Due to introduction of smart phones with data intensive multimedia and interactive applications and exponential growth of wireless devices, there is a shortage for useful radio spectrum. Even though the spectrum has become crowded, many spectrum occupancy measurements indicate that most of the allocated spectrum is underutilised. Hence radically new approaches in terms of allocation of wireless resources are required for better utilization of radio spectrum. This has motivated the concept of opportunistic spectrum sharing or the so-called cognitive radio technology that has great potential to improve spectrum utilization. The cognitive radio technology allows an opportunistic user namely the secondary user to access the spectrum of the licensed user (known as primary user) provided that the secondary transmission does not harmfully affect the primary user. This is possible with the introduction of advanced resource allocation techniques together with the use of wireless relays and spatial diversity techniques. In this thesis, various mathematical optimization techniques have been developed for the efficient use of radio spectrum within the context of spectrum sharing networks. In particular, optimal power allocation techniques and centralised and distributed beamforming techniques have been developed. Initially, an optimization technique for subcarrier and power allocation has been proposed for an Orthogonal Frequency Division Multiple Access (OFDMA) based secondary wireless network in the presence of multiple primary users. The solution is based on integer linear programming with multiple interference leakage and transmission power constraints. In order to enhance the spectrum efficiency further, the work has been extended to allow multiple secondary users to occupy the same frequency band under a multiple-input and multiple-output (MIMO) framework. A sum rate maximization technique based on uplink-downlink duality and dirty paper coding has been developed for the MIMO based OFDMA network. The work has also been extended to handle fading scenarios based on maximization of ergodic capacity. The optimization techniques for MIMO network has been extended to a spectrum sharing network with relays. This has the advantage of extending the coverage of the secondary network and assisting the primary network in return for the use of the primary spectrum. Finally, instead of considering interference mitigation, the recently emerged concept of interference alignment has been used for the resource allocation in spectrum sharing networks. The performances of all these new algorithms have been demonstrated using MATLAB based simulation studies.

Introduction: Autism Spectrum Disorder (ASD) is a behaviourally defined disorder characterised by impairments in three domains of social interaction, communication, and repetitive/restricted interests and behaviours (DSM-IV-TR; APA, 2000; ICD-10; WHO, 1992). Recent research suggests that this diagnostic triad may no longer fit as the best way to conceptualise ASD. Although not due for publication until 2013, a proposed revision of autistic disorder for DSM-V has merged three domains into two; i) Social/communication deficits and ii) Fixated interests and repetitive behaviours (APA, 2010). The aim of this study was to examine the structure of ASD symptom domains within the Adult Asperger Assessment (AAA; Baron-Cohen et al., 2005). Method: Confirmatory factor analysis was used to examine data from a clinical population of adults diagnosed with Asperger Syndrome (AS) and High Functioning Autism (HFA). Results: Analysis suggested that none of the theoretically-driven models were supported by the AAA data. However, it did highlight high correlations between social and communication factors (r > 0.9) within unmodified models. Discussion: The results of the analysis did not provide support for the move towards considering ASD as a dyad of ‘social-communication’ impairments and repetitive/restricted interests and behaviours, as none of the models were supported by the AAA data. The validity of the AAA as a diagnostic tool is discussed, as well as limitations and suggestions for future research. Conclusion: This study did not provide the evidence required to endorse a move towards the proposed DSM-V dyad. Further research to understanding the structure of autism symptoms could improve diagnostic and classification systems, and further studies of the genetic and neurobiological bases of ASD.

Master’s thesis is devoted to the study of cardinal invariants in the F-compact spaces class. Here and throughout the paper, the concept ”compact” would mean a compact Hausdorff space. In my thesis I have tried to present and explain all necessary concepts and statements necessary for the reader to get acquainted with F-compact spaces class. In order to understand the idea of F-compact spaces, it is necessary to understand what the inverse spectrum is from itself, it is necessary to know about the cardinality of sets and to understand that two infinite sets can have different cardinalities, know about closed and open sets, and much else that you will find in this paper. In the thesis the analysis of the scientific literature sources is presented; the theorems about the relationship between the characteristics of cardinality invariants in the F-compact spaces class are investigated; the relationships between the properties of perfect normality and hereditary normality in the F - compact spaces class of countable spectral height are studied. In the process of the investigation some propositions were found, proved and filled in the missing fragments of evidence. Conclusion: At present, the method of fully closed mappings (which is used in constructing of F - compact spaces ) is the most productive method of constructing counterexamples in general topology. I believe, that this paper will be interesting to all who wants to go beyond the ordinary, habitual way of thinking, because only by studying topology we can speak clearly and precisely about things related to the idea of continuity and infinity!

Background: Autism Spectrum Disorder (ASD) is a neurodevelopmental disability diagnosed in an increasing number of children. ASD has few effective treatment options. This study describes ASD prevalence and use of psychotropic medications among children and youth in Manitoba. Methodology: Administrative data from the Repository at the Manitoba Centre for Health Policy (MCHP) were used to create a cohort of children born in Manitoba. Diagnoses of ASD were based on medical claim records, hospital abstracts, or special education funding data. Results: Between 2010 and 2014, 3079 Manitoba children aged 0-14 had an ASD diagnosis (1.2% prevalence). Child demographic, health and education, and family environmental characteristics were compared between children with ASD and children in the general population; children with ASD with and without psychotropic medications; and among all children with psychotropic medications. Children with ASD were more likely to have a psychotropic medication than children in the general population. Children with ASD were more likely to receive a psychotropic medication if they were older than age 4, were diagnosed with ASD later than age 4, received special education funding, had participated in behavioural programming, had a co-occurring psychiatric condition, had a sibling diagnosed with ASD or had ever been in the care of child welfare. This study demonstrated that children with ASD received a greater number and intensity of psychotropic medications than children in the general population with similar demographic and psychiatric conditions. Conclusions: In Manitoba, the prevalence of ASD is increasing and differences exist between children with ASD and children in the general population. Future research and treatment planning for children with mental disorders and developmental disabilities should consider the appropriateness of the patterns of medication use and equity of treatment interventions found in this study. / October 2016

