A Topological Separation Condition for Fractal Attractors

We consider finite systems of contractive homeomorphisms of a complete metric space, which are non-redundant on every level. In general this separation condition is weaker than the strong open set condition and is not equivalent to the weak separation property. We prove that this separation condition is equivalent to the strong Markov property (see definition below). We also show that the set of $N$-tuples of contractive homeomorphisms, which are non-redundant on every level, is a $G_\delta$ set in the topology of pointwise convergence of every component mapping with an additional requirement that the supremum of contraction coefficients of mappings be strictly less than one. We give several sufficient conditions for this separation property. For every fixed $N$-tuple of $d\times d$ invertible contraction matrices from a certain class, we obtain density results for $N$-tuples of fixed points which define $N$-tuples of mappings non-redundant on every level.Comment: 19 page

Synthetic Studies in the Tetracycline Field

Abstract Not Provided

An Interdisciplinary Understanding of the Economic and Political Policies behind Network Neutrality in the United States

The focus of this paper is to explore the associative benefits to why network neutrality in the U.S. benefits the fundamental principles of freedom of speech and expression. While at the same time gaining a deeper understanding of why politics may incentivize or undermine data collection by billion-dollar conglomerate companies such as Tiktok and other internet service provider companies. In doing so, this paper will review internet privacy regulations on a federal level and examine the history of the FCC’s regulatory practices on ISPs over the last three decades. Lately, this paper will discuss the economics behind network neutrality and how they influence the everyday American consumer

Crinkly curves, Markov partitions and dimension

We consider the relationship between fractals and dynamical systems. In particular we look at how the construction of fractals in (D1) can be interpreted-in a dynamical setting and additionally used as a simple method of describing the construction of invariant sets of dynamical systems. There is often a confusion between Hausdorff dimension and capacity -which is much easier to compute- and we show that simple examples of fractals, arising in dynamical systems, exist for which the two quantities differ. In Chapter One we outline the mathematical background required in the rest of the thesis. Chapter Two reviews the work of F. M. Dekking on generating 'recurrent sets', which are types of fractals. We show how to interpret this construction dynamically. This approach enables us to calculate Hausdorff dimension and describe Hausdorff measure for certain recurrent sets. We also prove a conjecture of Dekking about conditions under which the best general estimate of dimension actually equals dimension. In Section One of Chapter Three recurrent sets are used to construct special Markou partitions for expanding endomorphisms of T2 and hyperbolic automorphisms of T3. These partitions have transition matrices closely related to the covering maps. It is also shown that Markov partitions can be constructed for the same map whose boundaries have different capacities. Section Two looks at the problem of coding between two Markov partitions for the same expanding endomorphism of T2. It is shown that there is a relationship between mean coding time and the capacities of the boundaries. Section Three uses recurrent sets to construct fractal subsets of tori which have non-dense orbits under the above mappings. Finally, Chapter Four calculates capacity and Hausdorff dimension for a class of fractals (which are also recurrent sets) whose scaling maps are-not similitudes. Examples are given for which capacity and Hausdorff dimension give different answers

Computational and Experimental Investigation into the Determinants of Protein Structure, Folding, and Stability in the β-Grasp Superfamily

Elucidating the mechanisms of protein folding and unfolding is one of the greatest scientific challenges in basic science. The overarching goal is to predict three-dimensional structures from their amino acid sequences. Understanding the determinants of protein folding and stability can be facilitated through the study of evolutionarily related but diverse proteins. Insights can also be gained through the study of proteins from extremophiles that may more closely resemble the primordial proteins. In this doctoral research, three aims were accomplished to characterize the structure, folding and unfolding behavior within the β-grasp superfamily. We propose that the determinants of structure, stability, and folding are conserved as sequence and interaction patterns in the β-grasp fold. To elucidate key residues, bioinformatics studies were conducted and identified nine structurally conserved amino acids in the core of the B1 domain of protein G (GB1). A network analysis of all long-range interactions in the structure of GB1 revealed the relative significance of each conserved amino acid. Within the β-grasp superfamily, two proteins, GB1 and the small archaeal modifier protein 1 (SAMP1), were investigated to elucidate the key determinants of structural stability at the level of individual interactions. They were subjected to high temperature molecular dynamics simulations and the detailed behavior of each long-range interaction was characterized. The results revealed that in GB1 the most stable region was the C-terminal hairpin and in SAMP1 it was the opposite, the N-terminal hairpin. The folding behavior of SAMP1 was investigated due to its nature as a divergent superfamily member and extremophile. The results revealed that SAMP1 at high ionic strength folds more rapidly than in low ionic strength. These findings clearly indicate that adaption at high salt produces rapid and less-frustrated folding. The results of these research aims provide insight into determinants of the β-grasp fold and the folding and unfolding behavior of two key members. Perhaps the most surprising finding is the presence of a significant number of non-native long-range interactions during unfolding which has largely gone unnoticed in the scientific community and appears to be pivotal

