Dimensions of Copeland-Erdos Sequences

The base-$k$ {\em Copeland-Erd\"os sequence} given by an infinite set $A$ of positive integers is the infinite sequence \CE_k(A) formed by concatenating the base-$k$ representations of the elements of $A$ in numerical order. This paper concerns the following four quantities. The {\em finite-state dimension} \dimfs (\CE_k(A)), a finite-state version of classical Hausdorff dimension introduced in 2001. The {\em finite-state strong dimension} \Dimfs(\CE_k(A)), a finite-state version of classical packing dimension introduced in 2004. This is a dual of \dimfs(\CE_k(A)) satisfying \Dimfs(\CE_k(A)) \geq \dimfs(\CE_k(A)). The {\em zeta-dimension} \Dimzeta(A), a kind of discrete fractal dimension discovered many times over the past few decades. The {\em lower zeta-dimension} \dimzeta(A), a dual of \Dimzeta(A) satisfying \dimzeta(A)\leq \Dimzeta(A). We prove the following. \dimfs(\CE_k(A))\geq \dimzeta(A). This extends the 1946 proof by Copeland and Erd\"os that the sequence \CE_k(\mathrm{PRIMES}) is Borel normal. \Dimfs(\CE_k(A))\geq \Dimzeta(A). These bounds are tight in the strong sense that these four quantities can have (simultaneously) any four values in $[0,1]$ satisfying the four above-mentioned inequalities.Comment: 19 page

Dimensions of Copeland-Erdos Sequences

The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite sequence CEk(A) formed by concatenating the base-k representations of the elements of A in numerical order. This paper concerns the following four quantities. • The finite-state dimension dimFS(CEk(A)), a finite-state version of classical Hausdorff dimension introduced in 2001. • The finite-state strong dimension DimFS(CEk(A)), a finite-state version of classical packing dimension introduced in 2004. This is a dual of dimFS(CEk(A)) satisfying DimFS(CEk(A)) ≥ dimFS(CEk(A)). • The zeta-dimension Dimζ(A), a kind of discrete fractal dimension discovered many times over the past few decades. • The lower zeta-dimension dimζ(A), a dual of Dimζ(A) satisfying dimζ(A) ≤ Dimζ(A). We prove the following. 1. dimFS(CEk(A)) ≥ dimζ(A). This extends the 1946 proof by Copeland and Erdös that the sequence CEk(PRIMES) is Borel normal. 2. DimFS(CEk(A)) ≥ Dimζ(A). 3. These bounds are tight in the strong sense that these four quantities can have (simultane-ously) any four values in [0, 1] satisfying the four above-mentioned inequalities

Understanding the Dynamics of Gene Regulatory Systems : Characterisation and Clinical Relevance of cis-Regulatory Polymorphisms

Peer reviewedPublisher PD

The nuclear envelope as a chromatin organizer

In the past 15 years our perception of nuclear envelope function has evolved perhaps nearly as much as the nuclear envelope itself evolved in the last 3 billion years. Historically viewed as little more than a diffusion barrier between the cytoplasm and the nucleoplasm, the nuclear envelope is now known to have roles in the cell cycle, cytoskeletal stability and cell migration, genome architecture, epigenetics, regulation of transcription, splicing and DNA replication. Here we will review both what is known and what is speculated about the role of the nuclear envelope in genome organization, particularly with respect to the positioning and repositioning of genes and chromosomes within the nucleus during differentiation

Signalling entropy: A novel network-theoretical framework for systems analysis and interpretation of functional omic data

a b s t r a c t A key challenge in systems biology is the elucidation of the underlying principles, or fundamental laws, which determine the cellular phenotype. Understanding how these fundamental principles are altered in diseases like cancer is important for translating basic scientific knowledge into clinical advances. While significant progress is being made, with the identification of novel drug targets and treatments by means of systems biological methods, our fundamental systems level understanding of why certain treatments succeed and others fail is still lacking. We here advocate a novel methodological framework for systems analysis and interpretation of molecular omic data, which is based on statistical mechanical principles. Specifically, we propose the notion of cellular signalling entropy (or uncertainty), as a novel means of analysing and interpreting omic data, and more fundamentally, as a means of elucidating systems-level principles underlying basic biology and disease. We describe the power of signalling entropy to discriminate cells according to differentiation potential and cancer status. We further argue the case for an empirical cellular entropy-robustness correlation theorem and demonstrate its existence in cancer cell line drug sensitivity data. Specifically, we find that high signalling entropy correlates with drug resistance and further describe how entropy could be used to identify the achilles heels of cancer cells. In summary, signalling entropy is a deep and powerful concept, based on rigorous statistical mechanical principles, which, with improved data quality and coverage, will allow a much deeper understanding of the systems biological principles underlying normal and disease physiology

Advances in Microbial Fermentation Processes

This book covedered high-quality contributions (original research articles or review papers) providing a picture on innovations in microbial fermentative processes, including improvements of quality/safety of fermented foods and beverages, production of high added-values products, and valorization/recovery of agro-food wastes

