Discrete Function Representations Utilizing Decision Diagrams and Spectral Techniques

All discrete function representations become exponential in size in the worst case. Binary decision diagrams have become a common method of representing discrete functions in computer-aided design applications. For many functions, binary decision diagrams do provide compact representations. This work presents a way to represent large decision diagrams as multiple smaller partial binary decision diagrams. In the Boolean domain, each truth table entry consisting of a Boolean value only provides local information about a function at that point in the Boolean space. Partial binary decision diagrams thus result in the loss of information for a portion of the Boolean space. If the function were represented in the spectral domain however, each integer-valued coefficient would contain some global information about the function. This work also explores spectral representations of discrete functions, including the implementation of a method for transforming circuits from netlist representations directly into spectral decision diagrams

Observing convective aggregation

Convective self-aggregation, the spontaneous organization of initially scattered convection into isolated convective clusters despite spatially homogeneous boundary conditions and forcing, was first recognized and studied in idealized numerical simulations. While there is a rich history of observational work on convective clustering and organization, there have been only a few studies that have analyzed observations to look specifically for processes related to self-aggregation in models. Here we review observational work in both of these categories and motivate the need for more of this work. We acknowledge that self-aggregation may appear to be far-removed from observed convective organization in terms of time scales, initial conditions, initiation processes, and mean state extremes, but we argue that these differences vary greatly across the diverse range of model simulations in the literature and that these comparisons are already offering important insights into real tropical phenomena. Some preliminary new findings are presented, including results showing that a self-aggregation simulation with square geometry has too broad a distribution of humidity and is too dry in the driest regions when compared with radiosonde records from Nauru, while an elongated channel simulation has realistic representations of atmospheric humidity and its variability. We discuss recent work increasing our understanding of how organized convection and climate change may interact, and how model discrepancies related to this question are prompting interest in observational comparisons. We also propose possible future directions for observational work related to convective aggregation, including novel satellite approaches and a ground-based observational network

Multiscale analysis of financial volatility

This thesis is concerned with the modeling of financial time series data. It introduces to the economics literature a set of techniques for this purpose that are rooted in engineering and physics, but almost unheard of in economics. The key feature of these techniques is that they combine the available information in the time and frequency domains simultaneously, making it possible to enjoy the advantages of both forms of analysis. The thesis is divided into three sections. First, after briefly outlining the Fourier methods, a more exible technique that allows for the study of time-scale dependent phenomena (motivated from a discussion on Heisenberg's uncertainty principle) namely Wavelet method is defined. A complete account of discrete and continuous wavelet transformations, and wavelet variation is provided and the advantages of wavelet-multiresolution analysis over Fourier methods are demonstrated. In the second section, the statistical properties of financial returns at 1-day, 5-day and 10-day sampling intervals are studied using S&P500 index for over a decade, and the links between dependence properties of financial returns at lower sampling frequencies are explored. The concepts of temporal aggregation and skip sampling are discussed and the effects of temporal aggregation on long range dependent time series are theoretically outlined and then tested through simulations and empirically via S&P500. In the third section, the variation of two years of five-minute GBP/USD exchange rate is analysed and the notion of realised variation is explored. The characteristics of the intraday data at different sampling frequencies (5-minute, 30-minute, 60-minute, 10-hour, 1-day, and 5-day) are compared with each other and filtered out from seasonalities using the wavelet multiscaling technique. We find that temporal aggregation does not change the decay rate of autocorrelation functions of long-memory data of certain frequencies, however the level at which the autocorrelation functions start from move upward for daily data. This thesis adds to the literature by outlining and comparing the effects of aggregation between daily and intra-daily frequencies for the realised variances, which to our knowledge is a first. The effect temporal aggregation has on daily data is different from intra-daily data, and we provide three reasons why this might be. First, at higher frequencies strong periodocities distort the autocorrelation functions which could bring down the decay rate and mask the long memory feature of the data. Second, the choice of realised variance is crucial in this matter and different functions can result in contradictory outcomes. Third, as the order of aggregation increases the decay rate does not depend on the order of the aggregation

Solution structures of lipoyl domains of the 2-oxo acid dehydrogenase complexes from Azotobacter vinelandii : implications for molecular recognition