Configurations of control: An exploratory analysis

© 2015 Elsevier Ltd. There is growing interest in how management controls operate together as a package of interrelated mechanisms. Although theoretical debate dates back to the seminal paper of Otley (1980), there remains little empirical analysis of how control mechanisms combine. To increase knowledge in this area this study explores how multiple accounting and other control mechanisms commonly combine and the associations these combinations have with firm context. From a cross-sectional sample of 400 firms, this study presents an empirically derived taxonomy of five control configurations used by top managers, labelled as simple, results, action, devolved, and hybrid. Many of these patterns closely resemble control configurations common to the literature, while others represent distinctively contemporary arrangements, such as flexible variants of traditional bureaucracy (action), and instances where multiple and seemingly conflicting control types intermesh (hybrid). In analyzing these configurations this study provides accounting and control researchers with empirical observations to refine and extend existing control frameworks and theory

Matrix Big Brunch

Following the holographic description of linear dilaton null Cosmologies with a Big Bang in terms of Matrix String Theory put forward by Craps, Sethi and Verlinde, we propose an extended background describing a Universe including both Big Bang and Big Crunch singularities. This belongs to a class of exact string backgrounds and is perturbative in the string coupling far away from the singularities, both of which can be resolved using Matrix String Theory. We provide a simple theory capable of describing the complete evolution of this closed Universe.Comment: 15 pages, no figures. References adde

Effectors and Effects of Arginine Methylation

Arginine methylation is a ubiquitous and relatively stable post-translational modification (PTM) that occurs in three types: monomethylarginine (MMA), asymmetric dimethylarginine (ADMA) and symmetric dimethylarginine (SDMA). Methylarginine marks are catalyzed by members of the protein arginine methyltransferases (PRMTs) family of enzymes. Substrates for arginine methylation are found in most cellular compartments, with RNA-binding proteins forming the majority of PRMT targets. Arginine methylation often occurs in intrinsically disordered regions of proteins, which impacts biological processes like protein-protein interactions and phase separation, to modulate gene transcription, mRNA splicing and signal transduction. With regards to protein-protein interactions, the major \u27readers\u27 of methylarginine marks are Tudor domain-containing proteins, although additional domain types and unique protein folds have also recently been identified as methylarginine readers. Here, we will assess the current \u27state-of-the-art\u27 in the arginine methylation reader field. We will focus on the biological functions of the Tudor domain-containing methylarginine readers and address other domains and complexes that sense methylarginine marks

Modeling the emergence of universality in color naming patterns

The empirical evidence that human color categorization exhibits some universal patterns beyond superficial discrepancies across different cultures is a major breakthrough in cognitive science. As observed in the World Color Survey (WCS), indeed, any two groups of individuals develop quite different categorization patterns, but some universal properties can be identified by a statistical analysis over a large number of populations. Here, we reproduce the WCS in a numerical model in which different populations develop independently their own categorization systems by playing elementary language games. We find that a simple perceptual constraint shared by all humans, namely the human Just Noticeable Difference (JND), is sufficient to trigger the emergence of universal patterns that unconstrained cultural interaction fails to produce. We test the results of our experiment against real data by performing the same statistical analysis proposed to quantify the universal tendencies shown in the WCS [Kay P and Regier T. (2003) Proc. Natl. Acad. Sci. USA 100: 9085-9089], and obtain an excellent quantitative agreement. This work confirms that synthetic modeling has nowadays reached the maturity to contribute significantly to the ongoing debate in cognitive science.Comment: Supplementery Information available here http://www.pnas.org/content/107/6/2403/suppl/DCSupplementa