The Discrepancy of the Lex-Least De Bruijn Sequence

We answer the following question of R. L. Graham: What is the discrepancy of the lexicographically-least binary de Bruijn sequence? Here, "discrepancy" refers to the maximum (absolute) difference between the number of ones and the number of zeros in any initial segment of the sequence. We show that the answer is $\Theta(2^n \log n/n)$.Comment: 11 pages, 0 figure

Testing of random matrices

Let $n$ be a positive integer and $X = [x_{ij}]_{1 \leq i, j \leq n}$ be an $n \times n$\linebreak \noindent sized matrix of independent random variables having joint uniform distribution \hbox{Pr} {x_{ij} = k \hbox{for} 1 \leq k \leq n} = \frac{1}{n} \quad (1 \leq i, j \leq n) \koz. A realization $\mathcal{M} = [m_{ij}]$ of $X$ is called \textit{good}, if its each row and each column contains a permutation of the numbers $1, 2,..., n$. We present and analyse four typical algorithms which decide whether a given realization is good

Testing of sequences by simulation

Let $\xi$ be a random integer vector, having uniform distribution $$\mathbf{P} \{\xi = (i_1,i_2,...,i_n) = 1/n^n \} \ \hbox{for} \ 1 \leq i_1,i_2,...,i_n\leq n.$$ A realization $(i_1,i_2,...,i_n)$ of $\xi$ is called \textit{good}, if its elements are different. We present algorithms \textsc{Linear}, \textsc{Backward}, \textsc{Forward}, \textsc{Tree}, \textsc{Garbage}, \textsc{Bucket} which decide whether a given realization is good. We analyse the number of comparisons and running time of these algorithms using simulation gathering data on all possible inputs for small values of $n$ and generating random inputs for large values of $n$

Compact genome of the Antarctic midge is likely an adaptation to an extreme environment

The midge, Belgica antarctica, is the only insect endemic to Antarctica, and thus it offers a powerful model for probing responses to extreme temperatures, freeze tolerance, dehydration, osmotic stress, ultraviolet radiation and other forms of environmental stress. Here we present the first genome assembly of an extremophile, the first dipteran in the family Chironomidae, and the first Antarctic eukaryote to be sequenced. At 99 megabases, B. antarctica has the smallest insect genome sequenced thus far. Although it has a similar number of genes as other Diptera, the midge genome has very low repeat density and a reduction in intron length. Environmental extremes appear to constrain genome architecture, not gene content. The few transposable elements present are mainly ancient, inactive retroelements. An abundance of genes associated with development, regulation of metabolism and responses to external stimuli may reflect adaptations for surviving in this harsh environment

Metagenomic analysis shows the presence of bacteria related to free-living forms of sulfur-Oxidizing Chemolithoautotrophic Symbionts in the rhizosphere of the seagrass Zostera marina

Seagrasses play an important role as ecosystem engineers; they provide shelter to many animals and improve water quality by filtering out nutrients and by controlling pathogens. Moreover, their rhizosphere promotes a myriad of microbial interactions and processes, which are dominated by microorganisms involved in the sulfur cycle. This study provides a detailed insight into the metabolic sulfur pathways in the rhizobiome of the seagrass Zostera marina, a dominant seagrass species across the temperate northern hemisphere. Shotgun metagenomic sequencing revealed the relative dominance of Gamma- and Deltaproteobacteria, and comparative analysis of sulfur genes identified a higher abundance of genes related to sulfur oxidation than sulfate reduction. We retrieved four high-quality draft genomes that are closely related to the gill symbiont of the clam Solemya velum, which suggests the presence of putative free-living forms of symbiotic bacteria. These are potentially highly versatile chemolithoautotrophic bacteria, able to alternate their metabolism between parallel pathways of sulfide oxidation (via sqr and fcc), nitrate reduction (denitrification or DNRA) and carbon fixation (via CBB or TCA cycle), depending on the environmental availability of sulfide. Our results support the hypothesis that seagrass meadows might function as a source of symbionts for invertebrates that inhabit within or around seagrass meadows. While providing ideal conditions for the proliferation of these free-living forms of symbionts, seagrasses would benefit from their genetic versatility, which contributes to sulfide detoxification and ammonium production, the seagrasses' preferred nitrogen source.European Union ERC 322551 European Science Foundation ConGenOmics program 6349 Fundacao para a Ciencia e Tecnologia (FCT) SFRH/BPD/63/03/2009 SFRH/BPD/107878/2015info:eu-repo/semantics/publishedVersio

Computation and programmability at the nano-bio interface

PhD ThesisThe manipulation of physical reality on the molecular level and construction of devices operating on the nanoscale has been the focal point of nanotechnology. In particular, nanotechnology based on DNA and RNA has a potential to nd applications in the eld of Synthetic Biology thanks to the inherent compatibility of nucleic acids with biological systems. Sca olded DNA origami, proposed by P. Rothemund, is one of the leading and most successful methods in which nanostructures are realised through rational programming of short 'staple' oligomers which fold a long single-stranded DNA called the 'sca old' strand into a variety of desired shapes. DNA origami already has many applications; including intelligent drug delivery, miniaturisation of logic circuits and computation in vivo. However, one of the factors that are limiting the complexity, applicability and scalability of this approach is the source of the sca old which commonly originates from viruses or phages. Furthermore, developing a robust and orthogonal interface between DNA nanotechnology and biological parts remains a signi cant challenge. The rst part of this thesis tackles these issues by challenging the fundamental as- sumption in the eld, namely that a viral sequence is to be used as the DNA origami sca old. A method is introduced for de novo generation of long synthetic sequences based on De Bruijn sequence, which has been previously proposed in combinatorics. The thesis presents a collection of algorithms which allow the construction of custom- made sequences that are uniquely addressable and biologically orthogonal (i.e. they do not code for any known biological function). Synthetic sca olds generated by these algorithms are computationally analysed and compared with their natural counter- parts with respect to: repetition in sequence, secondary structure and thermodynamic addressability. This also aids the design of wet lab experiments pursuing justi cation and veri cation of this novel approach by empirical evidence. The second part of this thesis discusses the possibility of applying evolutionary op- timisation to synthetic DNA sequences under constraints dictated by the biological interface. A multi-strand system is introduced based on an alternative approach to DNA self-assembly, which relies on strand-displacement cascades, for molecular data storage. The thesis demonstrates how a genetic algorithm can be used to generate viable solutions to this sequence optimisation problem which favours the target self- assembly con guration. Additionally, the kinetics of strand-displacement reactions are analysed with existing coarse-grained DNA models (oxDNA). This thesis is motivated by the application of scienti c computing to problems which lie on the boundary of Computer Science and the elds of DNA Nanotechnology, DNA Computing and Synthetic Biology, and thus I endeavour to the best of my ability to establish this work within the context of these disciplines

The Great Umar Khayyam

The Rubáiyát by the Persian poet ‘Umar Khayyæm (1048-1131) is used in contemporary Iran as a resistance literature, symbolizing the secularist voice in cultural debates. While Islamic fundamentalists criticize Khayyæm as an atheist and materialist philosopher who questions God’s creation and the promise of reward or punishment in the hereafter, secularist intellectuals see in him an example of a scientist who scrutinizes the mysteries of the world. Others see a spiritual master, a Sufi, who guides people to the truth. This volume collects eighteen essays on the history of the reception of ‘Umar Khayyæm in various literary traditions, exploring how his philosophy of doubt, carpe diem, hedonism, and in vino veritas has inspired generations of poets, novelists, painters, musicians, calligraphers and film-makers