The 2-oxo acid dehydrogenase complexes are large multienzyme complexes that catalyse the irreversible oxidative decarboxylation of a specific 2-oxo acid to the corresponding acyl-CoA derivative. The pyruvate dehydrogenase complex (PDHC) converts the product of the glycolysis, pyruvate, to acetyl-CoA, which enters the tricarboxylic acid cycle. The 2-oxoglutarate dehydrogenase complex (OGDHC functions in the tricarboxylic acid cycle itself by converting 2-oxoglutarate to succinyl-CoA. The branched-chain 2-oxo acid dehydrogenase complex (BCDHC) is involved in the catabolism of branched-chain amino acids. Since these complexes play vital roles in metabolism, impairment in their functioning by genetic defects naturally causes severe diseases in humans, e.g. lactic acidosis (PDHC deficiency) and maple syrup urine disease (BCDHC deficiency) (Patel & Harris, 1995).The 2-oxo acid dehydrogenase complexes have a very similar design and share many structural and catalytic properties. They convert their substrate by the combined activity of multiple copies of three enzymes: a substrate-specific 2-oxo acid dehydrogenase (El), an acyltransferase (E2), and a lipoamide dehydrogenase (E3). The E2 component forms the central oligomeric core of the complex to which the peripheral subunits El and E3 are noncovalently bound. The acyltransferase (E2) component is a highly segmented and multifunctional protein in which three different independently folded domains can be recognised, connected by mobile linker sequences. The N-terminal part consists of one to three lipoyl domains (- 80 amino acid residues each) containing the covalently bound prosthetic group lipoic acid. Between the lipoyl domain(s) and the C-terminal catalytic domain (- 29 kDa), which bears the acyltransferase active site and which aggregates to form the oligomeric core of the complex, the peripheral subunit-binding domain (- 35 amino acid residues) is found.The lipoyl domains play a crucial role in coupling the activities of the three multienzyme components by providing swinging arms that are mobile and responsible for substrate channelling among the three successive active sites. A specific lysine side chain of each lipoyl domain is modified with lipoic acid to form a lipoyl group, which transports acyl groups from El to E2, and reduction equivalents from E2 to E3. The structure of the lipoyl domain is required for the efficient reaction of its lipoyl group with the El component. Furthermore, for E. coli PDHC and OGDHC it was shown that lipoyl domains can only be reductively acylated by the El enzyme of their parent complex, which indicates that molecular recognition occurs between El components and lipoyl domains (Graham et al., 1989).The research presented in this thesis aimed at gaining insight in the interaction between lipoyl domains and El components, and in particular what part of the lipoyl domain determines the specificity of the reductive acylation reaction. By the determination and comparison of the three-dimensional structures of the lipoyl domains of PDHC and OGDHC from A. vinelandii, for which their specificities in the reductive acylation reaction were determined, we expected to shed already some light on this process of molecular recognition. It also provides the structural basis for further studies on the specific interaction between El and the lipoyl domain, some of which are described in this thesis. The results of this work are summarised hereafter.The N-terminal lipoyl domain (residues 1-79) of the Up component of PDHC and the single lipoyl domain of the E2o component of OGDHC have both been sub-cloned and expressed in E. coli (chapters 2 and 3). The expression exceeded the capacity of the E. coli cells to lipoylate all the produced lipoyl domain, and only 5- 10% of the lipoyl domain was found to be modified with lipoic acid. The unlipoylated and lipoylated forms of the lipoyl domain could be separated by anion-exchange chromatography. Addition of a supplementary amount of lipoic acid to the growth medium resulted in full lipoylation of the expressed lipoyl domain. The ability of the purified lipoylated lipoyl domains to become reductively acylated by the El components of their parent complex proved that their folding and modification were correct. The correct modification of the E2p lipoyl domain has been confirmed by electrospray mass spectrometry.Two-dimensional homo- and heteronuclear NMR studies of the A . vinelandii lipoyl domains have resulted in sequential 1H and 15N resonance assignments and the secondary structure of both domains (chapters 2 and 3). The 2D 1H-NOESY spectra of the unlipoylated and lipoylated forms of the Up lipoyl domain are almost superimposable, except for several additional resonances that could be assigned to the lipoic acid moiety, and small differences in chemical shift of protons of residues in the direct vicinity of the lipoyl-lysine residue (chapter 2). No changes in NOE intensities connecting these residues nor addition or loss of NOEs could be observed however, suggesting that the structure of the lipoyl domain is not altered much if any upon lipoylation. A detailed comparison of the NMR-derived parameters of both lipoyl domains, i.e. chemical shifts, NH-exchange rates, NOEs, and 3 J HNαcoupling constants suggests a high structural similarity in solution between the two lipoyl domains, despite their amino acid sequence identity of only 25% (chapter 3).The three-dimensional solution structures of the two lipoyl domains have been determined using distance geometry and/or dynamical simulated annealing calculations (chapters 4 and 5). The overall fold of both lipoyl domains is very similar and can be described as a beta-barrel-sandwich hybrid, which is now known to be typical for lipoyl domains. The domain is formed by two very similar and almost parallel four-stranded antiparallel P-sheets connected by loops and turns. The β- sheets each consist of three major and one minor strand, and are formed around a well-defined core of hydrophobic residues. At the far end of one of the sheets the lipoyl-lysine residue is presented to the solvent in a beta-turn connecting two successive strands. The N-terminal and C-terminal ends of the folded domain meet at the exact opposite of the domain in two adjacent beta-strands of the other sheet. The lipoyl domains display a remarkable internal symmetry that projects one beta- sheet onto the other beta-sheet after rotation of approximately 