The aim of this thesis is to propose the construction of selected types of hunting equipment and subsequently implement as part of targeted Business Training Forest Enterprise Masaryk Forest Křtiny. For inspiration, the proposals include a literary resources devoted to this topic, consultation with users of these devices in routine practice and personal experience. During implementation are used ideas and improvements, which may facilitate the construction or use of these devices. Within the work it is necessary to make economic calculation and determine the benefits or disadvantages of the implementation of the construction of these facilities as part of targeted actions for student collaboration. It is necessary to compare the selected types of devices with similar devices on the market.

RBFs are useful in scientific computing. In this thesis, we are interested in the positions of collocation points and RBF centers which causes the matrix for RBF interpolation singular and ill-conditioned. We explore the best bases by minimizing error function in supremum norm and root mean squares. We also use radial basis function to interpolate shifted data and find the best basis in certain sense. In the second part, we solve ill-posed problems by radial basis collocation method with different radial basis functions and various number of bases. If the solution is not unique, then the numerical solutions are different for different bases. To construct all the solutions, we can choose one approximation solution and add the linear combinations of the difference functions for various bases. If the solution does not exist, we show the numerical solution always fail to satisfy the origin equation.

This thesis describes a program of research that investigated the sensitivity of healthy young adults, healthy older adults and individuals with Alzheimer’s disease (AD) to happiness, sadness and fear emotion specified in facial expressions. In particular, the research investigated the sensitivity of these individuals to the distinctions between spontaneous expressions of emotional experience (genuine expressions) and deliberate, simulated expressions of emotional experience (posed expressions). The specific focus was to examine whether aging and/or AD effects sensitivity to the target emotions. Emotion-categorization and priming tasks were completed by all participants. The tasks employed an original set of cologically valid facial displays generated specifically for the present research. The categorization task (Experiments 1a, 2a, 3a, 4a) required participants to judge whether targets were, or were not showing and feeling each target emotion. The results showed that all 3 groups identified a genuine expression as both showing and feeling the target emotion whilst a posed expression was identified more frequently as showing than feeling the emotion. Signal detection analysis demonstrated that all 3 groups were sensitive to the expression of emotion, reliably differentiating expressions of experienced emotion (genuine expression) from expressions unrelated to emotional experience (posed and neutral expressions). In addition, both healthy young and older adults could reliably differentiate between posed and genuine expressions of happiness and sadness, whereas, individuals with AD could not. Sensitivity to emotion specified in facial expressions was found to be emotion specific and to be independent of both the level of general cognitive functioning and of specific cognitive functions. The priming task (Experiments 1b, 2b, 3b,4b) employed the facial expressions as primes in a word valence task in order to investigate spontaneous attention to facial expression. Healthy young adults only showed an emotion-congruency priming effect for genuine expressions. Healthy older adults and individuals with AD showed no priming effects. Results are discussed in terms of the understanding of the recognition of emotional states in others and the impact of aging and AD on the recognition of emotional states. Consideration is given to how these findings might influence the care and management of individuals with AD.

The first processing stage in computational vision, also called early vision, consists in decoding 2D images in terms of properties of 3D surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detection. These are inverse problems, which are often ill-posed or ill-conditioned. We review here the relevant mathematical results on ill-posed and ill-conditioned problems and introduce the formal aspects of regularization theory in the linear and non-linear case. More general stochastic regularization methods are also introduced. Specific topics in early vision and their regularization are then analyzed rigorously, characterizing existence, uniqueness, and stability of solutions.

This paper deals with the characterization of multiplication operators, especially with its behavior in the ill-posed case. We want to classify the different types and degrees of ill-posedness. We give some connections between this classification and regularization methods.

This thesis outlines a novel approach to make ill-posed inverse source problem well-posed exploiting inhomogeneous media. More precisely, we use Maxwell fish-eye lens to make scattered field emanating from distinct regions of an object of interest more directive and concentrated onto distinct regions of observation. The object of interest in this thesis is a thin slab placed conformally to the Maxwell fish-eye lens. Focused Green’s function of the background medium results in diagonal dominance of the matrix to be inverted for inverse problem solution. Hence, the problem becomes well-posed. We have studied one-dimensional variation of a very thin dielectric slab of interest having conformal shape to the lens. This method has been tested solving the forward problem using both Mie series and using COMSOL. Most common techniques for solving inverse problem are full non-linear inversion techniques, such as: distorted Born iterative method (DBIM) and contrast source inversion (CSI). DBIM needs to be regularized at every iteration. In some cases, it converges to a solution, and, in some cases, it does not. Diffraction tomography does not utilize regularization. It is a technique under Born approximation. It eliminates ill-posedness, but it works only for small contrast. Our proposed method works for high contrast and also provides well-posedness. In this thesis, our objective is to demonstrate inverse source problem and inverse scattering problem are not inherently ill-posed. They are ill-posed because conventional techniques usually use homogeneous or non-focusing background medium. These mediums do not support separation of scattered field. Utilization of background medium for scattered field separation casts the inverse problem in well-posed form.

