386 research outputs found

    Neural-Kalman Schemes for Non-Stationary Channel Tracking and Learning

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    This Thesis focuses on channel tracking in Orthogonal Frequency-Division Multiplexing (OFDM), a widely-used method of data transmission in wireless communications, when abrupt changes occur in the channel. In highly mobile applications, new dynamics appear that might make channel tracking non-stationary, e.g. channels might vary with location, and location rapidly varies with time. Simple examples might be the di erent channel dynamics a train receiver faces when it is close to a station vs. crossing a bridge vs. entering a tunnel, or a car receiver in a route that grows more tra c-dense. Some of these dynamics can be modelled as channel taps dying or being reborn, and so tap birth-death detection is of the essence. In order to improve the quality of communications, we delved into mathematical methods to detect such abrupt changes in the channel, such as the mathematical areas of Sequential Analysis/ Abrupt Change Detection and Random Set Theory (RST), as well as the engineering advances in Neural Network schemes. This knowledge helped us nd a solution to the problem of abrupt change detection by informing and inspiring the creation of low-complexity implementations for real-world channel tracking. In particular, two such novel trackers were created: the Simpli- ed Maximum A Posteriori (SMAP) and the Neural-Network-switched Kalman Filtering (NNKF) schemes. The SMAP is a computationally inexpensive, threshold-based abrupt-change detector. It applies the three following heuristics for tap birth-death detection: a) detect death if the tap gain jumps into approximately zero (memoryless detection); b) detect death if the tap gain has slowly converged into approximately zero (memory detection); c) detect birth if the tap gain is far from zero. The precise parameters for these three simple rules can be approximated with simple theoretical derivations and then ne-tuned through extensive simulations. The status detector for each tap using only these three computationally inexpensive threshold comparisons achieves an error reduction matching that of a close-to-perfect path death/birth detection, as shown in simulations. This estimator was shown to greatly reduce channel tracking error in the target Signal-to-Noise Ratio (SNR) range at a very small computational cost, thus outperforming previously known systems. The underlying RST framework for the SMAP was then extended to combined death/birth and SNR detection when SNR is dynamical and may drift. We analyzed how di erent quasi-ideal SNR detectors a ect the SMAP-enhanced Kalman tracker's performance. Simulations showed SMAP is robust to SNR drift in simulations, although it was also shown to bene t from an accurate SNR detection. The core idea behind the second novel tracker, NNKFs, is similar to the SMAP, but now the tap birth/death detection will be performed via an arti cial neuronal network (NN). Simulations show that the proposed NNKF estimator provides extremely good performance, practically identical to a detector with 100% accuracy. These proposed Neural-Kalman schemes can work as novel trackers for multipath channels, since they are robust to wide variations in the probabilities of tap birth and death. Such robustness suggests a single, low-complexity NNKF could be reusable over di erent tap indices and communication environments. Furthermore, a di erent kind of abrupt change was proposed and analyzed: energy shifts from one channel tap to adjacent taps (partial tap lateral hops). This Thesis also discusses how to model, detect and track such changes, providing a geometric justi cation for this and additional non-stationary dynamics in vehicular situations, such as road scenarios where re ections on trucks and vans are involved, or the visual appearance/disappearance of drone swarms. An extensive literature review of empirically-backed abrupt-change dynamics in channel modelling/measuring campaigns is included. For this generalized framework of abrupt channel changes that includes partial tap lateral hopping, a neural detector for lateral hops with large energy transfers is introduced. Simulation results suggest the proposed NN architecture might be a feasible lateral hop detector, suitable for integration in NNKF schemes. Finally, the newly found understanding of abrupt changes and the interactions between Kalman lters and neural networks is leveraged to analyze the neural consequences of abrupt changes and brie y sketch a novel, abrupt-change-derived stochastic model for neural intelligence, extract some neuro nancial consequences of unstereotyped abrupt dynamics, and propose a new portfolio-building mechanism in nance: Highly Leveraged Abrupt Bets Against Failing Experts (HLABAFEOs). Some communication-engineering-relevant topics, such as a Bayesian stochastic stereotyper for hopping Linear Gauss-Markov (LGM) models, are discussed in the process. The forecasting problem in the presence of expert disagreements is illustrated with a hopping LGM model and a novel structure for a Bayesian stereotyper is introduced that might eventually solve such problems through bio-inspired, neuroscienti cally-backed mechanisms, like dreaming and surprise (biological Neural-Kalman). A generalized framework for abrupt changes and expert disagreements was introduced with the novel concept of Neural-Kalman Phenomena. This Thesis suggests mathematical (Neural-Kalman Problem Category Conjecture), neuro-evolutionary and social reasons why Neural-Kalman Phenomena might exist and found signi cant evidence for their existence in the areas of neuroscience and nance. Apart from providing speci c examples, practical guidelines and historical (out)performance for some HLABAFEO investing portfolios, this multidisciplinary research suggests that a Neural- Kalman architecture for ever granular stereotyping providing a practical solution for continual learning in the presence of unstereotyped abrupt dynamics would be extremely useful in communications and other continual learning tasks.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Luis Castedo Ribas.- Secretaria: Ana García Armada.- Vocal: José Antonio Portilla Figuera