The role of lamin A and emerin in mediating genome organisation

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The nuclear matrix (NM) is proposed to be a permanent network of core filaments underlying thicker fibres, present regardless of transcriptional activity. It is found to be both RNA and protein rich; indeed, numerous important nuclear proteins are components of the structure. In addition to mediating the organisation of entire chromosomes, the NM has also been demonstrated to tether telomeres via their TTAGGG repeats. In order to examine telomeric interactions with the NM, a technique known as the DNA halo preparation has been employed. Regions of DNA that are tightly attached to the structure are found within a so-called residual nucleus, while those sequences forming lesser associations produce a halo of DNA. Coupled with various FISH methodologies, this technique allowed the anchorage of genomic regions by the NM, to be analysed. In normal fibroblasts, the majority of chromosomes and telomeres were extensively anchored to the NM. Such interactions did not vary significantly in proliferating and senescent nuclei. However, a decrease in NM-associated telomeres was detected in quiescence. Since lamin A is an integral component of the NM, it seemed pertinent to examine chromosome and telomere NM-anchorage in Hutchinson-Gilford Progeria Syndrome (HGPS) fibroblasts, which contain mutant forms of lamin A. Indeed, genome tethering by the NM was perturbed in HGPS. In immortalised HGPS fibroblasts, this disrupted anchorage appeared to be rescued; the implications of this finding will be discussed. This study also suggested that telomere-NM interactions are aberrant in X-linked Emery-Dreifuss Muscular Dystrophy (X-EDMD), which is caused by mutant forms of emerin, another NM-associated protein. The positioning of selected genes in control and X-EDMD cell lines was examined in un-extracted nuclei using 2D and 3D FISH. Subtle shifts in the organisation of these genes were detected in diseased cells; however, their expression levels remained unaltered. Furthermore, in order to examine the architectural integrity of the nuclear lamina in lamin A and emerin mutant cell lines, scanning electron microscopy (SEM) was employed. This work revealed that such structures were indeed compromised in disease. The findings presented in this thesis highlight the importance of lamin A and emerin in mediating the organisation of the genome and taken together, promote the hypothesis that dysfunctional NM dynamics may well contribute to disease pathology.EU FP6 Programme (Eurolaminopathies), Brunel University and the Progeria Research Fund

Analysis of Gene Targeting Techniques for Huntington’s Disease and Gene Expression in Human Cells

Gemstone Team CHANGEHuntington’s disease (HD) is an inherited neurodegenerative disorder that is caused by a CAG trinucleotide repeat expansion in the huntingtin (HTT) gene. Our team performed a literature analysis to investigate the current state of research for treating HD and identified a new technology called prime editing that could be applied to HD in combination with single nucleotide polymorphisms (SNPs). We found that at least 729 SNPs within the HTT gene are compatible with our proposed approach. Experimentally, we performed preliminary studies using Western Blots and RT-qPCR to examine the differences in expression of HTT in a variety of cell lines. Our literature-based work suggests that prime editing is a promising tool for addressing the basis of a variety of genetic disorders. Our experimental-based work confirms that human fibroblast cells express HTT and therefore may be used in proof of concept studies of gene targeting techniques to address HD

DISPERSAL, GENETIC STRUCTURE, NETWORK CONNECTIVITY AND CONSERVATION OF AN AT-RISK, LARGE-LANDSCAPE SPECIES

Wide-ranging species face many threats to genetic connectivity. In light of these threats, one major challenge is the efficient use of scarce resources for the conservation of these species. Setting conservation priorities for landscapes and connectivity can be informed using molecular genetics, and can ensure the efficient use of scare resources to maximize returns in biodiversity conservation. The greater sage-grouse (Centrocercus urophasianus; hereafter sage grouse) is a species of conservation concern that spans eleven state boundaries, land managed by multiple agencies, and one international boundary. Across the species’ distribution, the threats to the genetic connectivity range from agricultural conversion to energy development, to catastrophic wildfire. In order to prioritize management as threats loom, there is considerable interest in gaining insight into the species’ population genetic substructure, dispersal capabilities, and range-wide genetic connectivity. The insights gained and be used to prioritize management efforts to preserve or restore genetic diversity and connectivity. This dissertation is composed of an investigation of population genetic substructure, breeding season dispersal, and the characterization of a range-wide genetic network for conservation prioritization. Limitations in greater sage-grouse dispersal have resulted in the existence of five subpopulations across the northeastern range of the species, none of which appears to be genetically isolated. The genetic structure discovered appears to have been shaped by the natural landscape and ecological features. However, recent disturbances associated with human alteration of the landscape may have increased subpopulation divergence. Existing state conservation areas align well with genetic subpopulation structure allowing straightforward translation of management planning to the conservation of genetic diversity and connectivity. Simulation-based evaluation of the analytical methods used to detect subpopulation structure provided insight into interpretation of the evolutionary history of subpopulation divergence. While many individuals remained philopatric to the same breeding sites (leks) year after year, more individuals dispersed to alternate leks. Evidence for sex-biased dispersal did not exist: either in tendency to disperse nor in distances traveled. Dispersal appears costly, as there was a greater occurrence of mortality among farther dispersing individuals. Individuals dispersed within, into and out of designated conservation areas, providing additional evidence that these areas are not isolated. Breeding dispersal likely counteracts the effect of philopatry, fostering gene flow. Using network theory, I characterized the patterns of range-wide genetic connectivity among spring breeding congregations (leks), finding that connectivity is greatest among neighboring leks. The entire network is connected such that there are no isolated subunits. Hubs of genetic connectivity exist, evidenced by increased measures of both local and global network centrality, indicative of their importance to maintaining gene flow across the entire species’ iv range. These high-centrality hubs are centrally located within the species’ distribution, with concentrations within the Upper Snake River Basin of Idaho and the Green River Basin of Wyoming. Conservation efforts to protect these areas could prove essential to securing range-wide genetic connectivity into the future. Overall, this research provides insight into how to use molecular genetic analyses of substructure, dispersal, and connectivity of a continuously distributed species across a vast landscape to inform management and prioritize conservation actions