La sécurité de la cryptographie à clés publiques repose sur des problèmes mathématiques difficiles, notamment en théorie des nombres, tels que la factorisation pour RSA ou le logarithme discret pour ElGamal. Cependant les progrès des algorithmes rendent les protocoles basés sur des problèmes de théorie des nombres de moins en moins efficaces. De plus, l'arrivée de l'ordinateur quantique rendrait ces cryptosystèmes inutilisables. La cryptographie basée sur les codes en métrique rang est une alternative crédible pour concevoir des cryptosystèmes post-quantiques en raison de sa rapidité et de la faible taille de ses clés. Le but de cette thèse est d'étudier les problèmes difficiles en métrique rang et les algorithmes permettant de les résoudre, ainsi que de chercher de nouvelles attaques et de nouvelles primitives basées sur ces problèmes. / Security of public keys cryptography is based on difficult mathematic problems, especially in number field theory, such as the factorization for RSA or the discrete logarithm for ElGamal. However, algorithms are more and more efficient to solve these problems. Furthermore, quantum computers would be able to easily break these cryptosystems. Code-based cryptography in rank metric is a solid candidate to design new postquatum cryptosystems since it is fast and has low weight keysize. The goals of this thesis are to study hard problems in rank metric and algorithms which solve them, also to search for new attacks and new primitives based on these problems.

This thesis studies the problem of measuring freedom of choice. It analyzes the concept of freedom of choice, discusses conditions that a measure should satisfy, and introduces a new class of measures that uniquely satisfy ten proposed conditions. The study uses a decision-theoretical model to represent situations of choice and a metric space model to represent differences between options. The first part of the thesis analyzes the concept of freedom of choice. Different conceptions of freedom of choice are categorized into evaluative and non-evaluative, as well as preference-dependent and preference-independent kinds. The main focus is on the three conceptions of freedom of choice as cardinality of choice sets, representativeness of the universal set, and diversity of options, as well as the three conceptions of freedom of rational choice, freedom of eligible choice, and freedom of evaluated choice. The second part discusses the conceptions, together with conditions for a measure and a variety of measures proposed in the literature. The discussion mostly focuses on preference-independent conceptions of freedom of choice, in particular the diversity conception. Different conceptions of diversity are discussed, as well as properties that could affect diversity, such as the cardinality of options, the differences between the options, and the distribution of differences between the options. As a result, the diversity conception is accepted as the proper explication of the concept of freedom of choice. In addition, eight conditions for a measure are accepted. The conditions concern domain-insensitivity, strict monotonicity, no-choice situations, dominance of differences, evenness, symmetry, spread of options, and limited function growth. None of the previously proposed measures satisfy all of these conditions. The third part concerns the construction of a ratio-scale measure that satisfies the accepted conditions. Two conditions are added regarding scale-independence and function growth proportional to cardinality. Lastly, it is shown that only one class of measures satisfy all ten conditions, given an additional assumption that the measures should be analytic functions with non-zero partial derivatives with respect to some function of the differences. These measures are introduced as the Ratio root measures.

Research on the estimation of age at death, sex and stature from skeletal remains has received more attention than methods used to evaluate ancestry. While this may be due to the stigma attached to classifying people into groups, the application, interpretation and precision of non-metric methods used to predict ancestry need to be examined; as these variables are routinely applied to forensic case work in South Africa. The aim of this study was to score fifteen non-metric cranial traits, namely nasal bone structure, nasal breadth, nasal overgrowth, anterior nasal spine, inferior nasal margin, interorbital breadth, zygomaxillary suture shape, malar tubercle, alveolar prognathism, mandibular and palatine tori, shovelshaped incisors, Carabelli’s cusps and the transverse palatine suture shape on a South African sample, with the intent to assess the influence of sex, ancestry and age at death on these facial features. A total of 520 crania were obtained from the Pretoria Bone, Raymond A. Dart and Kirsten Collections in South Africa and included 237 (135 males, 102 females) Africans, 158 (94 males, 63 females) Europeans and 125 (87 males, 38 females) persons of Coloured origin. Data were analyzed using SPSS v.11.5 for Windows. Ordinal regression was used to evaluate the effect the independent variables (age, sex and ancestry) had on the dependent variable (non-metric traits). Results showed that all the variables were associated with ancestral differences among and within groups. Interorbital breadth, nasal bone structure, nasal breadth and shovel-shaped incisors exhibited statistically significant interactions with sex and ancestry, whereas the appearance of the anterior nasal spine, alveolar prognathism, incisor shovelling of the upper incisors, and Carabelli’s cusp morphology were correlated with age at death. If traditional classification methods are used, then these non-metric traits are not a valid prediction of ancestry in South African populations. Future research is to focus on several statistical approaches, including multi-variate analysis, for the classification of non-metric traits. Copyright / Dissertation (MSc)--University of Pretoria, 2010. / Anatomy / unrestricted

