DISTRIBUTION OF R-PATTERNS IN THE KERDOCK-CODE BINARY SEQUENCES AND THE HIGHEST LEVEL SEQUENCES OF PRIMITIVE SEQUENCES OVER Z2lZ_{2^l}

The distribution of r-patterns is an important aspect of pseudorandomness for periodic sequences over finite field.The aim of this work is to study the distribution of r-patterns in the Kerdock-code binary sequences and the highest level sequences of primitive sequences over $Z_{2^l}$.By combining the local Weil bound with spectral analysis,we derive the upper bound of the deviation to uniform distribution.As a consequence,the recent result on the quantity is improved

The development of a convergence diagnostic for Markov Chain Monte Carlo estimation

The development and investigation of a convergence diagnostic for Markov Chain Monte Carlo (MCMC) posterior distributions is presented in this paper. The current method is an adaptation of an existing convergence diagnostic based on the Cumulative Sum (CUSUM, Page 1954; Yu & Mykland, 1998; Brooks, 1998c) procedure. The diagnostic under development is seen to be an improvement over the technique upon which it is based because it offers a simple way to remove one of the two major assumptions made by the previous method, namely that the shape of the distribution under consideration is symmetric. Results are mixed, but there is some evidence to indicate that the new technique is sensitive to the degree of autocorrelation present and the stability of the chains. Also, the new diagnostic behaves differently than three existing convergence diagnostics

Direct Antenna Modulation using Frequency Selective Surfaces

In the coming years, the number of connected wireless devices will increase dramatically, expanding the Internet of Things (IoT). It is likely that much of this capacity will come from network densification. However, base stations are inefficient and expensive, particularly the downlink transmitters. The main cause of this is the power amplifier (PA), which must amplify complex signals, so are expensive and often only 30% efficient. As such, the cost of densifying cellular networks is high. This thesis aims to overcome this problem through codesign of a low complexity, energy efficient transmitter through electromagnetic design; and a waveform which leverages the advantages and mitigates the disadvantages of the new technology, while being suitable for supporting IoT devices. Direct Antenna Modulation (DAM) is a low complexity transmitter architecture, where modulation occurs at the antenna at transmit power. This means a non-linear PA can efficiently amplify the carrier wave without added distortion. Frequency Selective Surfaces (FSS) are presented here as potential phase modulators for DAM transmitters. The theory of operation is discussed, and a prototype DAM for QPSK modulation is simulated, designed and tested. Next, the design process for a continuous phase modulating antenna is explored. Simulations and measurement are used to fully characterise a prototype, and it is implemented in a line-of-sight end-to-end communications system, demonstrating BPSK, QPSK and 8-PSK. Due to the favourable effects of spread spectrum signalling on FSS DAM performance, Cyclic Prefix Direct Sequence Spread Spectrum (CPDSSS) is developed. Conventional spreading techniques are extended using a cyclic prefix, making multipath interference entirely defined by the periodic autocorrelation of the sequence used. This is demonstrated analytically, through simulation and with experiments. Finally, CPDSSS is implemented using FSS DAM, demonstrating the potential of this new low cost, low complexity transmitter with CPDSSS as a scalable solution to IoT connectivity

Efficient, concurrent Bayesian analysis of full waveform LaDAR data

Bayesian analysis of full waveform laser detection and ranging (LaDAR) signals using reversible jump Markov chain Monte Carlo (RJMCMC) algorithms have shown higher estimation accuracy, resolution and sensitivity to detect weak signatures for 3D surface profiling, and construct multiple layer images with varying number of surface returns. However, it is computational expensive. Although parallel computing has the potential to reduce both the processing time and the requirement for persistent memory storage, parallelizing the serial sampling procedure in RJMCMC is a significant challenge in both statistical and computing domains. While several strategies have been developed for Markov chain Monte Carlo (MCMC) parallelization, these are usually restricted to fixed dimensional parameter estimates, and not obviously applicable to RJMCMC for varying dimensional signal analysis. In the statistical domain, we propose an effective, concurrent RJMCMC algorithm, state space decomposition RJMCMC (SSD-RJMCMC), which divides the entire state space into groups and assign to each an independent RJMCMC chain with restricted variation of model dimensions. It intrinsically has a parallel structure, a form of model-level parallelization. Applying the convergence diagnostic, we can adaptively assess the convergence of the Markov chain on-the-fly and so dynamically terminate the chain generation. Evaluations on both synthetic and real data demonstrate that the concurrent chains have shorter convergence length and hence improved sampling efficiency. Parallel exploration of the candidate models, in conjunction with an error detection and correction scheme, improves the reliability of surface detection. By adaptively generating a complimentary MCMC sequence for the determined model, it enhances the accuracy for surface profiling. In the computing domain, we develop a data parallel SSD-RJMCMC (DP SSD-RJMCMCU) to achieve efficient parallel implementation on a distributed computer cluster. Adding data-level parallelization on top of the model-level parallelization, it formalizes a task queue and introduces an automatic scheduler for dynamic task allocation. These two strategies successfully diminish the load imbalance that occurred in SSD-RJMCMC. Thanks to the coarse granularity, the processors communicate at a very low frequency. The MPIbased implementation on a Beowulf cluster demonstrates that compared with RJMCMC, DP SSD-RJMCMCU has further reduced problem size and computation complexity. Therefore, it can achieve a super linear speedup if the number of data segments and processors are chosen wisely