    A Construction of Asymptotically Optimal Cascaded CDC Schemes via Combinatorial Designs

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    A coded distributed computing (CDC) system aims to reduce the communication load in the MapReduce framework. Such a system has KK nodes, NN input files, and QQ Reduce functions. Each input file is mapped by rr nodes and each Reduce function is computed by ss nodes. The objective is to achieve the maximum multicast gain. There are known CDC schemes that achieve optimal communication load. In some prominent known schemes, however, NN and QQ grow too fast in terms of KK, greatly reducing their gains in practical scenarios. To mitigate the situation, some asymptotically optimal cascaded CDC schemes with r=sr=s have been proposed by using symmetric designs. In this paper, we put forward new asymptotically optimal cascaded CDC schemes with r=sr=s by using 11-designs. Compared with earlier schemes from symmetric designs, ours have much smaller computation loads while keeping the other relevant parameters the same. We also obtain new asymptotically optimal cascaded CDC schemes with more flexible parameters compared with previously best-performing schemes

    Coded Caching Schemes for Multiaccess Topologies via Combinatorial Design

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    This paper studies a multiaccess coded caching (MACC) where the connectivity topology between the users and the caches can be described by a class of combinatorial designs. Our model includes as special cases several MACC topologies considered in previous works. The considered MACC network includes a server containing NN files, Γ\Gamma cache nodes and KK cacheless users, where each user can access LL cache nodes. The server is connected to the users via an error-free shared link, while the users can retrieve the cache content of the connected cache-nodes while the users can directly access the content in their connected cache-nodes. Our goal is to minimise the worst-case transmission load on the shared link in the delivery phase. The main limitation of the existing MACC works is that only some specific access topologies are considered, and thus the number of users KK should be either linear or exponential to Γ\Gamma. We overcome this limitation by formulating a new access topology derived from two classical combinatorial structures, referred to as the tt-design and the tt-group divisible design. In these topologies, KK scales linearly, polynomially, or even exponentially with Γ\Gamma. By leveraging the properties of the considered combinatorial structures, we propose two classes of coded caching schemes for a flexible number of users, where the number of users can scale linearly, polynomially or exponentially with the number of cache nodes. In addition, our schemes can unify most schemes for the shared link network and unify many schemes for the multi-access network except for the cyclic wrap-around topology.Comment: 48 page