180° about a 2-fold rotational symmetry axis. The last six and two C-terminal residues of the cloned fragments of the PDHC and OGDHC lipoyl domains, respectively, are poorly defined and belong to the flexible linker sequences connecting the lipoyl domains to the remainder of the acyltransferase chain. These residues also show a significant narrower linewidth of their amide protons in the NMR spectra, which is an indication of increased mobility.The number of long-range NOE-distance constraints that have been obtained for the two lipoyl domains is not very large, but is comparable to the number obtained for other lipoyl domains, i.e. from B. stearothermophilus PDHC and E. coli PDHC (Dardel et al., 1993; Green et al., 1995). This seems inherited with the particular type of protein structure, in combination with the absence (A. vinelandii PDHC lipoyl domain) or low amount (only one Trp residue in the core of the A. vinelandii OGDHC lipoyl domain) of aromatic residues. Many long-range contacts between hydrophobic residues in the core of the domains are side-chain side-chain contacts. The unambiguous assignment of many of these contacts is impaired by overlap, and these contacts will only be accessible after 13C- labelling of the lipoyl domains. Although the three-dimensional structures of the lipoyl domains that have been determined are not of high resolution, they provide good and suitable structural models for comparisons and the design of significant mutants to investigate the specific interactions between lipoyl domains and other complex components.A comparison of the structures of the A . vinelandii PDHC and OGDHC lipoyl domains with those of the PDHC lipoyl domains of B . stearothennophilus and E. coli shows that their overall fold is strikingly similar. In particular, that fact that the two A . vinelandii lipoyl domains, for which their specificity in the reductive acylation reactions has been demonstrated now (chapter 6), have similar structures, indicates that molecular recognition of lipoyl domains by El is a result of only delicate differences among lipoyl domains. On the basis of a careful comparison of lipoyl domain structures and sequences, potential residues of the lipoyl domain that could be important for molecular recognition are proposed. These include residues of an exposed loop connecting the first two beta-strands in the sequence, and which lies close in space to the lipoylation site. In this loop the largest structural differences among lipoyl domains are found. Other potential candidates are the two amino acid residues immediately succeeding the lipoyl-lysine residue.Site-directed mutagenesis experiments of the exposed loop of the A . vinelandii OGDHC lipoyl domain, and cross-acylation experiments of A . vi nelandii PDHC and OGDHC lipoyl domains catalysed by E. coli complexes, were performed to investigate the role of this loop in molecular recognition (chapter 6). These experiments indicate that this loop is very likely involved in the interaction with the El component, but that it is probably not the single determinant conferring specificity to the reductive acylation reaction. Additional site-directed mutagenesis experiments on this loop and the residues following the lipoyl-lysine residue are required to further investigate their role in molecular recognition.All studies on the interaction between lipoyl domains and El components are impaired by the lack of a three-dimensional structure of any El component. Furthermore, although the interaction between the lipoyl domain and El is specific, it is supposedly weak (Graham & Perham, 1990). This has been substantiated by initial NMR experiments in which, upon addition of A . vinelandii E1p to the 15N-labelled lipoylated E2p lipoyl domain (1:2 ratio), no broadening or shift of the lipoyl domain resonances could be observed (Berg et al., 1996) (not described in this thesis). From addition of pyruvate to this NMR sample it was suggested that also the acetylated form of the lipoyl domain does not bind to E1p, at least not under the applied conditions. Together this implies that the lipoyl domain does not interact (strongly) with the El component, except when the hydroxyethyl-ThDP moiety is present in El. Such a ping-pong type of mechanism may be advantageous for the lipoyl domain that needs to interdigitate rapidly among the different active sites in the complex, but is unfortunately less advantageous for the observer.A final remark is dedicated to the rotational flexibility of the lipoyl group of the lipoyl domain, that is thought to be required to act as a swinging arm in the complex (Reed, 1974). Recently, the X-ray crystal structures of the H-protein of the glycine decarboxylase system with its lipoyl group loaded with methylamine (Cohen-Addad et al., 1995), and of the biotinyl domain of acetyl-CoA carboxylase (Athappilly & Hendrickson, 1995), showed that their lipoyl/biotinyl group binds back to the protein surface. This may even not be very surprising considering the hydrophobic nature of the lipoyl group, and the question if this also could happen with lipoyl groups of 2-oxo acid dehydrogenase complexes is therefore relevant. In the case of the H-protein, only the methylamine-loaded form of the lipoyl group binds to the protein, while the oxidised lipoyl group does not. Furthermore, the methylamine-loaded lipoyl group binds to residues that are conserved in H-proteins, several of which are located in a N-terminal helix that is absent in lipoyl domains. In the case of the biotinyl domain, the biotinyl group is partly buried in a thumblike protruding loop that is not found in lipoyl domains. For the lipoyl domains of 2-oxo acid dehydrogenase complexes no X-ray crystal structures, or NMR structures of their lipoylated form, are available. As mentioned earlier, only small differences in chemical shifts of residues close in space to the lipoylation site (average difference - 0.15 ppm), including residues of the exposed loop (average difference - 0.07 ppm), are observed between the lipoylated and unlipoylated forms of the lipoyl domain (chapter 2). These differences are considered too small to suggest binding of the lipoyl group to e.g. the exposed loop. Together with the fact that in the H-protein and the biotinyl domain the lipoyl/biotinyl group binds to parts of the protein that are absent in lipoyl domains, this indicates that the lipoyl groups of 2-oxo acid dehydrogenase complexes are likely to swing freely