The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.

Type I noise storms constitute a sizeable fraction of the active-Sun component of solar radiation at meter wavelengths. The storms occur over a prolonged duration as intense, narrow-band spikes, superposed on a low-intensity broadband continuum, in the 30-400 MHz frequency range. Either component of the noise storm radiation has a very high degree of ordinary-mode circular polarization (~ 100 %), and is widely believed to be generated by the plasma emission mechanism. Existence of large sunspot groups or active region complexes, with a high degree of complexity and strength in the associated magnetic topology, have a remarkable spatio-temporal correlation to the occurance of noise storms. Hence type I noise storm events were employed as tracers in estimating the solar cycle activity, with specific relevance to resolving the mimimum-phase occuring between solar cycles 22 and 23, to a precise yet unique epoch of 1998 October,in consonance with the monthly average sunspot count and the 10.7 cm solar radio flux data. The latter have a proven close link with associated sunspot activity. Spatio-temporal correlation of energetic eruptive event termed Coronal Mass Ejection ( CME ), with the type I noise storm events has been convincingly established, from the point of view of ``Space Weather'' prediction. A particular aspect of this study has been the choice of limb-event CMEs as against the halo ones; this criterion has aided in an unambiguous position-angle determination for the eruption- site of the CMEs. Noise storms are found to be the precursors, temporally succeeded by the CME events over a time-scale of 1 to 14 hours. Large scale reconfiguration of the photospheric magnetic field topology, by way of reconnection, merging, cancellation or submergence, in the ambience of pre-existing lines of magnetic flux, triggered by the shearing and twisting motion of the footpoints, and leading to the sigmoid-to-arcade evolution of coronal magnetic loops, traces the event-specific linkage involving the type I noise storms and CMEs. Phenomena that occur at metric wavelengths in the solar corona, and vary on short time scales, are investigated, with the aid of a prototype, custom-built antenna-receiver system to the Gauribidanur RadioHeliograph ( GRH ). The GRH is a transit-mode instrument, while the time-delay control implemented on the prototype enables a radio source to be followed, as it traverses the sky at the sidereal rate. The delay-tracking scheme has been implemented on the front-end electronics, as this would eliminate the otherwise cumbersome task of mechanical-steering of the log-periodic dipole array, while also permitting radio observations over a significantly wider frequency band. The performance of the Gauribidanur Prototype Tracking System ( GPTS ) has been validated on the basis of exhaustive tests, in order to characterise its attenuation, phase, and pointing-accuracy, and optimised for solar observations at 77.5 MHz. Continuous Sun observation was performed with the GPTS, over a period from 24th of June, 2002 to 20th of August, 2002. The daily schedule involved solar observations at seven beam-positions on either side of the local meridian,spaced apart by ~ 9 deg., for about four hours each day. Absolute radio flux calibration was performed by following an identical observing schedule for the intense, unresolvable radio source Cygnus A. Periods of enhanced radio emission, corresponding to global rise in the solar radio radiation, were detected on several days. On each of those days of enhanced activity, the absolute deviation from the mean-flux, corresponding to the various beam-positions for that day, was determined. From this, the intra-day quasi-periodicity in solar radio flux was found to be 110 minutes, with the fluctuation in flux being 3 (+/- 1.5) sfu. Positional information from the Nancay (sic) Radioheliograph data, and features of the causative Active Regions of the underlying photospheric disk from the full-disk H-alpha images of the Big Bear Solar Observatory, along with the radio-spectral data published in the Solar Geophysical Data Reports led to conclusion that, heightened flux emission had been the result of the type I noise storms, known for their sharply defined directivity characteristics. The continuum component of type I noise storms is studied for variation in the frequency-dependent flux characteristics. Swept-frequency data from the Gauribidanur Radio Spectrograph, on 26th and 27th September 2000, in the 30-80 MHz band, were analyzed. The quiet-sun and burst components in the acquired data were excised-out. Absolute flux calibration was performed from spectral observations of Cygnus A in the same band. The spectral-index of the continuum was found to be ~ +3.7 . From a knowledge of the continuum source-size at various other spot frequency imaging