On Self-Dual Quantum Codes, Graphs, and Boolean Functions

A short introduction to quantum error correction is given, and it is shown that zero-dimensional quantum codes can be represented as self-dual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes with high minimum distance can be described as nested regular graphs having minimum regular vertex degree and containing long cycles. Two graphs correspond to equivalent quantum codes if they are related by a sequence of local complementations. We use this operation to generate orbits of graphs, and thus classify all inequivalent self-dual additive codes over GF(4) of length up to 12, where previously only all codes of length up to 9 were known. We show that these codes can be interpreted as quadratic Boolean functions, and we define non-quadratic quantum codes, corresponding to Boolean functions of higher degree. We look at various cryptographic properties of Boolean functions, in particular the propagation criteria. The new aperiodic propagation criterion (APC) and the APC distance are then defined. We show that the distance of a zero-dimensional quantum code is equal to the APC distance of the corresponding Boolean function. Orbits of Boolean functions with respect to the {I,H,N}^n transform set are generated. We also study the peak-to-average power ratio with respect to the {I,H,N}^n transform set (PAR_IHN), and prove that PAR_IHN of a quadratic Boolean function is related to the size of the maximum independent set over the corresponding orbit of graphs. A construction technique for non-quadratic Boolean functions with low PAR_IHN is proposed. It is finally shown that both PAR_IHN and APC distance can be interpreted as partial entanglement measures.Comment: Master's thesis. 105 pages, 33 figure

Constructing Hyper-Bent Functions from Boolean Functions with the Walsh Spectrum Taking the Same Value Twice

Hyper-bent functions as a subclass of bent functions attract much interest and it is elusive to completely characterize hyper-bent functions. Most of known hyper-bent functions are Boolean functions with Dillon exponents and they are often characterized by special values of Kloosterman sums. In this paper, we present a method for characterizing hyper-bent functions with Dillon exponents. A class of hyper-bent functions with Dillon exponents over $\mathbb{F}_{2^{2m}}$ can be characterized by a Boolean function over $\mathbb{F}_{2^m}$, whose Walsh spectrum takes the same value twice. Further, we show several classes of hyper-bent functions with Dillon exponents characterized by Kloosterman sum identities and the Walsh spectra of some common Boolean functions

Design of Stream Ciphers and Cryptographic Properties of Nonlinear Functions

Block and stream ciphers are widely used to protect the privacy of digital information. A variety of attacks against block and stream ciphers exist; the most recent being the algebraic attacks. These attacks reduce the cipher to a simple algebraic system which can be solved by known algebraic techniques. These attacks have been very successful against a variety of stream ciphers and major efforts (for example eSTREAM project) are underway to design and analyze new stream ciphers. These attacks have also raised some concerns about the security of popular block ciphers. In this thesis, apart from designing new stream ciphers, we focus on analyzing popular nonlinear transformations (Boolean functions and S-boxes) used in block and stream ciphers for various cryptographic properties, in particular their resistance against algebraic attacks. The main contribution of this work is the design of two new stream ciphers and a thorough analysis of the algebraic immunity of Boolean functions and S-boxes based on power mappings. First we present WG, a family of new stream ciphers designed to obtain a keystream with guaranteed randomness properties. We show how to obtain a mathematical description of a WG stream cipher for the desired randomness properties and security level, and then how to translate this description into a practical hardware design. Next we describe the design of a new RC4-like stream cipher suitable for high speed software applications. The design is compared with original RC4 stream cipher for both security and speed. The second part of this thesis closely examines the algebraic immunity of Boolean functions and S-boxes based on power mappings. We derive meaningful upper bounds on the algebraic immunity of cryptographically significant Boolean power functions and show that for large input sizes these functions have very low algebraic immunity. To analyze the algebraic immunity of S-boxes based on power mappings, we focus on calculating the bi-affine and quadratic equations they satisfy. We present two very efficient algorithms for this purpose and give new S-box constructions that guarantee zero bi-affine and quadratic equations. We also examine these S-boxes for their resistance against linear and differential attacks and provide a list of S-boxes based on power mappings that offer high resistance against linear, differential, and algebraic attacks. Finally we investigate the algebraic structure of S-boxes used in AES and DES by deriving their equivalent algebraic descriptions