    Row-column factorial designs and mutually orthogonal frequency rectangles

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    A (full) qᵏ factorial design with replication λ is the multi-set containing all possible q-ary sequences of length k, each occurring exactly λ times. An m × n row-column factorial design is any arrangement of λ replicates of the qᵏ factorial design in an m × n array. We say that the design has strength t if each row and column is an orthogonal array of strength t. We denote such a design by Iₖ (m,n,q,t). A frequency rectangle of type FR(m,n;q) is an m × n array based on a symbol set S of size q, such that each element of S appears exactly n/q times in each row and m/q times in each column. Two frequency rectangles of the same type are said to be orthogonal if each possible pair of symbols appears the same number of times when the two arrays are superimposed. By k–MOFR(m,n;q) we mean a set of k frequency rectangles of type FR(m,n;q) in which every pair is orthogonal. In Chapter 4, we give the necessary and sufficient conditions when a row-column factorial design of strength 1 exists. We show that an array of type Iₖ (m,n,q,1) exists if and only if (a) q|m, q|n and qᵏ|mn; (b) (k,q,m,n) ≠ (2,6,6,6) and (c) if (k,q,m) = (2,2,2) then 4 divides n. In Chapter 5, we discuss designs of strength 2 and above. We solve the case completely when t = 2 and q is a prime power: we show that there exists an array of type Iₖ(qᴹ,qᴺ,q,2) if and only if k ≤ M + N, k ≤ (qᴹ - 1)/(q - 1) and (k,M,q) ≠ (3,2,2). We also show that Iₖ+α(2αb,2ᵏ,2,2) exists whenever α ≥ 2 and 2α + α + 1 ≤ k < 2αb - α, assuming there exists a Hadamard matrix of order 4b. For strength 3 we restrict ourselves to the binary case, solving it completely when q is a power of 2. In Chapter 6, our focus is on mutually orthogonal frequency rectangles (MOFR). We use orthogonal arrays and Hadamard matrices to construct sets of MOFR. We also describe a new form of orthogonality for a set of frequency rectangles. We say that a k–MOFR(m,n;q) is t–orthogonal if each subset of size t, when superimposed, forms a qᵗ factorial design with replication mn/qᵗ. A set of vectors over a finite field is said to be t-independent if each subset of size t is linearly independent. We describe a relationship between a set of t–orthogonal MOFR and a set of t-independent vectors. We use known results from coding theory and related literature to formulate a table for the size of a set of t-independent vectors of length N ≤ 16, over F₂. We also describe a method to construct a set of (p - 1)–MOFR(2p,2p;2) where p is an odd prime, improving known lower bounds for all p ≥ 19

    Recommendations for consumer-centric products and efficient market design

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    Flexibility involves the adjustment of energy consumption or generation schedules to benefit the grid, for instance, providing services such as balancing, congestion management, and voltage control. Flexibility can be offered at different grid levels by flexibility service providers (FSPs) through market mechanisms. This study, produced in the context of the Horizon 2020 OneNet project, evaluates various TSO-DSO coordinated flexibility market models. In this assessment, the study considers factors like economic efficiency, consumer-centricity, existence of entry barriers, and value-stacking potential. The analysis highlights the importance of interface flow pricing and FSPs' bidding behaviour. The creation of local market layers can reduce entry barriers but may lead to market fragmentation. The study also explores bid forwarding mechanisms and methods to ensure grid safety. Overall, the work offers valuable insights for designing efficient and coordinated flexibility markets in Europe.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 957739

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    Not AvailableIntegrated farming system (IFS) approach is a powerful tool for ensuring the livelihood security of small and mar-ginal farmers. The precision of IFS experiments can be enhanced using statistical and computational tools. Two-part designs are helpful in selecting the best possible components in IFS. They involve two groups of treatment arranged in incomplete blocks with respect to both groups, and the concurrence of treatment pairs within and between groups is constant. The fusion of two in-complete block designs in a systematic manner can yield two-part designs. Further, for situations where certain experimental units are not available, two-part structurally incomplete designs are proposed.Not Availabl

    THE AFAR-ISSA/SOMALI CONFLICT IN EASTERN ETHIOPIA AND DJIBOUTI: A CASE STUDY OF AN INTRACTABLE CONFLICT AND THE ENSUING CHALLENGES OF CONFLICT RESOLUTION IN THE HORN OF AFRICA

