Determination the different categories of buyers based on the Jaynes’ information principle

Purpose: The article aims to reduce the volume of statistical data, necessary for determination the buyer’s structure. The correct clustering of clients is important for successful activity for both commercial and non-profit organizations. This issue is devoted to a large number of studies. Their main mathematical apparatus is statistical methods. Input data are results of buyer polls. Polls are labor-consuming and quite often annoying buyers. The problem of determination of structure (various categories) of buyers by the mathematical methods demanding a small amount of these polls is relevant. Design/Methodology/Approach: The approach offered in this report based on the Jaynes' information principle (principle of maximum entropy). Jaynes idea is as follows. Let us consider a system in which the conditions cannot be calculated or measured by an experiment. However, each state of the system has a certain measured implication, the average value of which is known (or can be defined), and the average result of these implications is known from the statistical data. Then the most objective are probabilities of states maximizing Shannon’s entropy under restrictions imposed by information about average implications of states. Findings: In this work the task of determination of percentage of buyers for computer shop by the average check is set and solved provided that average checks for each concrete category of buyers are known. Input data for calculation are their average checks. Determination of these values requires much less statistical data, than to directly determine relative number of buyers of various categories. Practical Implications: The results are of particular interest to marketing experts. Originality/Value: The article deals with practical situation when initially there are only three different groups of customers. For this case, the problem of maximizing entropy under given constraints reduced to the problem of finding a solution to a system of three equations, of which only one is nonlinear. This is a completely new result.peer-reviewe

A Comparison of PDF Projection with Normalizing Flows and SurVAE

Normalizing flows (NF) recently gained attention as a way to construct generative networks with exact likelihood calculation out of composable layers. However, NF is restricted to dimension-preserving transformations. Surjection VAE (SurVAE) has been proposed to extend NF to dimension-altering transformations. Such networks are desirable because they are expressive and can be precisely trained. We show that the approaches are a re-invention of PDF projection, which appeared over twenty years earlier and is much further developed

Hybrid Noise Simulation for Enclosed Configurations

Future air traffic regulations are going to further limit the noise and pollutant emissions of aero engines in a way that can only be met by the comprehensive migration towards lean premixed combustion based aero engine designs. Compared to conventional rich-quench-lean setups, these next generation combustion systems are more prone to thermoacoustic instabilities caused by combustion noise. For this reason, improved methods for the prediction and investigation of combustion noise and thermoacoustic instabilities are required. Consequently, a hybrid Computational Aeroacoustics (CAA) method is devised, implemented and applied to two enclosed, reactive configurations in this work. The method comprises a low Mach number flow solver, a dedicated acoustics tool and a coupling layer, which bridges the different numerical schemes and physical phenomena. In addition to traditional aeroacoustic problems, the method is applicable to enclosed configurations with complex geometries, while maintaining the favorable computational efficiency of common hybrid methods. Its key components are the newly developed acoustics solver and the corresponding coupling layer. For the description of the reacting flow field, an established, finite volume based flow solver is equipped with the coupling interface. By employing the high order spectral/hp element method in a discontinuous Galerkin formulation, the CAA solver efficiently accounts for acoustic wave propagation in complex, three-dimensional geometries. Its implementation is focused on stability and flexibility to allow for an easy adaption to industrial applications, such as combustion noise. This is achieved by solving the unconditionally stable Acoustic Perturbation Equations (APE) and using a set of Riemann solvers that can operate on variable density base flows. The developed coupling layer enables bi-directional communication of both solvers at run-time, without limiting their spatial and temporal resolutions, even when applied to coinciding domains. Their different length scales and discretization methods are overcome by a linear interpolation in time and a spatial, implicit low pass filter, that operates on an intermediate representation of the flow fields. The applicability of the hybrid CAA method is investigated by means of two laboratory scale combustors of increasing complexity. The first setup features a half-dump combustor, that facilitates a basic validation of the CAA solver and the coupling. It is shown that the short length scale base flow fields are sufficiently represented in terms of the CAA expansion by the coupling layer. In the obtained acoustic fields, the behavior of the system's first eigenmode is well reproduced. The instigation of a second eigenmode was not observed in the experimental noise spectrum but is in agreement with a similar hybrid CAA simulation. The second configuration is a pressurized burner, operated by a swirl stabilized, premixed flame. It is already beyond the capabilities of most available CAA tools and features most phenomena present in industry scale combustion systems. In the considered frequency range, the prevalent eigenmode is very well predicted. Independent of the acoustic governing equations, the developed method is estimated to require less than a fifth of the computational effort of a direct noise simulation for the considered configuration