The supernova cosmology cookbook: Bayesian numerical recipes

Theoretical and observational cosmology have enjoyed a number of significant successes over the last two decades. Cosmic microwave background measurements from the Wilkinson Microwave Anisotropy Probe and Planck, together with large-scale structure and supernova (SN) searches, have put very tight constraints on cosmological parameters. Type Ia supernovae (SNIa) played a central role in the discovery of the accelerated expansion of the Universe, recognised by the Nobel Prize in Physics in 2011. The last decade has seen an enormous increase in the amount of high quality SN observations, with SN catalogues now containing hundreds of objects. This number is expected to increase to thousands in the next few years, as data from next-generation missions, such as the Dark Energy Survey and Large Synoptic Survey Telescope become available. In order to exploit the vast amount of forthcoming high quality data, it is extremely important to develop robust and efficient statistical analysis methods to answer cosmological questions, most notably determining the nature of dark energy. To address these problems my work is based on nested-sampling approaches to parameter estimation and model selection and neural networks for machine-learning. Using advanced Bayesian techniques, I constrain the properties of dark-matter haloes along the SN lines-of-sight via their weak gravitational lensing effects, develop methods for classifying SNe photometrically from their lightcurves, and present results on more general issues associated with constraining cosmological parameters and testing the consistency of different SN compilations.Comment: 119 pages, 29 figures, Doctoral Thesis in Theoretical Physics, ISBN 978-91-7447-953-

Genomics as a tool for natural product structure elucidation

Natural product discovery is in the midst of a transition from a largely serendipity-based effort to an informatics-driven one. For most of the 20th century, natural product discovery relied on genome-blind bioassay-guided isolation. This was initially exceptionally productive, yielding the golden age of antibiotics. The fact that a majority of all medicines—especially antibiotics—are in some way derived from or inspired by natural products is a testament to the importance of understanding and harnessing the chemical strategies for biological interaction that have evolved over millions of years. Unfortunately, the overwhelmingly frequent rediscovery rate of known compounds among screened natural extracts meant that what was initially a life-saving torrent of new drugs eventually dried up into a costly trickle. Unfortunately, this has coincided with the rise of drug-resistance superbugs as our initial stockpiles of antibiotics have become overdeployed. Fortunately, we are now poised to enact an antibiotic renaissance powered by the ease and affordability of large-scale genomic analysis. The ability to genome-gaze has not only revealed hundreds of thousands of yet-untapped secondary metabolites in sequenced organisms but also can facilitate strain prioritization, novelty determination (dereplication), structure elucidation, three principal bottlenecks in the discovery process, as reviewed in Chapter 1. We report here progress in the use of genomics to facilitate the discovery and contextualization of new chemical matter. In Chapter 2, we report the discovery, isolation, and structural elucidation of streptomonomicin (STM), an antibiotic lasso peptide from Streptomonospora alba, and report the genome for its producing organism. STM-resistant clones of Bacillus anthracis harbor mutations to walR, the gene encoding a response regulator for the only known widely-distributed and essential two-component signal transduction system in Firmicutes. Our results demonstrate that understudied microbes remain fruitful reservoirs for the rapid discovery of novel, bioactive natural product and also highlight the usefulness of genomics in combination with NMR and HR-MS/MS for determining the structure of ribosomal natural products. In Chapter 3, we use HR-MS/MS, reactivity-based screening, NMR, and bioinformatic analysis to identify Streptomyces varsoviensis as a novel producer of JBIR-100, a fumarate-containing hygrolide. Using a combination of NMR and bioinformatic analysis, we elucidated the stereochemistry of the natural product. We investigated the antimicrobial activity of JBIR-100, with preliminary insight into mode of action indicating that it perturbs the membrane of Bacillus subtilis. S. varsoviensis is known to produce compounds from multiple hygrolide sub-families, namely hygrobafilomycins (JBIR-100 and hygrobafilomycin) and bafilomycins (bafilomycin C1 and D). In light of this, we identified the biosynthetic gene cluster for JBIR-100, which, to our knowledge, represents the first reported for a hygrobafilomycin. Finally, we performed a bioinformatic analysis of the hygrolide family using our RODEO algorithm from Chapter 4, describing clusters from known and predicted producers. Our results indicate that potential remains for the Actinobacteria to yield novel hygrolide congeners and provides a survey of the hygrolide landscape. In Chapter 4, we report RODEO (Rapid ORF Description and Evaluation Online), an algorithm which combines hidden Markov model-based analysis, heuristic scoring, and machine learning to identify biosynthetic gene clusters and predict RiPP precursor peptides. We initially focused on lasso peptides, which display intriguing physiochemical properties and bioactivities, but their hypervariability renders them challenging prospects for automated mining. Our approach yielded the most comprehensive mapping of lasso peptide space, revealing >1,300 compounds. We characterized the structures and bioactivities of six lasso peptides, prioritized based on predicted structural novelty, including an unprecedented handcuff-like topology and another with a citrulline modification exceptionally rare among bacteria. These combined insights significantly expand the knowledge of lasso peptides, and more broadly, provide a framework for future high-throughput genome mining. In addition to lasso peptides, RODEO provides the ability to analyze local genomic regions using custom profile hidden Markov models (pHMMs) and is suitable for RiPP, polyketide (PKS), nonribosomal peptide (NRPS), and other natural product biosynthetic gene cluster types; as part of an effort to make it available as a community resource we have created a web portal with its code and tutorials