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    Der Afar-Issa/Somali-Konflikt ist ein schwer lösbarer Konflikt am Horn von Afrika. Der Konflikt dauert seit mehr als einem Jahrhundert an. Er ist extrem gewalttätig und fordert viele unschuldige Menschenleben. Beide Seiten sind der Meinung, dass er nicht friedlich gelöst werden kann, da er mit hohen psychologischen, militärischen und wirtschaftlichen Investitionen verbunden ist, die von beiden Parteien als wesentliches und grundlegendes Ziel für ihr Überleben als Gemeinschaft angesehen werden. Bei allen Versuchen, den Konflikt zu lösen, wurden nie Kompromisse oder Zugeständnisse in Erwägung gezogen. Der Konflikt ist insofern von zentraler Bedeutung, als sowohl die Afar- als auch die Issa/Somali-Gemeinschaften einschließlich ihrer Diaspora ständig und kontinuierlich in den Konflikt verwickelt sind. Der Konflikt zeichnet sich auch durch seine Komplexität aus, die eine transnationale Dimension hat, die politische Akteure an den Grenzen von Äthiopien, Dschibuti, Eretria und Somalia/Somaliland einbezieht, sowie durch die Vielfalt der beteiligten Akteure, einschließlich der Diaspora und anderer internationaler Akteure. Verschiedene Wissenschaftler haben den Konflikt aus verschiedenen Blickwinkeln erklärt: Der Wettbewerb um knappe pastorale Ressourcen ist das vorherrschende Interpretationsschema; ein Ressourcenkonflikt zwischen zwei benachbarten pastoralen Gruppen um Wasser und Weideland (Ali 1997; Markakis 2003); andere Studien erklären den Konflikt aus einer geopolitischen Perspektive (Mu'uz 2009; Yasin 2011). Der Afar-Issa/Somali-Konflikt wird auch mit wirtschaftlichen Aspekten erklärt, insbesondere mit dem Wettbewerb um den Schmuggelhandel und die Handelsrouten (Markakis 2003; Menbere 2013). Andere Wissenschaftler erklären den Konflikt als einen Territorialkonflikt, der durch das ethnische Design der äthiopischen und dschibutischen (nicht direkt ethnischen) Föderationen, die seit 1992 eingerichtet wurden, noch verschärft wird (Asnake 2009). Obwohl all diese Studien ein gewisses Licht auf die Natur des Afar-Issa/Somali-Konflikts geworfen haben, wurde er in keiner von ihnen als unlösbarer Konflikt betrachtet. Unter Berücksichtigung der Langlebigkeit und Komplexität des Konflikts und unter Rückgriff auf den sozialpsychologischen Analyserahmen für die Untersuchung hartnäckiger Konflikte (Northrup & Thorson, 1989; Kriesberg 1995; Bar-Tal, 2013) wurde der Afar-Issa/Somali-Konflikt in der Studie als eine Art hartnäckiger Konflikt betrachtet. Mit dem Schwerpunkt auf seiner Hartnäckigkeit analysierte die Studie die sozialpsychologischen Grundlagen des Afar- und Issa/Somali-Konflikts, insbesondere die kollektiven Erinnerungen (sowohl populär als auch offiziell), kollektive emotionale Orientierungen und das Ethos der Afar-Issa/Somlai. Darüber hinaus analysierte die Studie, wer die regionalen Akteure sind und warum viele Konfliktlösungsversuche gescheitert sind, um den hartnäckigen Konflikt zwischen Afar und Issa/Somali zu lösen, und argumentierte, dass der konstruktivistische Ansatz für seine Lösung geeignet ist. Konkret wurden in der Studie unter Berücksichtigung der Langlebigkeit und Komplexität des Konflikts und unter Rückgriff auf den sozialpsychologischen Analyserahmen für die Untersuchung hartnäckiger Konflikte die Ursachen, Akteure und Ereignisse des Afar-Issa/Somali-Konflikts als eine Art hartnäckiger Konflikt analysiert. Dabei stützt sich die Studie auf den sozialpsychologischen Analyserahmen von Daniel Bar-Tal (2013) für die Untersuchung hartnäckiger Konflikte, der das kollektive Gedächtnis der Konfliktparteien, das Konfliktethos und die kollektive emotionale Orientierung der Afar- und Issa/Somali-Bevölkerung an dem Konflikt untersucht. Dabei wurden die folgenden grundlegenden Fragen untersucht: Was sind die eigentlichen Ursachen des Afar-Issa/Somali-Konflikts? Wer sind die Akteure, die behaupten, die Ansichten und Interessen der Afar und Issa/Somali zu vertreten? Welche Rolle spielen die externen Akteure in dem Konflikt? Wie hat sich der Charakter des Konflikts im Laufe der Zeit verändert? Wie nehmen die Afar und die Issa/Somali die Konfliktsituation wahr und wie definieren sie sie? Werden die strittigen Fragen in existenziellen Begriffen formuliert, etwa mit Bezug auf Identität und Geschichte? Was macht den Afar-Issa/Somali-Konflikt unlösbar? Welches sind die offiziellen und kollektiven Erinnerungen, das Konfliktethos und die kollektive emotionale Ausrichtung des Konflikts? Welches sind die wichtigsten gesellschaftlichen Überzeugungen: gesellschaftliche Ziele, Selbstbilder, Mythen, kollektive Erinnerungen, Normen und Gruppenbilder bei den Afar und den Issa/Somali, die für die Bewältigung des hartnäckigen Konflikts funktional sind und ideologische Rechtfertigungen für die Fortsetzung des Konflikts liefern? Welches sind die wichtigsten regionalen Akteure des unlösbaren Konflikts zwischen Afar und Issa/Somali? Was ist ihr Engagement in dem Konflikt? Was sind ihre Bedürfnisse? Welche Rolle haben diese regionalen Akteure in dem hartnäckigen Konflikt zwischen den Afar und den Issa/Somali gespielt? Was sind die Bedingungen der verschiedenen Konfliktlösungsinterventionen durch staatliche und nichtstaatliche Akteure? Warum sind die verschiedenen Konfliktlösungsmaßnahmen gescheitert? Welche Aussichten gibt es, den Afar-Issa/Somali-Konflikt zu transformieren? Welches Modell der Konfliktlösung und -transformation ist das geeignetere? Das Forschungsdesign für diese Studie ist ein qualitativer Untersuchungsansatz, der explorative und erklärende Forschungstypen kombiniert und eine Fallstudie verwendet. In Bezug auf die Untersuchung kombiniert die Studie deskriptive und erklärende Ansätze. Beim deskriptiven Untersuchungsansatz beschreibt