This thesis describes a program of research that investigated the sensitivity of healthy young adults, healthy older adults and individuals with Alzheimer’s disease (AD) to happiness, sadness and fear emotion specified in facial expressions. In particular, the research investigated the sensitivity of these individuals to the distinctions between spontaneous expressions of emotional experience (genuine expressions) and deliberate, simulated expressions of emotional experience (posed expressions). The specific focus was to examine whether aging and/or AD effects sensitivity to the target emotions. Emotion-categorization and priming tasks were completed by all participants. The tasks employed an original set of cologically valid facial displays generated specifically for the present research. The categorization task (Experiments 1a, 2a, 3a, 4a) required participants to judge whether targets were, or were not showing and feeling each target emotion. The results showed that all 3 groups identified a genuine expression as both showing and feeling the target emotion whilst a posed expression was identified more frequently as showing than feeling the emotion. Signal detection analysis demonstrated that all 3 groups were sensitive to the expression of emotion, reliably differentiating expressions of experienced emotion (genuine expression) from expressions unrelated to emotional experience (posed and neutral expressions). In addition, both healthy young and older adults could reliably differentiate between posed and genuine expressions of happiness and sadness, whereas, individuals with AD could not. Sensitivity to emotion specified in facial expressions was found to be emotion specific and to be independent of both the level of general cognitive functioning and of specific cognitive functions. The priming task (Experiments 1b, 2b, 3b,4b) employed the facial expressions as primes in a word valence task in order to investigate spontaneous attention to facial expression. Healthy young adults only showed an emotion-congruency priming effect for genuine expressions. Healthy older adults and individuals with AD showed no priming effects. Results are discussed in terms of the understanding of the recognition of emotional states in others and the impact of aging and AD on the recognition of emotional states. Consideration is given to how these findings might influence the care and management of individuals with AD.

This is a thesis about how mollification can be used as a regularization method to reduce noise in ill-posed problems in order to make them well-posed. Ill-posed problems are problems where noise get magnified during the solution process. An example of this is how measurement errors increases with differentiation. To correct this we use mollification. Mollification is a regularization method that uses integration or weighted average to even out a noisy function. The different types of error that occurs when mollifying are the truncation error and the propagated data error. We are going to calculate these errors and see what affects them. An other thing worth investigating is the ability to differentiate a mollified function even if the function itself can not be differentiated. An application to mollification is a blood vessel problem in biometrics where the goal is to calculate the elasticity of the blood vessel’s wall. To do this measurements from the blood and the blood vessel are required, as well as equations for the calculations. The model used for the calculations is ill-posed with regard to specific variables which is why we want to apply mollification. Here we are also going to take a look at how the noise level affects the final result as well as the mollification radius.

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Yes / Understanding the detailed differences between posed and spontaneous smiles is an important topic with a range of applications such as in human-computer interaction, automatic facial emotion analysis and in awareness systems. During the past decade or so, there have been very promising solutions for accurate automatic recognition and detailed facial emotion analysis. To this end, many methods and techniques have been proposed for distinguishing between spontaneous and posed smiles. Our aim here is to go beyond the present state of the art in this field. Hence, in this work, we are concerned with understanding the exact distribution of a smile – both spontaneous and posed – across the face. To do this, we utilise a lightweight computational framework which we have developed to analyse the dynamics of human facial expressions. We utilise this framework to undertake a detailed study of the smile expression. Based on computing the optical flow across the face – especially across key parts of the face such as the mouth, the cheeks and around the eyes – we are able to accurately map the dynamic weight distribution of the smile expression. To validate our computational model, we utilise two publicly available datasets, namely the CK + dataset in which the subjects express posed smiles and the MUG dataset in which the subjects express genuine smiles. Our results not only confirm what already exists in the literature – i.e. that the spontaneous genuine smile is truly in the eyes – but it also gives further insight into the exact distribution of the smile across the face.