Nature-inspired Methods for Stochastic, Robust and Dynamic Optimization

Nature-inspired algorithms have a great popularity in the current scientific community, being the focused scope of many research contributions in the literature year by year. The rationale behind the acquired momentum by this broad family of methods lies on their outstanding performance evinced in hundreds of research fields and problem instances. This book gravitates on the development of nature-inspired methods and their application to stochastic, dynamic and robust optimization. Topics covered by this book include the design and development of evolutionary algorithms, bio-inspired metaheuristics, or memetic methods, with empirical, innovative findings when used in different subfields of mathematical optimization, such as stochastic, dynamic, multimodal and robust optimization, as well as noisy optimization and dynamic and constraint satisfaction problems

CHARACTERIZATION AND MODELING OF III-V TRANSISTORS FOR MICROWAVE CIRCUIT DESIGN

New mobile communication technologies have given a boost to innova-tions in electronic for telecommunications and microwave electronics. It’s clear that the increasing request for mobile data availability, as proved by the growth of 69% of mobile data traffic in 2014, poses great challenges to indus-tries and researchers in this field. From this point of view a rapid diffusion of wireless mobile broadband network data standards, like LTE/4G, should be seen, which requests a state-of-the-art transceiver (i.e., transmitter/receiver) electronics. It will be mandato-ry to use higher frequencies, with wider bandwidth and excellent efficiency, to improve battery duration of mobile phones and reduce the energy consump-tion of the network infrastructures (i.e. base stations). Moreover, the microwave electronics is ubiquitous in satellite systems. As an example the GPS-GLONASS systems, developed respectively by United-States and Russian Federation for geo-spatial positioning, now are commonly used as navigation support for planes, ships, trains, automobiles, and even people. Other interesting applications are the earth-observation satellites, like the Italian system COSMO-SkyMed: a constellation of four satellites developed for the observation of the entire planet. These systems are able to produce a detailed image of the earth surface exploiting a microwave synthetic aperture radar, with the possibility to observe an area even by night or with bad weather conditions. Clearly these features are impossible for traditional opti-cal systems. Even if a lot of electronic applications are focused on the system architec-ture, in microwave electronics the single transistor still plays a key role. In-deed, the number of transistors in high-frequency circuits is low and wide ar-eas are occupied by numerous passive elements, required to optimize the sys-tem performance. There is a lot of interest in finding the optimum transistor operating condition for the application of interest, because the high-frequency electron-device technologies are relatively young and often still in develop-ment, so the transistor performance is generally poor. As a matter of fact, transistor characterization plays a very important role: various measurement systems, developed for this purpose, have been pro-posed in literature, with different approaches and application fields. Moreover, a meticulous characterization of the transistor is the basis for the identification of accurate models. These models, allowing to predict the tran-sistor response under very different operating conditions, represent a funda-mental tool for microwave circuit designers. This thesis will resume three years of research in microwave electronics, where I have collaborated in research activities on transistor characterization and modelling oriented to microwave amplifier design. As various kinds of amplifiers (i.e., low-noise amplifier, power amplifier) have been developed, various characterization techniques have been exploited. In the first chapter, after a presentation of the most common large-signal characterization systems, a low-frequency large-signal characterization setup, oriented to transistor low-frequency dispersion analysis and power amplifier design, will be described as well as the development of the control algorithm of the measurement system and its application to the design of a Gallium-Nitride class-F power-amplifier, operating at 2.4 GHz with 5.5 W of output power and 81% efficiency. Another application of the proposed setup for fast-trap characterization in III-V devices is then reported. Successively, an exten-sion of the setup to very low frequencies will be presented. In the second chapter, small-signal characterization techniques will be dealt with, focusing on noise measurement systems and their applications. Af-ter a brief introduction on the most relevant small-signal measurement system (i.e., the vector network analyzer), an innovative formulation will be intro-duced which is useful to analyze the small-signal response of Gallium-Arsenide and Gallium-Nitride transistors at very low frequencies. Successive-ly, the application of neural network to model the low-frequency small signal response of a Gallium-Arsenide HEMT will be investigated. The third and last chapter will deal with the EM-based characterization of Gallium-Nitride transistor parasitic structures and its usage, combined with small-signal and noise measurements, for developing a transistor model ori-ented to low-noise amplifiers design. In particular, the design of a three stages low-noise amplifier with more than 20 dB of gain and less than 1.8 dB of noise figure operating in Ku-band will be described

Robust and Efficient Probabilistic Approaches towards Parameter Identification and Model Updating