die Studie die Phänomene, wie sie existieren. Beim erklärenden Untersuchungsansatz geht die Studie über die bloße Beschreibung der Merkmale hinaus, um zu analysieren und zu erklären, warum oder wie die Fälle im hartnäckigen Afar-Issa/Somali-Konflikt entstanden sind. Was den Forschungsansatz betrifft, so wurde in der Studie eine Fallstudie verwendet, und zwar eine Mehrfach-Fallstudie. Da sich die Konfliktdynamik der Afar und der Issa/Somali innerhalb und außerhalb der Gruppe herausgebildet und kristallisiert hat, wurde ein qualitativer, eingebetteter Ansatz mit mehreren Fallstudien unter Verwendung von Interviews mit Schlüsselinformanten, Fokusgruppendiskussionen und Dokumentenanalyse als Datenquelle verwendet. Um die erforderlichen Daten zu erhalten, bediente sich der Forscher einer Reihe von Datenerhebungsmethoden: Befragung von Schlüsselinformanten, Fokusgruppendiskussionen (FGD), Regierungsarchive für offizielle Aufzeichnungen und Überprüfung von Sekundärquellen, um die erforderlichen Daten zu erhalten.:Acknowledgement Acronym and Glossary List of Figures, Maps and Official Memories Abstract and Keywords Chapter One: Introduction and Background of the Study 1.1. Introduction 1.2. The Research Problem 1.3. Objective of the Research 1.4. Research Questions 1.5. Research Design and Methodology 1.5.1. Data Collection Method 1.5.2. Sampling Process 1.5.3. Data Analysis 1.6. Significance of the Study 1.7. Limitation and Problems Encountered 1.8. Structure of the Study Chapter Two: Literature Review of Concepts and Topical Issues 2.1. Introduction 2.2. Conceptual Framework 2.2.1. Definition, Type and Nature of Conflict 2.2.2. The Concept of Intractability and Intractable Conflict 2.2.3. Characteristics of Intractable Conflicts 2.2.4. Challenges of Intractable Conflicts: Why different, why difficult to resolve? 2.3. Theoretical Framework of Intractable Conflicts 2.3.1. Socio-psychological Foundations of Intractable Conflicts 2.3.2. Conflict Resolution Theories: Are they Fit to Resolve Intractable Conflicts? 2.3.3. From Intractable Conflict to its Resolution 2.3.4. A Constructivist Approach for Intractable Conflict - Conclusion Chapter Three: The Land, Peoples and the Socio-Political Dynamics of the Afar and Issa/Somali 3.1. Introduction 3.2. The Land and Peoples of the Study Area 3.3. The Afar and the Issa/Somali Peoples 3.3.1. The Afar People in Ethiopia, Djibouti and Eritrea 3.3.2. The Issa/Somali People in Ethiopia, Djibouti and Somalia - Conclusion Chapter Four: Intricacies of the Afar-Issa/Somali Intractable Conflict 4.1. Introduction 4.2. Historical Background of the Afar-Issa/Somali Conflict 4.2.1. Historical Background of the Afar-Issa/Somali Conflict in Ethiopia 4.2.2. Historical Background of the Afar-Issa/Somali Conflict in Djibouti 4.3. Causes of Afar-Issa/Somali Intractable Conflict 4.3.1. Causes of the Afar-Issa/Somali Intractable Conflict in Ethiopia 4.3.2. Causes of the Afar-Issa/Somali Intractable Conflict in Djibouti - Conclusion Chapter Five: Social-Psychological Foundations of the Afar-Issa/Somali Intractable Conflict 5.1 Introduction 5.2. Collective Memories of the Afar and the Issa/Somali Intractable Conflict 5.2.1. The Popular Collective Memories of the Intractable Conflict 5.2.2. The Official Collective Memories of the Conflict 5.3. The Social Belief of the Afar-Issa/Somali Intractable Conflict 5.4. Collective Emotional Orientations of the Afar-Issa/Somali Intractable Conflict Conclusion Chapter Six: The Geopolitics of the Horn of Africa and the Intractability of the Afar-Issa/Somali Conflict 6.1. Introduction 6.2. Regional Dynamics of the Afar-Issa/Somali Intractable Conflict 6.3. The Geo-Politics of the Horn of Africa: The Pre, During and Post-colonial Periods 6.3.1. The Pre-Colonial Period of the Horn of Africa 6.3.2. Colonialism in the Horn of Africa and the Afar-Issa/Somali Intractable Conflict 6.3.3. The End of the Colonial Era and Its Impact on the Afar-Issa/Somali Intractable Conflict 6.3.4. The Post-Colonial Reconfiguration of the Horn and its Impact on the Afar-Issa/Somali Intractable Conflict 6.4. Regional Actors and the Afar-Issa/Somali Intractable Conflict 6.4.1. Government of Ethiopia 6.4.2. Government of Djibouti 6.4.3. Government of Eritrea 6.5. Regional Wars and the Afar-Issa/Somali Intractable Conflict 6.5.1. Ethiopia-Somalia Wars 6.5.2. Ethiopia-Eritrea War 6.5.3. Djibouti-Eritrea War 6.5.4. Somalis Internal Instability and Long Time Statelessness 6.5.5. The Afar Nationalism: Movement for Unified Afar Triangle 6.5.6. Three Countries, One Customary Leader: The Influence of the Issa/Somali Ugas 6.6. The Afar and the Issa/Somali Diaspora and its Engagement in the Intractable Conflict 6.6.1. The Afar Diaspora and the Intractable Conflict 6.6.2. The Issa/Somali Diaspora and the Intractable Conflict - Conclusion Chapter Seven: Conflict Resolution Attempts of the Afar-Issa/Somali Intractable Conflict 7.2. Customary Conflict Resolution Attempts of the Conflict 7.3. Governmental Conflict Resolution Attempts 7.3.1. Government of Ethiopia’s Conflict Resolution Attempts 7.3.2. The Attempt by the Government of Djibouti to resolve the Afar-Issa Intractable conflict 7.4. Non-Governmental Organizations Attempt of Conflict Resolution of the Afar and Issa/Somali 7.5. The Afar and Issa/Somali Diaspora Contributing for Peace 7.6. Constructivist Approach for Afar – Issa/Somali Intractable Conflict Resolution Chapter Eight: Summary and Conclusion 8.1. Introduction 8.2. Summary of Major Findings of the Study 8.3. Conclusion of Major Findings of the Study 8.4. Suggestions for Future Research Bibliography Annexes Annex I. List of Primary Sources Annex II. Information Sheet for Interview Participants Annex III. Consent Form for Interview Participants Declaratio

