This diploma thesis is devoted to the multivariate cryptosystems. It includes an overview of commutative algebra with emphasis on Gröbner bases. Of all algorithms, especially the ones using Gröbner bases are studied, i.e. Buchberger's algorithm, which is already implemented in Wolfram Mathematica, and F4 algorithm, for which a program package has been created in the Wolfram Mathematica environment. Also Zhuang-Zi algorithm is described. To simplify its steps a program to compute the Lagrange interpolation polynomial has been created in Python.

In Natural Language Processing (NLP), speech and text are parsed and generated with language models and parser models, and translated with translation models. Each model contains a set of numerical parameters which are found by applying a suitable training algorithm to a set of training data. Many such training algorithms are instances of the Expectation-Maximization (EM) algorithm. In [BSV15], a generic EM algorithm for NLP is described. This work presents a particular speech model, the Hidden Markov model, and its standard training algorithm, the Baum-Welch algorithm. It is then shown that the Baum-Welch algorithm is an instance of the generic EM algorithm introduced by [BSV15], from which follows that all statements about the generic EM algorithm also apply to the Baum-Welch algorithm, especially its correctness and convergence properties.:1 Introduction 1.1 N-gram models 1.2 Hidden Markov model 2 Expectation-maximization algorithms 2.1 Preliminaries 2.2 Algorithmic skeleton 2.3 Corpus-based step mapping 2.4 Simple counting step mapping 2.5 Regular tree grammars 2.6 Inside-outside step mapping 2.7 Review 3 The Hidden Markov model 3.1 Forward and backward algorithms 3.2 The Baum-Welch algorithm 3.3 Deriving the Baum-Welch algorithm 3.3.1 Model parameter and countable events 3.3.2 Tree-shaped hidden information 3.3.3 Complete-data corpus 3.3.4 Inside weights 3.3.5 Outside weights 3.3.6 Complete-data corpus (cont.) 3.3.7 Step mapping 3.4 Review Appendix A Elided proofs from Chapter 3 A.1 Proof of Lemma 3.8 A.2 Proof of Lemma 3.9 B Formulary for Chapter 3 Bibliography

This final year thesis introduces the principles and properties of the artificial immune systems to the reader, then abstracts the principles from this knowledge and applies the real artificial immune systems on them. It provides a view at the practical applications that use and extend given ideas.

This thesis deals with shortest paths problem in graphs. Shortest paths problem is the basic issue of graph theory with many pracitcal applications. We can divide this problem into two following generalizations: single-source shortest path problem and all-pairs shortest paths problem. This text introduces principles and algorithms for generalizations. We describe both classical and new more efficient methods. It contains information about how some of these algorithms were implemented and offers an experimental comparison of these algorithms.

This thesis present a Stochastic Volatility in Mean (SVM) model which is estimated using sequential Monte Carlo methods. The SVM model was first introduced by Koopman and provides an opportunity to study the intertemporal relationship between stock returns and their volatility through inclusion of volatility itself as an explanatory variable in the mean-equation. Using sequential Monte Carlo methods allows us to consider a non-linear estimation procedure at cost of introducing extra computational complexity. The recently developed PaRIS-algorithm, introduced by Olsson and Westerborn, drastically decrease the computational complexity of smoothing relative to previous algorithms and allows for efficient estimation of parameters. The main purpose of this thesis is to investigate the volatility feedback effect, i.e. the relation between expected return and unexpected volatility in an empirical study. The results shows that unanticipated shocks to the return process do not explain expected returns. / Detta examensarbete presenterar en stokastisk volatilitets medelvärdes (SVM) modell som estimeras genom sekventiella Monte Carlo metoder. SVM-modellen introducerades av Koopman och ger en möjlighet att studera den samtida relationen mellan aktiers avkastning och deras volatilitet genom att inkludera volatilitet som en förklarande variabel i medelvärdes-ekvationen. Sekventiella Monte Carlo metoder tillåter oss att använda icke-linjära estimerings procedurer till en kostnad av extra beräkningskomplexitet. Den nyligen utvecklad PaRIS-algoritmen, introducerad av Olsson och Westerborn, minskar drastiskt beräkningskomplexiteten jämfört med tidigare algoritmer och tillåter en effektiv uppskattning av parametrar. Huvudsyftet med detta arbete är att undersöka volatilitets-återkopplings-teorin d.v.s. relationen mellan förväntad avkastning och oväntad volatilitet i en empirisk studie. Resultatet visar på att oväntade chockar i avkastningsprocessen inte har förklarande förmåga över förväntad avkastning.