Designing for self-transcendent experiences in virtual reality

This thesis contributes to Psychology and Human-Computer Interaction (HCI) research with a focus on the design of immersive experiences that support self-transcendence. Self-transcendence is defined as a decrease in a sense of self and a increase in unity with the world. It can change what individuals know and value, their perspective on the world and life, evolving them as a grown person. Consequently, self-transcendence is gaining attention in Psychology, Philosophy, and Neuroscience. But, we are still far from understanding the complex phenomenological and neurocognitive aspects of self-transcendence, as well as its implications for individual growth and psychological well-being. In reviewing the methods for studying self-transcendence, we found differing conceptual models determine different ways for understanding and studying self-transcendence. Understanding self-transcendence is made especially challenging because of its ineffable qualities and extraordinary conditions in which it takes place. For that reason, researchers have began to look at technological solutions for both eliciting self-transcendence to better study it under controlled and replicable conditions as well as giving people greater access to the experience. We reviewed immersive, interactive technologies that aim to support positive experiences such as self-transcendence and extracted a set of design considerations that were prevalent across experiences. We then explored two different focuses of self-transcendence: awe and lucid dreaming. First, we took an existing VR experience designed specifically to support the self-transcendent experience of awe and looked at how the mindset and physical setting surrounding that VR experience might better support the experience of and accommodation of awe. Second, we delved deep into lucid dreaming to better understand the aspects that could help inform the design of an immersive experience that supports self-transcendence. We put those design ideas into practice by developing a neurofeedback system that aims to support lucid dreaming practices in an immersive experience. Through these review papers and design explorations, we contribute to the understanding of how one might design and evaluate immersive technological experiences that support varieties of self-transcendence. We hope to inspire more work in this area that holds promise in better understanding human nature and living our best lives

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior