In his paper, Conway presents his remarkable findings, leaving the task of careful examination and verification to us. He unveils a special link between the extraFib series and the Empire State Building, and reveals an unexpected relationship between Fibonacci numbers, Lucas numbers, and trigonometric formulas. This fresh concept, labeled "Fibonometry," underscores the potential connections between diverse mathematical concepts. As we engage with this paper, we take on the responsibility of exploring and confirming these intriguing mathematical relationships.

Dit onderzoek gaat over de mogelijkheden en onmogelijkheden met betrekking tot constructies met passer en ongemarkeerde liniaal. Hier werken we met de euclidische meetkunde en zullen we dus ook beginnen met de vijf postulaten van Euclides en een aantal toepassingen ervan. Er zal besproken worden wat het betekent voor een punt of constructie om construeerbaar te zijn, hiervoor zal gedefinieerd moeten worden wat het betekent voor een getal om construeerbaar te zijn. Vervolgens komen de volgende meetkundige problemen aan bod: de driedeling van een hoek, de verdubbeling van een kubus, de kwadratuur van een cirkel en de construeerbaarheid van regelmatige veelhoeken. Om te laten zien wat wel en niet mogelijk is wordt er gebruik gemaakt van moderne algebra, zo kan een constructie probleem omgeschreven worden naar een concreet algebraïsch probleem. Hiervoor maken we gebruik van de theorie rondom lichaamsuitbreidingen en de Galois theorie.

In recent years, the large increase in connected devices and the data that is collected by these devices has caused a heightened interest in distributed processing. Many practical distributed networks are of heterogeneous nature. Because of this, algorithms operating within these networks need to be simple, robust against network dynamics and resource efficient. Additionally, if privacy preservation methods are properly implemented, they add to the power of distributed processing by making it possible to leverage the data of many different users, without infringing the privacy of the individuals involved.
In this study we focus on the primal-dual method of multipliers (PDMM), which is a promising dis- tributed optimisation algorithm that seems to be suitable for distributed optimisation in heterogeneous networks. Most theoretical work that can be found in existing literature focuses on synchronous ver- sions of PDMM. However, in heterogeneous networks, asynchronous algorithms are favourable over synchronous algorithms. So far, simulation results have indicated that asynchronous PDMM converges and can even converge in the presence of transmission losses.
In this work we analyse the properties of stochastic PDMM, which is a general framework that can model variations of PDMM such as asynchronous PDMM and PDMM with transmission losses. We build upon previous empirical results of PDMM and formulate theoretical proofs to substantiate these results. After defining stochastic PDMM and proving its convergence, we compare a number of PDMM variations that have been mentioned throughout the literature. Lastly, we derive a lower bound for the variance of the auxiliary variable in the context of stochastic PDMM, assuming uniform updating probabilities. This lower bound indicates that subspace based privacy preservation is applicable to certain instances of stochastic PDMM, like asynchronous PDMM.
The main result of this work is a theoretical proof that shows that stochastic PDMM converges almost surely if the updating probabilities of each auxiliary variable are nonzero. Two important conclusions that follow from this proof are the almost sure convergence of asynchronous PDMM and unicast PDMM with transmission losses. Another useful result is the fact that subspace based privacy preservation is effective when using asynchronous PDMM.