    ε\varepsilon-Almost collision-flat universal hash functions and mosaics of designs

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    We introduce, motivate and study ε\varepsilon-almost collision-flat (ACFU) universal hash functions f:X×SAf:\mathcal X\times\mathcal S\to\mathcal A. Their main property is that the number of collisions in any given value is bounded. Each ε\varepsilon-ACFU hash function is an ε\varepsilon-almost universal (AU) hash function, and every ε\varepsilon-almost strongly universal (ASU) hash function is an ε\varepsilon-ACFU hash function. We study how the size of the seed set S\mathcal S depends on ε,X\varepsilon,|\mathcal X| and A|\mathcal A|. Depending on how these parameters are interrelated, seed-minimizing ACFU hash functions are equivalent to mosaics of balanced incomplete block designs (BIBDs) or to duals of mosaics of quasi-symmetric block designs; in a third case, mosaics of transversal designs and nets yield seed-optimal ACFU hash functions, but a full characterization is missing. By either extending S\mathcal S or X\mathcal X, it is possible to obtain an ε\varepsilon-ACFU hash function from an ε\varepsilon-AU hash function or an ε\varepsilon-ASU hash function, generalizing the construction of mosaics of designs from a given resolvable design (Gnilke, Greferath, Pav{\v c}evi\'c, Des. Codes Cryptogr. 86(1)). The concatenation of an ASU and an ACFU hash function again yields an ACFU hash function. Finally, we motivate ACFU hash functions by their applicability in privacy amplification