observations, the source-size of the particular event was estimated, from interpolation and curve-fitting, to be 13.2 +/- 1.2 arcmin. From a knowledge of the continuum radio flux and its source-size, the brightness-temperature was found to vary from 1.07 x 1e7 to 1.96 x 1e7 K, in the 50 - 80 MHz band. Plasma emission is widely believed to bethe radiation mechanism for the continuum. The excitation of plasma waves by trapped, energetic electron beams moving along the coronal magnetic loops, and their coalescence with the low-frequency ion-acoustic waves or upper-hybrid waves excited due to shock-waves generated by magnetic reconnections above the active region complexes, at sites of coronal density inhomogeneities, are the cause for the noise storm radiation. From knowing the brightness-temperature in the source-region, the supra-thermal density in the electron-beam is estimated. Corroborative evidence, in the form of complementary observations for source-size, extent of the active region complexes, and the associated variations in strength and polarity of magnetic flux on the photosphere, the density enhancement over that of the tenuous coronal density, as per the Newkirk's model, above such active regions, the emission-measure, density, and brightness-temperature in the large-scale coronal loops interconnecting the trans-equatorial active regions in this case, in extreme uv and soft X Ray wavelengths, is applied to validate the assumptions, and estimations on various parameters involved in this plasma emission phenomenon. The burst component of type I noise storms is studied with the newly commissioned high temporal and spectral resolution spectrograph at the Gauribidanur Radio Observatory. The bursts reveal themselves as narrow-band, spiked events on the dynamic spectral records, and their occurance is of a stochastic nature. Isolated Type I bursts were chosen based on their bandwidth (2-2.5 MHz ), fractional-bandwidth ( 1.5 ), lifetime ( 1.5 seconds ), and their radio flux (~ 20-40 sfu ) distribution. The dynamic~- spectrum was calibrated from galactic background observations towards the direction of the North and the South Galactic poles. The flux calibration scheme is ideally suited for those radio telescopes capable of a low spatial resolution, wherein the predominant contribution to the system temperature arrives from the galactic background radiation. The frequency and time profiles of the bursts were analyzed on a case-by-case basis. The results of the study reveal that, a majority of the frequency profiles show a remarkable gaussian symmetrical distribution as compared to the less significant assymmetry in either the ascending or the descending limb ( which appear as enhanced tail-like features ) of the corresponding gaussians. This, in consonance with their narrow emission bandwidth, endorses the view that, the source region for Type I bursts are in a state of extreme homogeneity, as regards their plasma density and temperature. The time profiles on the other hand show a greater level of asymmetry on either their ascending or descending segments; deviations from the gaussian fit, to each of the bursts' time profiles, reveal a higher incidence in abrupt rise or fall on either of the limbs, to cases where the profiles conform to a symmetric gaussian. Since the rise and decay in the time profiles correspond to growth of plasma instabilities and damping of the plasma waves, respectively, they portray a region of the turbulent corona that is replete with magnetic reconnections contributing to the energetics of plasma waves.

The Metric Travelling Salesman Problem, henceforth metric TSP, is a fundamental problem in combinatorial optimization which consists of finding a minimum cost Hamiltonian cycle (also called a TSP tour) in a weighted complete graph in which the costs are metric. Metric TSP is known to belong to a class of problems called NP-hard even in the special case of graph-TSP, where the metric costs are based on a given graph. Thus, it is highly unlikely that efficient methods exist for solving large instances of these problems exactly. In this thesis, we develop a new heuristic for metric TSP based on extending ideas successfully used by Mömke and Svensson for the special case of graph-TSP to the more general case of metric TSP. We demonstrate the efficiency and usefulness of our heuristic through empirical testing. Additionally, we turn our attention to graph-TSP. For this special case of metric TSP, there has been much recent progress with regards to improvements on the cost of the solutions. We find the exact value of the ratio between the cost of the optimal TSP tour and the cost of the optimal subtour linear programming relaxation for small instances of graph-TSP, which was previously unknown. We also provide a simplified algorithm for special graph-TSP instances based on the subtour linear programming relaxation.