Code-Based Cryptography is a branch of the Post-Quantum Cryptography research area. As such, its focus is on developing algorithms that can be used in the current communication systems to secure them against an adversary powered in the (near) future by a quantum computer. A code-based type cryptosystem is a public key cryptosystem that is resistant or slightly reduces its security level against attacks by the known quantum algorithms. The biggest drawback of this otherwise secure cryptosystem is its large public key. This thesis considers a specific type of linear codes, large minimum distance self-dual codes, and punctured codes derived from them that can provide the same security level as the original McEliece system with approximately a 30% smaller public key. Estimation of the bit security level of a cryptosystem using a small example of such a code for its private key confirms that increasing the minimum weight of the code significantly reduces the public key size of the system. Further, we determine the parameters of putative self-dual codes with a large minimum weight providing classical bit security of 80, 128 and 256 bits (quantum 67, 101, and 183 bits), respectively. For the parameters corresponding to the classical 80 bits security of the McEliece Cryptosystem, a particular example of a binary high minimum distance self-dual code is constructed. It is the first code of its type and length. A punctured code of this example is used for the private key of the McEliece cryptosystem. A new decoding algorithm is introduced, which is suitable for the specific construction of the new self-dual code. Moreover, we present a decryption strategy that decodes the complete code instead of the punctured private key. All this results in a McEliece type cryptosystem with 80 bits security classical (68 bits quantum) and reduced public key size of around 38.5% compared to the original system. Reducing the key size makes the quantum safe McEliece Cryptosystem more attractive for practical use.

In 1977 the RSA system was designed by Ron Rivest, Adi Shamir and Len Adleman. The RSA system is a part of modern cryptography. Modern cryptography makes sure that one can secure important information - like data, communication or banking accounts - on the computer. There are several attacks on the RSA system where the private key can be cracked. In this report two of such attacks are discussed.

Climate change challenges the resiliency of our cities, and lack of spaces in densely paved areas makes it impossible to implement adaptation and mitigation strategies on the street level. However, buildings have often unused roofs, which can be converted into sustainable roofing options. Green roofs are systems which allow for the growth of different types of vegetation, mitigating heat and capturing water. Blue roofs are layers for water collection, which provide temporary storage and slow release of rainwater. Yellow roof is another name to indicate roofs with photovoltaic (PV) panels. Some areas of the city may be more subject to flooding and heat. Some buildings may instead receive more solar radiation. Therefore, prioritizing which option to install where may be the key to the success of sustainable roofing placement. In this study, we construct an optimization model that evaluates the benefits of the roofing option in each potential location and chooses the combination of roofs and roofing options which maximizes the total societal benefits. The reduction of flooding and heat risks and the production of clean energy are modeled considering both climate variables and the city’s characteristics. However, the derived data and parameters are uncertain by nature. Climate data is used in ensembles and is integrated into the problem by formulating the model into a stochastic and robust version. We take Schiedam as our case study area and solve the model. We also perform uncertainty analysis, making use of clustering and classification tree regression. This analysis allows to understand which parameters are driving which type of solutions, and to understand how robust the constructed model is. Moreover, we formulate the same problem in the shape of a multi-time step model, where the decision maker can make the optimal placement decision every year. In this case, it is possible to simplify the decision process into a one-branch tree for which we present a methodology. The results show that our model is robust in terms of placement choice when parameters change, and we discover which parameters drive the main variations. The total benefits are instead much more reliant on the uncertainty of the problem.

In this thesis, we design and assess a multi-slice resource allocation framework that is based on machine learning techniques (subset of artificial intelligence techniques). The proposed framework employs two machine learning techniques namely, artificial neural networks and reinforcement learning for resource management in sliced RAN. Alternative multi-slice resource allocation methods that involve only artificial neural networks but not reinforcement learning are also defined.

LoRaWAN is amongst the most prominent LPWAN (Low Power Wide Area Networking) technologies and provides an operation mode, called Class B, where devices can be reached with limited latency. One of the most important features of LoRaWAN Class B is multicast, which allows a single transmission to be shared by multiple multicast group member end-devices. This enables key IoT functionalities such as FOTA (Firmware Over The Air) and other applications that need to transfer multiple packets to a set
of end-devices. This thesis will delve into LoRaWAN Class B multicast and study its scalability -- the most important behavior to study in all IoT technologies. An ns-3 module for LoRaWAN Class B multicast has been extended and used for in-depth analysis and drawing scalability insights. The study also explores methods to improve performance as well as enhance scalability.