Advances in Quantum Nonlinear Optics: a nonclassical journey from the optimization of silicon photomultipliers for Quantum Optics to quantum second-harmonic generation

openIn this thesis, we present our experimental and theoretical work on modern and old topics of Nonlinear Quantum Optics. The thesis is structured as follows. In the first chapter, we provide a general introduction about the basis of this field, in particular about the main concepts and results that will be needed in the following. In the second and third chapters, we explain our research on the role of silicon photomultipliers in Quantum Optics experiments. After a specific characterization of the sensors, we used them to detect nonclassical states of light. Different strategies for the estimation of experimental quantities are suggested. In the fourth chapter, we propose our quantum description for the second-harmonic-generation process, based on well-known perturbative methods. After a general introduction on the state of the art, we immediately dive into the problem by explaining the employed methods and showing our analytical results. Finally, we resume the essence of our achievements and draw our conclusions.openFisica e astrofisicaChesi, GiovanniChesi, Giovann

The Inverted yield curve and hidden Markov models in predicting future bear markets

Previous studies have shown very clearly that there is a connection between the inversion of the yield curve and future recessions measured as contractions in the GDP. The focus of this study was, however, the connection between financial markets and the inverted yield curve, which has not been studied as much as the production related dependencies. Although it is difficult to draw a clear line between stock market crashes and the preceding inversions of the yield curve, the data suggests that the inverted yield curve is a sign of more volatile times ahead, which clearly heightens the risk of a major stock market down-turn. The empirical part of the study combined other factors and tools – hidden Markov models, credit spreads, S&P 500 returns, NY Fed recession probability model and the CAPE ratio – with the inverted yield curve in order to improve the predictability of future stock market crashes, which was then used to construct allocation strategies between the stock market and risk-free US Treasury rates. The proposed strategies managed to beat the benchmark and the conducted transaction cost sensitivity analysis proves that the strategies are feasible at reasonable transaction cost levels. The greater annualized returns and lesser volatility of the strategies lead to significantly better risk-adjusted returns than what one would achieve using the simple buy and hold strategy. The obtained Sharpe ratios range from 0,531 to 0,824, whereas the Sharpe ratio of the benchmark total US stock market return is 0,499 during the (pseudo) out-of-sample forecasting period of 1986–2019. It should be noted that the analysis is conducted using past data and the true acid test of the strategies will be made during the current inversion period. Although greater volatility leads to greater opportunities in the market, the effectiveness of the proposed strategies in this study is based on prudence and patience: the best option for the average investor could very well be to weather the storm in safer assets and then return to the stock market once the volatility of the market is lower again.Aiempi tutkimus osoittaa selkeästi yhteyden kääntyneen korkokäyrän ja sitä seuraavan bruttokansantuotteen laskulla mitatun reaalitalouden laman välillä, mutta kyseisen korkokäyrän vaikutuksia rahoitus- ja ennen kaikkea osakemarkkinoilla ei ole akateemisesti tutkittu yhtä paljon kuin kansantaloustieteellisiä vaikutuksia. Vaikka selkeitä syy-seuraussuhteita osakemarkkinaromahdusten ja niitä edeltävien korkokäyrien kääntymisten välille on vaikea vetää, läpikäyty aineisto osoittaa kääntyvän korkokäyrän olevan merkki lähitulevaisuudessa kasvavasta volatiliteetista, joka kasvattaa olennaisesti vakavan osakemarkkinaromahduksen riskiä. Tutkimuksen empiirinen osuus yhdistää kääntyvään korkokäyrään muita faktoreita ja työkaluja – kuten esimerkiksi piilotetut Markov-mallit, korkospreadit ja S&P 500 -tuotot –, joiden avulla pelkän korkokäyrän ennustevoimaa pyritään parantamaan sekä siten muodostamaan toimivia allokaatiostrategioita osakemarkkinoiden sekä riskittömän tuoton välillä. Esitetyt strategiat onnistuivat voittamaan vertailuindeksinsä ja transaktiokustannuksista tehty herkkyysanalyysi osoittaa, että muodostetut strategiat ovat toteuttamiskelpoisia realistisilla transaktiokustannuksilla. Strategioiden vertailuindeksiä parempien keski-määräisten vuosituottojen sekä pienemmän volatiliteetin ansiosta niiden riskikorjattu tuotto on merkittävästi parempi kuin pelkästään vertailuindeksiin sijoittamalla. Tutki-muksessa esitettyjen strategioiden Sharpen luvut ovat välillä 0,531–0,824, kun taas vertailuindeksinä toimivan koko Yhdysvaltain osakemarkkinan kokonaistuoton Sharpen luku on 0,499 aikavälillä 1986–2019, joka toimii tutkimuksen (pseudo-)ennustejaksona. On kuitenkin huomattava, että strategioiden todellinen tulikoe tapahtuu vuonna 2019 tapahtuneen korkokäyrän kääntymisen jälkeisessä lähitulevaisuudessa. Vaikka suurempi volatiliteetti johtaa suurempiin mahdollisuuksiin markkinoilla, niin tässä tutkimuksessa esitettyjen strategioiden tehokkuus perustuu ennen kaikkea kärsivällisyyteen ja varovaisuuteen: tavallisen sijoittajan paras vaihtoehto markkinoiden mylleryksessä voisi useimmiten olla hakeutuminen turvallisempien omaisuuserien pariin sekä palaaminen osakemarkkinoille myrskyn laantuessa