This diploma work concentrates on metrics for providers of IT support. Its origins are in a project for DHL IT Services. This company has recently moved centre of support for IT services serving to logistic giant DHL in EMEA region to Prague. The goal of the project was to find suitable metrics for measuring support requirements of IT services and productivity of people who provide the support. The objective of this paper is to introduce reasons for creation, principles, benefits, risks and experience from pilot implementation newly developed metric Support Point Analysis (SPA). To meet all objectives, the diploma was split into three integral parts. In the first part there are briefly summed general theoretical theses about metrics in IT, in the second part all aspects of the metrics Support Point Analysis were described in detail. In the last part there is analysis of possible areas of using SPA. There is also experience from pilot implementation in DHL IT Services write down in the last part. The main benefit of this paper consists in evaluation of SPA results and analysis of its strengths and weaknesses. Besides there are suggestions of possible ways of SPA further development.

Diploma work is focused on implementation Business Intelligence applications in medium software company in order to support Corporate Performance Management. It creates suitable metrics portfolio according to Balanced Scorecard methodology. Implementation part presents development of the reporting system on the Cognos 8 BI platform in the current software company environment. The system evaluates the metrics every month. Metrics values are based on current data in transactional system. Diploma work has two parts: theory and reporting project. Theoretical part deals with BI system architecture in general. It is focused on reporting issues. It analyses typical usage and expected benefits of BI applications used for Corporate Performance Management in order to specify applications that are suitable for implementation in the company environment. Next issue of the theoretical part deals with IS development methodology that can be used in Business Intelligence projects. According to chosen criteria and weights with regard to this project it evaluates the best methodology for this project. It will be used in the next part. Practical part reporting project is both about development issues and usage the BI application from the end user view. This example provides information about activities, which are necessary for this development from initial study to testing phase. Project scope includes analysis of the environment, analysis of used metrics, design new metrics, metrics selection and implementation on Cognos platform. This example presents analytical usage of the Metric Studio tool and dymamical reports usage from the manager's view. The final part brings together critical success factors (CSF), which appear in this project.

The diploma thesis deals with the analysis of the benefits of the information system of an important food manufacturer. The main aim is to analyse the benefits of the information system -- something which has yet to happen. The analysis of the information system should provide a recommendation for the company, which will include an evaluation of the strong and weak aspects of the system. Highlighting the strong and weak aspects should help the company perfect the system, provide a competitive advantage, increased profits and an improved company image. The secondary aim is to inform the reader about the system, understand its functionality, describe the metrics used for analysis and the choice of methods employed. The aims of the theoretical section will be achieved through analysis of internal documentation and electronic sources. The analysis of the benefits will be carried out using "historical" data obtained from the reporting system, database or internal documentation. The use of this work lies principally in its highlighting of the positive and negative effects of the system. The work can also help students or company employees understand the functionality of the real system and to broaden their current knowledge.

The diploma thesis is focused on creation of a controlling model, which follows the structure of a reference model for management of business informatics MBI. The model is being developed under the grant project at the Department of Information Technologies, at the University of Economics in Prague and cooperation with Czech Technical University in Prague. The theoretical part provides a brief introduction with the MBI model and the area of controlling. The practical part contains three main objectives. The first objective focuses on creating fundamental controlling objects in the MBI model. The second objective is to design metrics and dimensions, which provides the possibility to measure and view controlling from a different perspective. The third objective deals with the creation of an analytical application, which is used for tracking costs, expenses and effects of the controlling in company. The main contribution of this work is the created controlling model in the information basis MBI. Created objects serve companies as a starting points for implementation and operation of controlling. The model also enables watching and analyzing contributions and costs of controlling. Newly created objects are designed in a way that companies can use just some of them without the need of deployment the whole model.