Σκοπός την εργασίας είναι η δημιουργία ενός ολοκληρωμένου ηλεκτρονικού καταστήματος το οποίο θα παρέχει στους χρήστες μεταξύ άλλων, δυνατότητα χωρικής αναζήτησης προϊόντων, και προσωποποίησης. Η εφαρμογή υποστηρίζει όλες τις λειτουργίες ενός σύγχρονου ηλεκτρονικού καταστήματος προσθέτοντας σε αυτές ένα πλήθος καινοτόμων λειτουργιών. Συγκεκριμένα υποστηρίζει λειτουργία καλαθιού αγορών και παραγγελιών μέσω πιστωτικής κάρτας χρησιμοποιώντας ένα εικονικό σύστημα τραπεζικών συναλλαγών, πλήθος λειτουργιών αναζήτησης προϊόντων, διαφορετικά είδη προσωποποίησης, πολλαπλά επίπεδα ασφάλειας με χρήση κρυπτογράφησης, δημιουργία λογαριασμών χρηστών, forum κα. Στις καινοτομίες της εφαρμογής συγκαταλέγονται η χωρική αναζήτηση προϊόντων με χρήση Τ.Κ., η αναζήτηση αντίστοιχων τιμών σε άλλα καταστήματα και η social προσωποποίηση με χρήση βαρών στους παράγοντες προσωποποίησης. Ιδιαίτερη βαρύτητα έχει δοθεί επίσης στην συντηρησιμότητα του συστήματος και στη φιλικότητα προς τον χρήστη. Οι τεχνολογίες που χρησιμοποιήθηκαν είναι κατά κύριο λόγο HTML, CSS, PHP, Postgresql, smarty και λειτουργικό σύστημα Linux. / The purpose of this thesis is the development of a comprehensive online store that supports all functions of a modern e-shop plus a host of innovative features. Specifically, the application supports shopping cart, orders pipeline using a virtual banking system, many search products features, different kinds of personalization, multiple levels of security using encryption, user accounts, forum etc.. Innovations in the application include spatial search for products using postal codes, search for corresponding values in other e-shops and social personalization using weights to the personalization factors. Special attention was also given to the maintainability of the system and user friendliness. For the implementation of the application were used HTML, CSS, PHP, Postgresql, smarty and Linux operating system.

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Quantum walks have been utilized by many quantum algorithms which provide improved performance over their classical counterparts. Quantum search algorithms, the quantum analogues of spatial search algorithms, have been studied on a wide variety of structures. We study quantum walks and searches on the Cayley graphs of finitely-generated free groups. Return properties are analyzed via Green’s functions, and quantum searches are examined. Additionally, the stopping times and success rates of quantum searches on random networks are experimentally estimated. / Mathematics

Random walks describe diffusion processes, where movement at every time step is restricted only to neighbouring locations. Classical random walks are constructed using the non-relativistic Laplacian evolution operator and a coin toss instruction. In quantum theory, an alternative is to use the relativistic Dirac operator. That necessarily introduces an internal degree of freedom (chirality), which may be identified with the coin. The resultant walk spreads quadratically faster than the classical one, and can be applied to a variety of graph theoretical problems. We study in detail the problem of spatial search, i.e. finding a marked site on a hypercubic lattice in d-dimensions. For d=1, the scaling behaviour of classical and quantum spatial search is the same due to the restriction on movement. On the other hand, the restriction on movement hardly matters for d ≥ 3, and scaling behaviour close to Grover’s optimal algorithm(which has no restriction on movement) can be achieved. d=2 is the borderline critical dimension, where infrared divergence in propagation leads to logarithmic slow down that can be minimised using clever chirality flips. In support of these analytic expectations, we present numerical simulation results for d=2 to d=9, using a lattice implementation of the Dirac operator inspired by staggered fermions. We optimise the parameters of the algorithm, and the simulation results demonstrate that the number of binary oracle calls required for d= 2 and d ≥ 3 spatial search problems are O(√NlogN) and O(√N) respectively. Moreover, with increasing d, the results approach the optimal behaviour of Grover’s algorithm(corresponding to mean field theory or d → ∞ limit). In particular, the d = 3 scaling behaviour is only about 25% higher than the optimal value.