Multi-Protocol Label Switching (MPLS) makes use of traffic engineering (TE) techniques and a variety of protocols to establish pre-determined highly efficient routes in Wide Area Network (WAN). Unlike IP networks in which routing decision has to be made through header analysis on a hop-by-hop basis, MPLS makes use of a short bit sequence that indicates the forwarding equivalence class (FEC) of a packet and utilises a predefined routing table to handle packets of a specific FEC type. Thus header analysis of packets is not required, resulting in lower latency. In addition, packets of similar characteristics can be routed in a consistent manner. For example, packets carrying real-time information can be routed to low latency paths across the networks. Thus the key success to MPLS is to efficiently control and distribute the bandwidth available between applications across the networks. A lot of research effort on bandwidth management in MPLS networks has already been devoted in the past. However, with the imminent roll out of 5G, MPLS is seen as a key technology for mobile backhaul. To cope with the 5G demands of rich, context aware and multimedia-based user applications, more efficient bandwidth management solutions need to be derived. This thesis focuses on the design of bandwidth management algorithms, more specifically QoS scheduling, in MPLS network for 5G mobile backhaul. The aim is to ensure the reliability and the speed of packet transfer across the network. As 5G is expected to greatly improve the user experience with innovative and high quality services, users’ perceived quality of service (QoS) needs to be taken into account when deriving such bandwidth management solutions. QoS expectation from users are often subjective and vague. Thus this thesis proposes the use of fuzzy logic based solution to provide service aware and user-centric bandwidth management in order to satisfy requirements imposed by the network and users. Unfortunately, the disadvantage of fuzzy logic is scalability since dependable fuzzy rules and membership functions increase when the complexity of being modelled increases. To resolve this issue, this thesis proposes the use of neuro-fuzzy to solicit interpretable IF-THEN rules.The algorithms are implemented and tested through NS2 and Matlab simulations. The performance of the algorithms are evaluated and compared with other conventional algorithms in terms of average throughput, delay, reliability, cost, packet loss ratio, and utilization rate. Simulation results show that the neuro-fuzzy based algorithm perform better than fuzzy and other conventional packet scheduling algorithms using IP and IP over MPLS technologies. / Tertiary Education Trust Fund (TETFUND)

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The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality". Several numerical results are presented to illustrate the promises and potential problems of these new algorithms. Comparisons with other numerical methods like Monte Carlo methods are also included. Development and analysis of the linear Shepard algorithm and its variants, all of which could be used for high dimensional scattered data interpolation problems, are also included here, as a candidate to help solve the master equation by building surrogate models in high dimensions. / Ph. D.

At Halmstad University a project was developed to provide recommendations forupgrading and downgrading the cloud resource app service plan based on the customersusage over the last 30 days. In today’s day and age, cloud resources and services are oftenquite expensive and offers a variety of different plans which can make it overwhelmingfor the customer to easily choose which tier they need for their plan. The result of thisscript indicate that the cloud users should consider changing subscription tier based onhow the historical data of their usage of the plan has looked like during the last 30 days.The proposed algorithm suggests an upgrade of a tier if the plan is overutilized andsuggest a downgrade of a tier if the plan is underutilized. The developed PowerShell codeuses the First-Fit and the Rule-based algorithmic approach from the related workresearched in the paper. The result found was that the code was able to give suitablerecommendations to scale up and down tiers for plans which were under and overutilizedbased on the percentual utilization rules set up and Legacy/DEV SKU mapping. Theresults obtained showed that the suggested plan can reduce costs by up to 30% and giveroughly 438.2% more performance per $USD spent. / Vid Högskolan i Halmstad utvecklades ett projekt för att ge förslag på uppgraderingaroch nedgraderingar av molnresursern app service plan baserat på användarens senaste 30dagars användning. Då dagens molnresurser och tjänster ofta är dyra och erbjuder ettöverflöd av planer, kan det vara förvirrande för användare att välja rätt nivå för sinabehov. Projektet föreslår att användarna ska överväga att byta plan beroende på hur denhistoriska datan har sett ut för planens användning, där en uppgradering rekommenderasom tjänsten är överanvänd och en nedgradering om planen är underanvänd. Denutvecklade PowerShell koden använder sig av First-fit och det regelbaserade algoritmtypen som utvecklades med inspiration från litteraturstudien. Resultatet av projektetindikerar att koden kunde ge optimala upp och ned skalnings rekommendationer beroendepå de olika procentuella trösklarna satta samt mappningen av Legacy och utvecklingstiers. Analyseringen av resultatet pekar på att det går att spara runt 30% på app serviceplan kostnaderna samt att app service planerna får 438,2% mer prestanda per spenderad$USD i jämförelse med nuvarande planen.

Synthetic Aperture Radar (SAR) is an emerging technique in remote sensing. The technology is capable of producing high-resolution images of the earth surface in all-weather conditions. Thesis work describes the present available methods for positioning and imaging targets using M-sequence UWB (Ultra-Wideband) radar signals with moving antennas and SAR algorithm to retrieve position and image of the target. M-sequence UWB radar technology used as signal source for transmission and receiving echoes of target. Pseudo random binary sequence is used as a transmitted signal. These radars have an ability to penetrate signal through natural and unnatural objects. It offers low cost and quality security system. Among a number of techniques of image retrieval in Synthetic Aperture Radar, study of Global back projection (GBP) algorithm is presented. As a time domain algorithm, GBP possesses inherent advantages over frequency domain algorithm like ability to handle long integration angle, wider bandwidth and unlimited aperture size. GBP breaks the full synthesis aperture into numbers of sub-apertures. These sub-apertures are treated pixel by pixel. Each sub-aperture is converted to a Cartesian image grid to form an image.  During this conversion the signal is treated with linear interpolation methods in order to achieve the best quality of the images. The objective of this thesis is the imaging of target using M-sequence UWB radar and processing SAR raw data using Global back projection algorithm.