Ubiquitous connectivity requirements and stringent quality-of-services (QoS)
in recent wireless communications demand new revolutionary wireless network
technologies to support the exponentially increasing traffic growth.
Massive multiple-input-multiple-output (MIMO) with the capability of high
spectral efficiency achieved by large multiplexing and diversity gains grabbed
a lot of attention as a promising solution for future cellular networks. Achieving
ultra-reliable and low latency communication is very challenging without
increasing the network infrastructure cost, or extra processing complexity.
Adapting space-time-block-codes (STBC) can improve the reliability of
the system, but this increases the downlink pilot overhead. Two precoders
are devised to exploit full spatial diversity with the blind combining process
to avoid downlink pilot overhead.

In a military environment, tactical networks enable information sharing between all the different entities in the field. In this environment, multiple groups of people from different organizations, and with different goals and policies have to share information. The information has to be shared without the risk of leaking information to unauthorized entities. Cryptography algorithms are used to encrypt information with a key to remain in control of when, where and to whom it is shared. All information is encrypted based on the concept of content-based encryption. In this unreliable environment, the cryptographic keys used to secure the data have to be available to continue collecting and processing information.

A key management architecture should be in place, to facilitate the generation and distribution of these keys. The purpose of this key management architecture is to provide the entities in the field with specific keys such that information access policies can be enforced. The challenge here is that in tactical networks, network partitionings are expected to happen. Therefore, the same keys have to be redundantly available at multiple locations to prevent a single point of failure. In a connected network, the keys can constantly be synchronized between these locations. However, the problem of key de-synchronization occurs if the network is split for some time, keys are changed on both sides, and then the network is recombined. This leads to possible conflicting keys because synchronization was temporarily not possible. The key management architecture must be able to handle such conflicts and reintegrate them as necessary.

In this thesis, we present a decentralized key management architecture with a solution for the key de-synchronization problem. We propose to use Conflict-free replicated data types, to store the keys at multiple locations and prevent conflicts. Conflict-free replicated data types is a concept to store and replicate data across multiple instances. This data type is characterized by the possibility to update the data in all instances independently, and concurrently, without coordination between the instances. Additionally, three approaches for the coordination of key creation are proposed with different levels of consistency and availability. The architecture and the three approaches are compared in experiments to evaluate the differences and prove the feasibility of the designs.

A phase estimation algorithm is presented to estimate the phase of a recurring pattern in a nonstationary signal. The signal is modelled by a template signal that represents one revolution of the recurring pattern, and that the frequency of this pattern can change at any time with no assumptions about local stationarity. The algorithm uses a constraint maximum likelihood estimator (MLE) to estimate the phase of the recurring pattern in the time series. Using the dynamic programming techniques from the dynamic time warping (DTW) algorithm, the solution is found in an efficient manner. The algorithm is applied to the digitization of meter readings from analog consumption meters.

As of today, analog consumption meters are still widely used to measure the consumption of gas, electricity and water. Often, smart home appliance use a simple reflective photosensor located on a rotating part of the meter to obtain information about the state of the consumption meter. The algorithm presented in this thesis accurately estimates the phase of the repeating pattern that occurs in the sensor observation when the meter rotates. Using this estimate, the signal of the photosensor can be converted to an estimate of the total resource consumption and consumption rate.

The algorithm improves in accuracy over conventional methods based on peak detection, and is shown to work in cases where the peak detection methods fails. Examples of this are signals where there is no distinctive peak in the signal or a signal where the recurring pattern is reversed. Furthermore, a template compression scheme is proposed that is used to decrease the computational complexity of the algorithm. Different time series compression methods are applied to the algorithm and evaluated on their performance.

