Recent discoveries uncovered flaws in machine learning algorithms such as deep neural networks. Deep neural networks seem vulnerable to small amounts of non-random noise, created by exploiting the input to output mapping of the network. Applying this noise to an input image drastically decreases classication performance. Such image is referred to as an adversarial example. The purpose of this thesis is to examine how known regularization/robustness methods perform on adversarial examples. The robustness methods: dropout, low-pass filtering, denoising autoencoder, adversarial training and committees have been implemented, combined and tested. For the well-known benchmark, the MNIST (Mixed National Institute of Standards and Technology) dataset, the best combination of robustness methods has been found. Emerged from the results of the experiments, ensemble of models trained on adversarial examples is considered to be the best approach for MNIST. Harmfulness of the adversarial noise and some robustness experiments are demonstrated on CIFAR10 (The Canadian Institute for Advanced Research) dataset as well. Apart from robustness tests, the thesis describes experiments with human classification performance on noisy images and the comparison with performance of deep neural network.

Learning from worked examples typically involves study activities, involving reading such materials carefully and attempting to understand the information presented. Considerable evidence has amassed regarding the benefits for novices of studying appropriately constructed worked examples paired with practice questions. However, prior research from the cognitive and sports psychology literatures suggests mental practice of worked examples may be an effective adjunct to studying such materials. Meta-analyses of these literatures suggest the utility of mental practice depends upon the degree of cognitive elements contained within a task, and also suggest that some prior knowledge of a task is necessary for mental practice to be effective. The present series of studies aimed to identify conditions under which mental practice is effective in educationally realistic, highly cognitive domains. Based on the above meta-analytic results, mental practice was hypothesised to enhance learning over further study in highly cognitive domains, but only when students either had sufficient prior knowledge, or were able to develop such knowledge over the course of an instructional intervention. Study activities were primarily expected to support knowledge acquisition, while imagining-based activities (mental practice) were expected to support knowledge automation. The experiments herein thus investigated interactions between levels of prior knowledge, complexity of instructional material, and levels of learning from imagination versus conventional study strategies. In Experiment 1, under conditions of low prior knowledge and complex material (HTML), students who studied worked examples outperformed those who imagined. Experiment 2, using simplified but still complex materials and a similar participant pool, found no differences between conditions, but Experiment 3, using stricter experimental design, found a study effect. In Experiment 4, an imagination effect was found under high prior knowledge. Experiment 5, using less experienced learners, suggested those who studied outperformed those whom imagined on acquisition questions. Experiment 6 found a sequence of study then imagination is more effective than imagination then study. The results have broad application for effective sequencing of these instructional strategies, but development of an accurate metric for imagination "readiness" is required to advance theory and practice, and more evidence is needed for a schema automation explanation of mental practice effects.

We present an example-based learning approach for locating vertical frontal views of human faces in complex scenes. The technique models the distribution of human face patterns by means of a few view-based "face'' and "non-face'' prototype clusters. At each image location, the local pattern is matched against the distribution-based model, and a trained classifier determines, based on the local difference measurements, whether or not a human face exists at the current image location. We provide an analysis that helps identify the critical components of our system.

Das deutsche Bildungssystem ist noch weit davon entfernt, Inklusion im Schulalltag und im Schulunterricht flächendeckend umzusetzen. Dies ist jedoch eine Verpflichtung, die Deutschland mit dem Beitritt zur Behindertenrechtskonvention eingegangen ist. Die Realisierung einer inklusiven Schulentwicklung gestaltet sich schwierig, da die in der Inklusion erfolgreichen Schulen es einerseits nicht schaffen, den notwendigen Bedarf aufzufangen und es andererseits auch nur in bedingtem Maße gelingt, ihr Wissen und ihre Praxiserfahrungen über Inklusion weiterzugeben. Zugleich zeigt sich im Schulalltag die Notwendigkeit eines Abbaus von Barrieren sowie einer Verbesserung der Lernsituation. Debatten über die Anerkennung der heterogenen Rahmenbedingungen und damit über die Umsetzung eines inklusionspädagogischen Ansatzes dürfen nicht nur theoretisch geführt werden. In dem Beitrag werden daher konkrete Möglichkeiten für den Fremdsprachenunterricht und Gute-Praxis-Beispiele aufgezeigt. Auch wenn ohne Frage umfangreichere finanzielle Mittel für eine Inklusionsumsetzung Voraussetzung wären, wird dabei sichtbar, dass adäquates Handeln und ein entsprechender Wille aus Verwaltung-, Schulleiter-, Lehrer- und Schülerperspektive schon vieles bewegen kann. Es wird aufgezeigt, welche Probleme und Herausforderungen sich in einer inklusiven Praxis ergeben können. / Inclusive education in foreign language teaching: Implementation and examples of best practice The German education system is still far from implementing the concept of inclusive education in its schools and classrooms. However, this is a commitment Germany made when signing the CRPD. The implementation is rather difficult because on the one hand successful schools that exist already all over Germany are not able to serve the needs, and on the other hand, they have only limited resources to pass on their knowledge and practical experience of an inclusive approach. It is important to reduce barriers in everyday school practice and improve the learning situation now. Debates on the recognition of a heterogeneous learning group and thus on the implementation of an inclusive pedagogical approach must not only take place hypothetically. In this paper, therefore, will be presented specific ways as well as best practices of teaching foreign languages in an inclusive education system. Although greater financial resources for implementing inclusive education in schools are necessary, an adequate attitude of the administration, the school headmaster, the teachers and also of the students as well as their voluntary to act accordingly can already change a lot. Problems and challenges that may arise however in an inclusive education practice will also be presented.