Autism spectrum disorder (ASD) has been attributed to genetic and non-genetic risk factors. Of the non-genetic factors, prenatal and perinatal complications have been extensively investigated, though few associations have been replicated consistently. We selected 2,562 families with at least one individual with ASD and one unaffected sibling. We investigated the relationships between 29 prenatal and perinatal complications and ASD, while considering the influences of confounding factors, comorbid conditions, and different ASD definitions. Although many complications were associated with ASD in the pairwise comparisons, only haematological disorders of the newborn and lower Apgar scores remained significant after adjusting for the effects of the confounders. After removing individuals with congenital anomalies, only 5-minute Apgar scores were associated with ASD. In conclusion, after considering confounding effects and four ASD definitions, several perinatal complications were associated with ASD with moderate effect sizes. Furthermore, comorbid conditions with ASD appear to be intertwined in these relationships. / October 2016

There are numerous applications of mathematics, specifically spectral graph theory, within the sciences and many other fields. This paper is an exploration of recent applications of spectral graph theory, including the fields of chemistry, biology, and graph coloring. Topics such as the isomers of alkanes, the importance of eigenvalues in protein structures, and the aid that the spectra of a graph provides when coloring a graph are covered, as well as others.The key definitions and properties of graph theory are introduced. Important aspects of graphs, such as the walks and the adjacency matrix are explored. In addition, bipartite graphs are discussed along with properties that apply strictly to bipartite graphs. The main focus is on the characteristic polynomial and the eigenvalues that it produces, because most of the applications involve specific eigenvalues. For example, if isomers are organized according to their eigenvalues, a pattern comes to light. There is a parallel between the size of the eigenvalue (in comparison to the other eigenvalues) and the maximum degree of the graph. The maximum degree of the graph tells us the most carbon atoms attached to any given carbon atom within the structure. The Laplacian matrix and many of its properties are discussed at length, including the classical Matrix Tree Theorem and Cayley's Tree Theorem. Also, an alternative approach to defining the Laplacian is explored and compared to the traditional Laplacian.

Telecommunication sector is one of the most developing in last 20 years. The speed of the progress in inventing new technologies has to be balanced by proper radio spectrum management since radio spectrum is a scarce resource. The methods of assignment used in past such as beauty contests or lotteries are no longer those that rule the sector. To keep pace with new technologies, spectrum auctions were presented as a new method that ensures the best results for state. Since the companies are competing for the licenses, final price is getting higher and thereby higher revenues go to the state treasury. In this thesis the behavior of final price in the spectrum auctions was examined. In the end of the work, recommendations to NRAs were presented to conclude the results of the empirical examination. Powered by TCPDF (www.tcpdf.org)

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This paper presents a segmented parabolic concentrator employing holographic spectral filters that provide focusing and spectral bandwidth separation capability to the system. Strips of low band gap silicon photovoltaic (PV) cells are formed into a parabolic surface as shown by Holman et. al. [1]. The surface of the PV segments is covered with holographic elements formed in dichromated gelatin. The holographic elements are designed to transmit longer wavelengths to silicon cells, and to reflect short wavelength light towards a secondary collector where high-bandgap PV cells are mounted. The system can be optimized for different combinations of diffuse and direct solar illumination conditions for particular geographical locations by controlling the concentration ratio and filtering properties of the holographic elements. In addition, the reflectivity of the back contact of the silicon cells is used to increase the optical path length and light trapping. This potentially allows the use of thin film silicon for the low bandgap PV cell material. The optical design combines the focusing properties of the parabolic concentrator and the holographic element to control the concentration ratio and uniformity of the spectral distribution at the high bandgap cell location. The presentation concludes with a comparison of different spectrum splitting holographic filter materials for this application.

Spectrum splitting is an approach to increasing the conversion efficiency of a photovoltaic (PV) system. Several methods can be used to perform this function which requires efficient spatial separation of different spectral bands of the incident solar radiation. In this paper several of holographic methods for implementing spectrum splitting are reviewed along with the benefits and disadvantages associated with each approach. The review indicates that a volume holographic lens has many advantages for spectrum splitting in terms of both power conversion efficiency and energy yield. A specific design for a volume holographic spectrum splitting lens is discussed for use with high bandgap InGaP and low bandgap silicon PV cells. The holographic lenses are modeled using rigorous coupled wave analysis, and the optical efficiency is evaluated using non-sequential raytracing. A proof-of-concept off-axis holographic lens is also recorded in dichromated gelatin film and the spectral diffraction efficiency of the hologram is measured with multiple laser sources across the diffracted spectral band. The experimental volume holographic lens (VHL) characteristics are compared to an ideal spectrum splitting filter in terms of power conversion efficiency and energy yield in environments with high direct normal incidence (DNI) illumination and high levels of diffuse illumination. The results show that the experimental VHL can achieve 62.5% of the ideal filter power conversion efficiency, 64.8% of the ideal filter DNI environment energy yield, and 57.7% of the ideal diffuse environment energy yield performance.