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

Primary Health Care

This book presents examples from various countries about the provision of health services at the primary care level. Chapters examine the role of professionals in primary healthcare services and how they can work to improve the health of individuals and communities. Written by authors from Africa, Asia, America, Europe, and Australia, this book provides up-to-date information on primary health care, including telehealth services in the era of COVID-19

Structural Diversity of Biological Ligands and their Binding Sites in Proteins

The phenomenon of molecular recognition, which underpins almost all biological processes, is dynamic, complex and subtle. Establishing an interaction between a pair of molecules involves mutual structural rearrangements guided by a highly convoluted energy landscape, the accurate mapping of which continues to elude us. The analysis of interactions between proteins and small molecules has been a focus of intense interest for many years, offering as it does the promise of increased insight into many areas of biology, and the potential for greatly improved drug design methodologies. Computational methods for predicting which types of ligand a given protein may bind, and what conformation two molecules will adopt once paired, are particularly sought after. The work presented in this thesis aims to quantify the amount of structural variability observed in the ways in which proteins interact with ligands. This diversity is considered from two perspectives: to what extent ligands bind to different proteins in distinct conformations, and the degree to which binding sites specific for the same ligand have different atomic structures. The first study could be of value to approaches which aim to predict the bound pose of a ligand, since by cataloguing the range of conformations previously observed, it may be possible to better judge the biological likelihood of a newly predicted molecular arrangement. The findings show that several common biological ligands exhibit considerable conformational diversity when bound to proteins. Although binding in predominantly extended conformations, the analysis presented here highlights several cases in which the biological requirements of a given protein force its ligand to adopt a highly compact form. Comparing the conformational diversity observed within several protein families, the hypothesis that homologous proteins tend to bind ligands in a similar arrangement is generally upheld, but several families are identified in which this is demonstrably not the case. Consideration of diversity in the binding site itself, on the other hand, may be useful in guiding methods which search for binding sites in uncharacterised protein structures: identifying those regions of known sites which are less variable could help to focus the search only on the most important features. Analysis of the diversity of a non-redundant dataset of adenine binding sites shows that a small number of key interactions are conserved, with the majority of the fragment environment being highly variable. Just as ligand conformation varies between protein families, so the degree of binding site diversity is observed to be significantly higher in some families than others. Taken together, the results of this work suggest that the repertoire of strategies produced by nature for the purposes of molecular recognition are extremely extensive. Moreover, the importance of a given ligand conformation or pattern of interaction appears to vary greatly depending on the function of the particular group of proteins studied. As such, it is proposed that diversity analysis may form a significant part of future large-scale studies of ligand-protein interactions