The use of new tools for mathematics at school wins increasingly Importance. It follows from this that they are consquences as well as on aims and contents of mathematics at school us like on methods in the lessons. It is not unusual, that students and parents and also university professors are to be feared, that the calculation competence is decreasing with the use of CAS. In the lesson should be showed a possible way to developing such competences in the beginning phase of the learning process in Algebra. The examples refer to a level of school mathematics for students in the middle school age. The methods tell apart phases with and without CAS and shows a didactic principles of mathematics lessons in the case of use of CAS handheld technology.

Η θεωρία κβαντικού ελέγχου είναι μια νέα αναπτυσσόμενη μαθηματική θεωρία, η οποία ανζητά μεθόδους για τον καθορισμό της συμπεριφοράς των κβαντικών συστημάτων. Ο πρώτος στόχος της παρούσης εργασίας είναι η επισήμανση και η διευκρίνηση των θεωρητικών ερωτημάτων που προκύπτουν από την παρουσίαση της θεωρίας του κβαντικού ελέγχου ως προέκτασης του κλασικού ελέγχου. Ο δεύτερος στόχος της εργασίας είναι η παρουσίαση ορισμένων απλών παραδειγμάτων και μεθόδων κβαντικού ελέγχου, έτσι ώστε ο αναγνώστης να αποκτήσει μιά πρώτη εικόνα σχετικά με τα προβλήματα που ανακύπτουν στην προσπάθεια των ερευνητών να τιθασεύσουν τον μικρόκοσμο. Καθώς ο κβαντικός έλεγχος είναι κοινό ερευνητικό πεδίο για την επιστήμη των ηλεκτρολόγων μηχανικών και των φυσικών, η εργασία αυτή είναι φτιαγμένη έτσι ώστε να παρέχει σε ένα μηχανικό και ένα φυσικό τις γνώσεις που είναι απαραίτητες για τη μελέτη του κβαντικού ελέγχου. Για το σκοπό αυτό το πρώτο κεφάλαιο απευθύνεται κυρίως σε φυσικούς και αποτελεί μια παρουσίαση των βασικών αρχών της κλασικής θεωρίας ελέγχου. Αντίστοιχα, το δεύτερο κεφάλαιο απευθύνεται σε μηχανικούς και παρέχει τις απαραίτητες γνώσεις κβαντομηχανικής. Τέλος, το τρίτο κεφάλαιο αποτελεί τον κύριο κορμό της εργασίας και απευθύνεται σε αναγνώστες που προέρχονται και από τους δύο επιστημονικούς κλάδους. / The theory of quantum control is a new mathematical theory, which investigates methods for the description of the behaviour of quantum systems. The first target of this work is the identification and discussion of the theoretical questions of the quantum control theory as an extension of the classical control theory. The second target is to present some simple examples and methos of of quantum control in order to give to the reader a first insight to the related problems. The work contains three chapters. The first one gives an overview of the principales of the classic control theory. The second chapter provides the basic principals of quantum mechanics. Finally, the third chapter, which is the main part of the work, contains the examples and their discussion.

The diploma thesis is devoted to the inter-subject relationships of mathematics and geography. The aim of this thesis is to study real situations from the environment of geography, which have a mathematical basis, and to create a set of application examples for teaching at primary and secondary school. The work should show that mathematics is connected not only to physics, chemistry, biology, but also to geography, and that it occurs in many real-world situations.

Deep neural networks have been recently achieving high accuracy on many important tasks, most notably image classification. However, these models are not robust to slightly perturbed inputs known as adversarial examples. These can severely decrease the accuracy and thus endanger systems where such machine learning models are employed. We present a review of adversarial examples literature. Then we propose new defenses against adversarial examples: a network combining RBF units with convolution, which we evaluate on MNIST and get better accuracy than with an adversarially trained CNN, and input space discretization, which we evaluate on MNIST and ImageNet and obtain promising results. Finally, we explore a way of generating adversarial perturbation without access to the input to be perturbed. 1

Diploma thesis deals especially with practical examples on the topic of conics. It is divided into two parts. The first part includes chapters with examples on the topics discussed in the course Geometry I. In the second part affine properties of conics, which can be used in construction tasks, Pascal's theorem and Brianchon's theorem and their use are mentioned. The aim of this thesis is to ilustrate the conics on typical examples for those interested and then to show them the interesting properties, for which there is no space in the course Geometry I.

Utilization of video camera at physical measurement This thesis is aimed to use of a camcoder during physical measurements purposed for high school students. The thesis includes theoretical part, which is about physics lesson basic structure viewed from the point of educational goals. Further it describes a manual for recording the video for video analysis and basic presentation of the Tracker program. The practical part shows applicable excercises and their physical analysis. Exemplary working sheets in an electronic form filled in according to videoanalyses in the Tracker program are included as well.