In engineering, the virtual behaviour of structures under operational and extreme conditions are investigated using mathematical or physics-based models. To obtain numerical responses that best reflect the structure under investigation, the physical input parameters describing the geometric, material, and damping properties of these models need to be identified or inferred. However, the presence of uncertainty poses significant challenges in parameter identification. Often, these uncertainties would stem from the following: 1) the aleatory uncertainty due the variations in the response measurements of nominal identical structures under same loading conditions due to manufacturing and material variability, thus, leading to the parameter not having a single "true" parameter value representation; 2) the epistemic uncertainty associated with the "fuzziness" to the knowledge of the parameter(s) as a result of the experimental data/measurements being usually affected by "noise"; and 3) the model uncertainty due to the modelling errors associated with the failure of the model in capturing the physics of the problem. This presents the need to not only perform an inference on the parameter(s), but also quantify the uncertainty associated with the estimates. An approach towards this would be Bayesian model updating, which serves as the context of this dissertation. The dissertation provides details to the efficient and robust approaches towards probabilistic parameter identification and model updating via the aforementioned approach. To realize this, an extensive literature review on Bayesian inference and the existing sampling tools is provided. This is done to identify the key research gaps, as well as limitations to the current sampling algorithms. From there, the Transitional Ensemble Markov Chain Monte Carlo sampler is proposed to which its strengths include its robustness in sampling from skewed distributions, quicker computational time, and the removal of any need for tuning by the users. To demonstrate this, the algorithm has been implemented on both numerical and real-world examples. The latter involves a structural health monitoring problem and the recent NASA-Langley Uncertainty Quantification challenge. Following which, the analysis is extended towards inferring time-varying parameter(s) via on-line Bayesian inference. This motivated the development of the Sequential Ensemble Monte Carlo sampler to which its strengths include its robustness in identifying the most probable Markov kernel under uncertainty. Such strengths are demonstrated through the experimental example involving a single-storey structure subjected to a time-varying Coulomb friction. Finally, the dissertation presents an approach to merge Artificial Intelligence tools with Bayesian statistics towards the probabilistic prediction of material properties for Nuclear power plant structures. Such development seeks to enable the Artificial Intelligence models to provide a more robust probabilistic prediction on the material properties under very limited data and model uncertainty. For the interest of the relevant practitioners, the algorithms to the proposed methods presented in the dissertation are made accessible on OpenCOSSAN, an open-source software for uncertainty quantification, as well as GitHub

Multi-task learning with Gaussian processes

Multi-task learning refers to learning multiple tasks simultaneously, in order to avoid tabula rasa learning and to share information between similar tasks during learning. We consider a multi-task Gaussian process regression model that learns related functions by inducing correlations between tasks directly. Using this model as a reference for three other multi-task models, we provide a broad unifying view of multi-task learning. This is possible because, unlike the other models, the multi-task Gaussian process model encodes task relatedness explicitly. Each multi-task learning model generally assumes that learning multiple tasks together is beneficial. We analyze how and the extent to which multi-task learning helps improve the generalization of supervised learning. Our analysis is conducted for the average-case on the multi-task Gaussian process model, and we concentrate mainly on the case of two tasks, called the primary task and the secondary task. The main parameters are the degree of relatedness ρ between the two tasks, and πS, the fraction of the total training observations from the secondary task. Among other results, we show that asymmetric multitask learning, where the secondary task is to help the learning of the primary task, can decrease a lower bound on the average generalization error by a factor of up to ρ2πS. When there are no observations for the primary task, there is also an intrinsic limit to which observations for the secondary task can help the primary task. For symmetric multi-task learning, where the two tasks are to help each other to learn, we find the learning to be characterized by the term πS(1 − πS)(1 − ρ2). As far as we are aware, our analysis contributes to an understanding of multi-task learning that is orthogonal to the existing PAC-based results on multi-task learning. For more than two tasks, we provide an understanding of the multi-task Gaussian process model through structures in the predictive means and variances given certain configurations of training observations. These results generalize existing ones in the geostatistics literature, and may have practical applications in that domain. We evaluate the multi-task Gaussian process model on the inverse dynamics problem for a robot manipulator. The inverse dynamics problem is to compute the torques needed at the joints to drive the manipulator along a given trajectory, and there are advantages to learning this function for adaptive control. A robot manipulator will often need to be controlled while holding different loads in its end effector, giving rise to a multi-context or multi-load learning problem, and we treat predicting the inverse dynamics for a context/load as a task. We view the learning of the inverse dynamics as a function approximation problem and place Gaussian process priors over the space of functions. We first show that this is effective for learning the inverse dynamics for a single context. Then, by placing independent Gaussian process priors over the latent functions of the inverse dynamics, we obtain a multi-task Gaussian process prior for handling multiple loads, where the inter-context similarity depends on the underlying inertial parameters of the manipulator. Experiments demonstrate that this multi-task formulation is effective in sharing information among the various loads, and generally improves performance over either learning only on single contexts or pooling the data over all contexts. In addition to the experimental results, one of the contributions of this study is showing that the multi-task Gaussian process model follows naturally from the physics of the inverse dynamics