5G networks are expected to be used in many markets, one of which is the Factories of the Future (FoF). In the FoF, applications like regular monitoring and controlling of components (e.g. temperature) are introducing the need of massive deployment of sensors and actuators. Additionally, sensors which are monitoring time-critical components of the factory (e.g. pressure in power plants) should experience low delays with a high reliability. The current LTE-based technology for machine-type communications, namely Cat-M1, imposes limitations in supporting massive connectivity and application with low delay and high reliability requirements, primarily due to the so-called ‘Random Access’ (RA) procedure which is used by the devices to establish a connection with the base station, before the actual transmission of their data. The key objectives of this study are to assess the RA procedure currently used in Cat-M1 networks as a baseline, and furthermore design and evaluate a new RA procedure for 5G networks, which targets typical FoF applications and their requirements. Based on the simulation assessment of the procedures studied, it was found that the so-called ‘Two-Step RA procedure’ is performing the best regarding end-to-end delay. Specifically, it was found that e.g. in a FoF network with 3000 devices an end-to-end delay of 16 ms can be achieved with 99.99% reliability, introducing a gain of 64 ms compared to the end-to-end delay in Cat-M1 networks.

Hearing aids as a form of audio preprocessing is increasingly common in everyday life. The goal of this thesis is to implement a blind approach to the cocktail party problem and challenge some of the regular assumptions made in literature. We approach the problemas wideband FD-BSS. From this field of research, the common assumption of contineous activity is dropped. Instead a number of users detection is implemented as a preprocessing step and ensure the appropriate number of demixing vectors for each time frequency bin. The validity of the standard mixing model used for STFT’s is challenged by looking at the response of a linear array. Source separation is achieved by demixing vectors based on the GSVD, derived in a model-based approach. While most ermutation solvers offer an a posteriori solution for all users, we looked at finding local solutions for a single user. Combining this with the user identification called the alignment step, we conclude that the permutation problem can be reduced to selecting a demixing vector for each discrete time-frequency instance.
The correlation coefficient proves to be a sufficient metric to couple reconstructions to the original data as it selects most of the active time-frequency bins. In the far-field case, our approach performs in a comparable
but not superior manner. We did find that our method is much more robust against inaccuracies introduced when narrowband channels are assumed but not actually available. This is strongly exemplified by our experiment of a changing DFT-size.
The Frobinius norm was suggested as a measure of distance between the estimate STFT and the orignial signals time frequency domain description but it resulted in counter intuitive results which didn’t correspond with other metrics used in this thesis. It is expected that there are effects induced by changing the size of the STFT which are not accounted for.
Our demixing vectors achieve comparable inteligibility, measured by STOI, as the compared techniques and it is more robust against smaller sample sizes than the theoretically SINR optimal MVDR.

Stochastic resonance (SR) is a phenomenon where the performance of a nonlinear system subjected to noise is better than it is without noise. This phenomenon can be found both in natural and artificial systems, especially in threshold-based systems such as comparators or a population of neurons. As noise always exists and interacts with the system, it is advantageous to design a system that purposefully uses SR to boost its performance. One possible use of SR is in the signal reconstruction. In this application, noise is added to the input signal and is processed by a comparator to produce a 1-bit output signal. This output can be averaged to recover the amplified input signal. In this thesis, three challenges regarding the use of SR in signal reconstruction are addressed. Firstly, to use SR not only to reconstruct the original signal, but also to implement mathematical operators, specifically a multiplier and an adder, that take two or more input signals. Secondly, to define the relevant metric(s) that can be used to measure the performance of the operators. Lastly, to build a system out of the proposed SR-based operators. The SR-based mathematical operators are implemented on the system level with a comparator as its fundamental building block. To analyze the behavior of the operators, formulas for noise and distortion power are derived. MATLAB simulation is then used to verify the theoretical analysis. Finally, these SR-based mathematical operators are used to build a Teager Energy Operator (TEO) for action potentials (APs) detection. An SR-based multiplier and adder can be implemented with the use of an XNOR logic gate and a binary half adder, respectively. The theoretical formulas are successful in predicting the noise and distortion behavior of the operators. In conclusion, it is possible to implement mathematical operators, specifically multipliers and adders, which use noise to boost their performance. The noise and distortion behavior of these operators can be predicted mathematically. Signal-to-noise ratio (SNR) and signal-to-noise-and-distortion ratio (SNDR) are used to measure the performance of the operators. Systems, specifically a TEO, can be built using the SR-based operators.