its application to practical optimization problems requiring a large number of expensive evaluations. Unfortunately, all practical applications are affected by measurement noises, and not much work has been done to address the issue of handling stochastic problems with multiple objectives and constraints. This work tries to bridge the gap by demonstrating three different frameworks for performing surrogate assisted optimization on multiobjective constrained problems with stochastic measurements. To make the algorithms applicable to real-world problems, heteroscedastic (non-uniform) noise is considered for all frameworks. The proposed algorithms are first validated on several multiobjective numerical problems (unconstrained and constrained) to verify their effectiveness, and then applied to the diesel engine calibration problem, which is expensive to perform and has measurement noises. A GT-SUITE model is used to perform the engine calibration study. Three control parameters, namely variable geometry turbocharger vane position, exhaust-gas-recirculating valve position, and the start of injection, are calibrated to obtain the trade-off between engine fuel efficiency performance (brake specific fuel consumption) and NOx emissions within the constrained design space. The results show that all three proposed extensions can handle the problems well with different measurement noise levels at a reduced evaluation budget. For the engine calibration problem, a good approximation of the optimal region is observed with more than 80\% reduction in evaluation budget for all the proposed methodologies.