    Doubly even self-orthogonal codes from quasi-symmetric designs

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    In this paper, we give a construction of doubly even self-orthogonal codes from quasi-symmetric designs. Further, we study orbit matrices of quasi-symmetric designs and give a construction of doubly even self-orthogonal codes from orbit matrices of quasi-symmetric designs of Blokhuis-Haemers type.Comment: 13 page

    Temperature Programming of the Second Dimension in Comprehensive Two-Dimensional Gas Chromatography (GC×GC)

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    Comprehensive two-dimensional gas chromatography (GC×GC) is a mature separation technique that is now over three decades old. It separates all sample components using two GC columns with different selectivities, connected in series through a special interface called a modulator to provide two dimensions of separation. Early research and development of this technique focused on the modulator, the most critical component in a GC×GC system. The modulator facilitates the collection and transfer of effluent from the first dimension (¹D) to the second dimension (²D) column. As the modulator development matured with various designs being commercialized, research focus shifted towards chemometrics and applications. However, a fundamental issue that has not been resolved thus far in GC×GC is the general elution problem in ²D due to the nearly isothermal conditions in this dimension during a single separation. This thesis details the development, testing, and application of a ²D temperature programming system for GC×GC to overcome this problem. Every stage of development for the ²D temperature programming system is described, from the proof-of-concept to the final design. The proof-of-concept system in Chapter 2 focused on the heating and cooling aspects of ²D temperature programming. It featured a ballistic heating system that synchronized the heating and cooling of the ²D column to the modulation period. Although the final temperature offset could be pre-calibrated, the system did not feature any real temperature control. Despite its simplicity, ballistic heating eliminated wraparound peaks while maintaining the separation of weakly retained compounds in the ²D. The first prototype of a true ²D temperature programming system, detailed in Chapter 3, featured an Arduino microcontroller for PID temperature control. The temperature difference between the ²D column and the GC oven was measured directly using two thermocouples connected differentially. Although ²D temperature programming with the prototype improved the peak capacity by 48 %, the fragility of the thermocouple attachment was an issue for commercial designs. The final version of the ²D temperature programming system (²DTPS), described in Chapter 4, tackled the robustness and user-friendliness of the system, building upon the core functions from the prior designs. The temperature measurement system was completely redesigned to determine the ²D column temperature based on the ²D column electrical resistance. The column connections and column cage were also redesigned to incorporate longer ²D columns and provide a more secure connection to the column for heating and resistance measurement. A real time clock and remote port were also added to allow the ²DTPS to be a completely standalone device for any GC×GC system. A Windows Forms application was written to control and monitor the ²DTPS. System compatibility was tested with both thermal and flow modulators, as well as a flame ionization detector (FID) and time-of-flight mass spectrometer (TOFMS). Finally, the ²DTPS was applied to the characterization of renewable hydrocarbon samples from a local Ontario company in Chapter 5. Samples from various points in the production process were characterized to help with product development. The GC×GC separation with the ²DTPS was optimized with both a normal and a reverse column set, as well as two detectors, an FID and a TOFMS. The ²DTPS improved the signal-to-noise ratio and peak capacity for the characterization of the samples
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